Essays on outsourcing, technological adoption and unemployment

ESSAYS ON OUTSOURCING, TECHNOLOGY ADOPTION AND UNEMPLOYMENT BY TAN CHIH WEI, RANDY (B. SOC. SCI., HONS., 2003) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SOCIAL SCIENCE DEPARTMENT OF ECONOMICS NATIONAL UNIVERSITY OF SINGAPORE 2005 ACKNOWLEDGEMENTS Much has happened during the past 2 years of my candidature here while doing this course, the most significant of which is the Lord’s guiding hand in bringing me into confession of my sins and acceptance of Christ. I recalled my feeling of being upset at my final exam for Mathematical Economics 2 and how worried I was about missing out on a 2nd upper. I was discussing this with my then, and now current, supervisor Dr Ho Kong Weng and he somehow shared the Gospel with me. Through my supervisor, who has assisted me in the understanding of the Gospel and explained some things in the Bible which I could not understand, the Lord has helped me to understand more of His revealed will. Looking back, it is interesting to think about how the Lord has shut the doors in my futile search for a job after completing my Honours in Economics and opening the door of a research scholarship and I am indeed indebted to the Lord for opening this door and shutting the others, convicting me of my sins and enabling me to embrace Christ as my and the only Saviour. I would also like to express my sincere and heartfelt appreciation to Dr Ho for his efforts and valuable time in sharing with me the word of God as well. I would like to express my heartfelt appreciation to Dr Ho for his supervision and a free hand in the process of doing this thesis as well as in the tutorial classes I have conducted for his module and research assistance rendered and his valuable and creative inputs throughout. Admittedly, I have a tendency of wanting things my own way and I would express my sincere apologies for the offence and unpleasantness caused. Much i has been learnt whilst working with him in that I have learnt to be more open and critical in my thought process, as well as how to help students learn and not excessively spoonfeeding them. These, and other lessons and attributes which I may have unintentionally omitted, have certainly made it a great privilege for me to have worked with Dr Ho. I must again thank him for the valuable assistance, time and opportunity cost incurred in helping me throughout the 3 years of supervision for my Honours and Masters theses. My sincere appreciation to Ms Sagi Kaur for her help in the administrative assistance rendered for the departmental graduate presentation I conducted and the summer meeting of the North American Economics and Finance Association held at the 80th Western Economics Association conference. I would also like to thank Mdm Foo and Mdm Woo for their assistance in the printing of the transparencies and handouts for the above-mentioned events. Financial assistance from NUS for the attendance and presentation at the conference is acknowledged. I would also like to thank the rest of the administrative staff for the handling of the administrative and teaching matters. I would like to thank the Lord for His providential hand in guiding me through the research programme, without which the completion of the coursework and thesis would have been impossible. I would also like to thank A/P Zeng Jinli and A/P Zhang Jie for sharing some research techniques during the Honours and Masters classes respectively, which have certainly been useful during the course of my research work. Comments for a shortened version of the first chapter from those who attended my presentation at the Graduate Students’ Seminar on 27 June 2005 and Professor Daniel Mitchell at the 2005 ii Summer Meeting of the North American Economics and Finance Association held during the 80th Western Economic Association conference is also much appreciated. Finally, I would also like to thank the following for the constant encouragement and friendship: Shirley Fong, Daniel Soh, Enrico Tanuwidjaja, Grace Yong, Kelvin Foo, Koh Phuay Leng, Oh Boon Ping, Yvonne Yau, Qiao Zhuo, Feng Shuang, Luckraz Shravan, Nicholas Sim, Terence Cheng, Kuhan Harichandra, Swee Eik Leong, Gabriel Wong, Koo Ping Shung, the Economics Graduate Students Society committee of 2004, students whom I have taught or who I have come into contact with as a tutor for Econometrics 2 or Macroeconomic Analysis 2 during the academic year 2004/05, everyone over at Pilgrim Covenant Church and friends from my secondary and college days. My sincere apologies go out to those whom I have omitted unintentionally. Any remaining errors or omissions in this thesis is mine and views expressed in this thesis do not necessarily represent those of the Department of Economics, National University of Singapore, or any of the abovenamed or group of individuals. iii ABSTRACT This thesis is made up of two distinct essays. In the first essay, titled “Technology Adoption and Unemployment”, a model with employment of workers as an investment decision within a small open economy is used to examine the relationship between technology adoption and employment. Human capital plays a crucial role in the technology adoption and, subsequently employment of workers. It is shown that as human capital level increases, level of technology adopted within the economy increases. There exists a threshold level of human capital beyond which employment falls, which equivalently translates into higher unemployment in our model. Two opposing effects are in place here as human capital increases. An increase in human capital enables better use of existing technology and reduces job loss. However, this also has a positive impact on the adoption of technology, thus raising the technology adoption aspect of creative destruction which raises job loss at an increasing rate and thus reduces employment. The latter effect dominates the former upon breaching the threshold, thus leading to the increase in unemployment. We have therefore a non-monotonic relationship between level of technology adopted and employment and hence human capital and employment. The second essay, titled “Integration versus Domestic Outsourcing: An Exploratory Study”, considers a two-country model of production of the service good that differs in quality. The firm in each country competes with each other in price and in quality. Constrained by local provision of the service good, the firm faces the choice of either adopting the integrated mode of production or outsourcing the intermediates iv domestically. There exists a threshold level of human capital whereby integration (outsourcing) is adopted when human capital level is below (above) the threshold. As human capital increases, the cost of outsourcing the intermediate decreases relative to wage cost, thus the firm is able to reduce the per unit employment sufficiently and yet produce a sufficiently high quality of the product at a low price-to-quality ratio. The endogenous quality choice in our model thus allows for an extra avenue of response towards increased competition. v CONTENTS Acknowledgements Abstract Contents List of Tables List of Figures i iv vi vii ix CHAPTER 1: TECHNOLOGY ADOPTION AND UNEMPLOYMENT 1.1 Introduction 1 1.2 The Model 10 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.3 Steady-State Analysis and Changes in Human Capital 1.3.1 1.3.2 1.3.3 1.3.4 1.4 The Production Process Employment Decisions Job Matching and Creative Destruction Dynamics Optimization Behaviour Across the Firm and the Economy Wage Bargaining Curve Steady State Equilibrium Parameterization Simulation Results Changes in the Human Capital Level of the Economically Active Changes in Other Parameters 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 20 37 Matching Parameters Wage Setting Parameters Rate of Global Technological Progress Productivity Parameter Cost Parameters 1.5 General Discussion 51 1.6 Conclusion 52 1.7 Appendices 54 1.7.1 1.7.2 Proof of Proposition 1 Mathematical Intuition of Proposition 2 vi CHAPTER 2: INTEGRATION VERSUS DOMESTIC OUTSOURCING 2.1 Introduction 58 2.2 The Model 67 2.2.1 2.2.2 2.3 Equilibrium and Changes in Human Capital Level 2.3.1 2.3.2 2.3.3 2.4 The Northern Firm Preferences Analytical Solution Numerical Example Changes in the Human Capital Level of the Northern Economy Other Comparative Statics 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 73 88 Price Charged by the Southern Firm Quality of the Southern Firm’s Service Good Cost of Outsourcing Manual Component Wage Cost General Productivity Level 2.5 Production Share Parameters 104 2.6 Modifying the Cost of Outsourcing 106 2.7 General Discussion 107 2.8 Conclusion and Further Research 109 References 113 LIST OF TABLES Table 1.1: Parameter values used for base case 22 Table 1.2: Summary of slopes of demarcation curves and approximate corresponding range of values of h 23 Table 1.3: Simulation results for baseline case 25 vii Table 1.4: Summary of outcomes of comparative statics exercise of an increase in respective parameters in 1.4.1 to 1.4.5 37 Table 1.5: Simulation results for (a) ε = 0.2 and (b) ε = 0.3 39 Table 1.6: Simulation results for (a) δ = 0.5 and (b) δ = 0.7 39 Table 1.7: Simulation results for (a) 10% fall in χ (=0.144) and (b) 10% rise in χ (=0.176) 41 Table 1.8: Simulation results for (a) γ = 1.1 and (b) γ = 1.7 41 Table 1.9: Simulation results for (a) 5% fall in ψ (=0.95) and (b) 5% rise in ψ (=1.05) 42 Table 1.10: Simulation results for (a) 5% fall in z (=0.0665) and (b) 5% rise in z (=0.0735) 45 Table 1.11: Simulation results for (a) 5% fall in B (=0.475) and (b) 5% rise in B (=0.525) 46 Table 1.12: Simulation results for (a) 10% fall in b (=0.09) and (b) 10% rise in b (=0.11) 48 Table 1.13: Simulation results for (a) 5% fall in q (=0.133) and (b) 5% rise in q (=0.147) 49 Table 1.14: Simulation results for (a) 25% fall in r (=0.03) and (b) 25% rise in r (=0.05) 50 Table 1.15: Simulation results for baseline case on the shift of demarcation loci 57 Table 2.1: Parameter values used for initial numerical analysis 80 Table 2.2: Comparison of roots obtained with HN = 0.5 81 Table 2.3: Numerical results under both forms of production for different values of HN 83 Table 2.4: Numerical results under both forms of production for different values of HN with a 20% fall in price charged by the Southern firm 90 viii Table 2.5: Numerical results under both forms of production for different values of HN with a 20% increase in the quality of the Southern firm’s service good 94 Table 2.6: Numerical results under both forms of production for different values of HN with a decrease in the cost of outsourcing (10% fall in ρ and 10% fall in δ) 97 Table 2.7: Numerical results under both forms of production for different values of HN with a 15% increase in the base wage rate 100 Table 2.8: Numerical results under both forms of production for different values of HN with a 20% increase in general per unit productivity 102 Table 2.9: Numerical results under both forms of production for different values of HN with a change in the productive share of the organizational component (β=1/3) Table 2.10: Summary of outcomes of comparative statics exercise of an increase in respective parameters in sections 2.3.3 and 2.4 under the relevant production mode 104 110 LIST OF FIGURES Figure 1.1: Demarcation curves for low level of human capital (h=0.25) 23 Figure 1.2: Demarcation curves for high level of human capital (h=0.7) 24 Figure 1.3: Effect of an increase in h when h is below the threshold level of human capital 31 Figure 1.4: Effect of an increase in h when h is above the threshold level of human capital 33 Figure 2.1: Graphs of the first-order conditions around the intersection point for HN=0.7 and HN=0.72 84 ix 1. TECHNOLOGY ADOPTION AND UNEMPLOYMENT 1.1 Introduction Human capital is known to have played a crucial role in the development process of many economies. The development of a more highly-skilled workforce through improved educational and training opportunities have helped to enhance the employability of workers at the individual level and reduce unemployment at the aggregate level. The presence of skilled labour would, in turn, be a crucial factor in the firm’s technology adoption decision, as implementation of newer and better technologies is often infeasible without the presence of more highly-skilled workers. Whilst it is true that firms may find it difficult to adopt new technologies, which usually raise productivity, without the availability of skilled workers (for example, see Haskel and Martin (1993); a mathematical exposition on the capital-skill complimentarily is found in Lloyd-Ellis and Roberts (2002)), increases in the human capital of workers actually present firms with the opportunity to implement a higher level of technology to replace workers. For example, strikes by port workers from the United States over the proposed retrenchment of workers involved in jobs that will be lost as a result of automation is just one of many similar situations that have taken place throughout history.1 The job of ticket conductors to punch bus tickets and collect payment was made redundant with the introduction of various technologies to collect bus fares and dispense bus tickets, enabling bus services to be run as one-man-operations. One good example 1 See, for example, The Wall Street Journal, 30 September 2002. 1 will be that of Singapore, where such a change has occurred in the late 1970s. IT professionals have also found themselves becoming redundant as new variants of computer technology become more intelligent. Highly-skilled journalists may no longer require a cameraman to accompany them in news reporting should future technological developments result in improved versions of the videophone. Thus, technological progress could potentially have destructive effects on employment, with serious repercussions on job creation within the economy as well. The above discussion leads to the following question: does improved skill profile amongst the economically active result in increased employment? More importantly, with the availability of better-skilled workers to work with better technology, will firms take advantage of this to reduce the use of workers in the production process? This paper attempts to study the relationship between technology adoption and unemployment in a general equilibrium analysis. More importantly, our model considers how the level of human capital within a small open economy affects the choice of technology implemented by firms, which subsequently affect the employment situation within the economy. The underlying difference between the small open economy and the large economy is its inability to play a significant role in pushing the world technological frontier. Any advancement in the small open economy’s technology frontier is due to its ability to adopt technologies quickly from the leading nations. Eaton and Kortum (1996) did an empirical study to assess the proportion of a nation’s growth that can be attributed 2 to its own research efforts and found that such efforts within major economies, namely United States, Japan and Germany, form a significant proportion of their growth. Nahuis and van de Ven (1999) further postulated that efforts that concentrate on the adaptation of technology are more appropriate for the small nations based on the empirical outcomes from Eaton and Kortum (1996). Computations by Howitt and Mayer-Foulkes (2002) revealed that 80% of the global R&D expenditure can be attributed to 5 countries, this figure rising to 95% with the inclusion of another 6 countries, thus suggesting that most other nations are embarking on technology adoption rather than being at the forefront of the global technological frontier. Therefore, unlike previous works that incorporate the research and development sector, this paper assumes that such a sector does not exist directly in the small open economy, that is, the small open economy concentrates solely on the adoption of technology. There have been a myriad of reasons presented regarding the technology adoption decisions of firms. These include the degree of willingness of workers to learn new skills associated with such technologies, the age profile of such workers, asymmetric information, availability of credit, externalities associated with network, market power and learning, the required human capital level for implementation of a given technology and the level of human capital available within the economy (see, for example, Besley and Case (1993), Basu and Weil (1998) and Canton, de Groot and Nahuis (2002)). We focus on the cost issues associated with the availability of human capital in the implementation of a particular technology. To illustrate, suppose the United States has developed a modern farming technology. With many studies showing that new variants 3 of technology are often skill-biased2, it is likely that such a technology is more suitable for farmers in the United States and other nations that share similar levels of human capital than the lowly-developed nations since they will be in a better position to make productive use of that technology. The availability of human capital plays a crucial role in the implementation of higher levels of technology, which often comes at a price. Firms thus face both implicit and explicit costs associated with such implementation. Explicit costs arise from the effective per unit cost of implementation of such technologies for a given level of human capital, which would generally include the purchase and installation of that unit as well as the additional training required to help workers gain proficiency in using that particular technology. Implicit costs may arise from the failure to harness fully the productive capabilities of such technologies, such as the potential opportunity cost incurred to train the workers during working hours as well as the possibility of damages caused resulting from improper use of that state-of-the-art technology. Acemoglu and Zilibotti (2001) highlighted that the mismatch between skill level and technology results in large differences in productivity between the North and LDCs and that such skill shortages play a key role in a multinational firm’s decision not to introduce such technologies in the latter group of countries. Also, empirical studies by Bartoloni and Baussola (2001) on the determinants influencing technology adoption decisions of Italian manufacturing firms have revealed that the human capital level of a firm’s employees does play an important role towards the firm’s decision on whether to adopt a certain technology.3 2 Empirical evidence on the skill-biased nature of technological innovations can be found in Berman, Bound and Machin (1998), Machin and van Reenen (1998) and Morrison Paul and Siegel (2001). 3 An indirect manner in which higher levels of technology can have a negative impact on employment would be that such technologies can actually allow firms to reorganize existing job scope to facilitate greater multi-tasking, subject to the availability of workers with the desired level of human capital. Lindbeck and Snower (1996) noted that technological advances have enabled firms to move from the Tayloristic structure to one that is more holistic. They 4 In our paper, the employment of workers is seen as an investment decision by the firms due to the presence of labour market frictions, similar to that by Yashiv (2000). Labour flow within the economy is determined by job creation and job destruction. Conventional job matching technology (see Pissarides (2000)) dictates that the rate of job match is determined by the unemployment and vacancy rates. Our paper takes on a different approach by considering this probability as a function of human capital level amongst the economically active and the level of unemployment. This suggests that from the firm’s point of view, it is the skill profile and the availability of workers that will determine whether a suitable applicant or interviewee can be matched to a position that has been vacated due to job destruction or created due to various factors. In our paper, we assume that these factors are taken into consideration in the firm’s decision in selecting the number of interviewees for consideration. A wage bargaining curve, which is dependent on the human capital of the workers and the level of employment within the economy, is also introduced to endogenize the wage rate. External and internal technological factors play the main role in the determination of job destruction. Our paper employs an implication resulting from the creative destruction effect arising from an increase in the pace of technological progress. As discussed in Aghion and Howitt (1994), growth is driven by the increase in knowledge and that this knowledge is embodied via state-of-the-art technologies. Thus, a more rapid increase in knowledge will translate into higher growth rates and higher job-turnover gave the example of how increased use of computers in disseminating information within firms has enabled greater complementarities across different tasks that were, in the past, clearly segregated. This would imply that firms can actually require workers to undertake a wider job scope encompassing the different tasks with fewer workers. A more complex work environment arising from such changes in the work environment, according to Tuijnman (1999), will favour the more highly-skilled as they are more able to adapt to newer technologies and management strategies. 5 rates, with a more rapid introduction of new technologies leading to greater job destruction. Given the inability of the small open economy to shift the world technological frontier, one can thus postulate that such effects are beyond the control of a small open economy. Should the rate of creative destruction increase, the additional value of introducing a relatively higher level of technology diminishes, since the time available for the firm to recover various costs is reduced, which also reduces the profitability of the firm’s production and will subsequently influence the firm’s decision on job creation. On the whole, these will create a negative impact on job-loss within the small open economy. To endogenize overall job-loss, we incorporate the role of domestic technology and human capital. This is in view of the increasingly workerreplacing capability of newer technologies that can be used in the production process with the availability of better-trained workers in the workforce. Our model uncovers an interesting result regarding the non-monotonic relationship between technology adoption and employment under the onslaught of increasing levels of human capital. Using appropriate parameters for our numerical simulation, we find that while increases in human capital encourage adoption of higher levels of technology and raises the sum of future discounted profits of an additional worker, wages and interview rate, such increases can only raise employment up to a threshold level of human capital. Employment falls, or equivalently in our model, unemployment rises upon the economy’s human capital level exceeding the threshold. The adjustment process in the short run that brings about the above long-run outcome can be summarized as follows. On the one hand, we have a job creation effect whereby having higher-skilled workers means that it is easier to find workers and that you can 6 make better use of existing technology, which would contribute positively towards future discounted profits and thus reducing job loss or promoting employment. However, we have the job destruction effect where the presence of higher-skilled workers promotes adoption of better technologies, thus raising the technological aspect of creative destruction and job loss, reduces total future discounted profits (which is a negative influence on job creation as well) and thus reduces employment. Before crossing the threshold, the former effect dominates the latter. Recalling that the employment decision of the firms is likened to that of an investment decision, increases in human capital level that are below the threshold would actually result in the long-run outcome of higher employment on the whole since there exist future gains in terms of higher total future discounted profits by employing additional workers. However, upon crossing the threshold, the latter effect dominates. Thus, having additional workers over and above the optimal level of employment will result in future losses in terms of lower total future discounted profits from having these surplus workers, which will thus necessitate the laying off or reduction in the optimal level of employment amongst the firms. Hence, we have this non-monotonic relationship between unemployment and technology adoption and also unemployment and human capital. Various comparative statics analysis will be carried out to study the effect on employment, technology adoption, threshold level of human capital, the sum of discounted future profits of an additional worker, wages and interview rate upon changes in job matching, wage setting, global technological progress, productivity and cost parameters. The majority of existing literature has uncovered the relationship between human capital and technology, human capital and unemployment and technology and 7 unemployment. Regarding the first instance, Nelson and Phelps (1966) showed that human capital plays a crucial role in learning and technological diffusion. Acemoglu (1997b) showed that an increase in human capital may or may not raise the level of technology adopted. Chander and Thangavelu (2004) found that higher investment in education by workers can provide the incentive for entrepreneurs to adopt better technology. Empirical findings by Papageorgiou (2003) based on World Bank data revealed that post-primary education contributes significantly towards technology innovation and adoption whilst primary education contributes towards final output production. Hollanders and Weel (2002) found a positive relationship between skill upgrading and R&D intensity in manufacturing based on an empirical study of six OECD countries. Several writers have examined the issue of the relationship between technology and unemployment, without incorporating the issue of human capital. Using a model of frictional unemployment, the findings in Postel-Vinay (2002) do show that an increased pace of technological progress raises equilibrium unemployment via job obsolescence. However, the model does not feature any underlying mechanism that motivates firms to adopt higher levels of technology. The findings by Aghion and Howitt (1994) suggest that higher exogenous growth rate of leading technology can raise or lower unemployment, depending on the rate of growth and that higher endogenous growth arising from an increase in innovation size will strictly raise unemployment. Hoon (1993) found that the effect of an increase in the level of technology on unemployment is entirely transient in that unemployment rises only in the short run. However, increased pace of technological progress will raise unemployment. In an empirical study, 8 Danninger and Mincer (2000) found that an increase in the pace of technology has an uncertain short-run impact on unemployment but can result in a fall in unemployment in the long run as less skilled workers receive training. Nakanishi (2002) found in an empirical study on Japan that there exists a negative relationship between IT capital and labour and further indicated that the impact has increased during recent times. Other writers have also studied the relationship between human capital and unemployment. An increase in education capital is found to reduce unemployment by Davis and Reeve (2003), regardless of whether the economy is closed or open. Empirical studies by Richardson and van der Berg (2001) and Chan and Suen (2003) on evaluating the effectiveness of training policies on employability of workers indicate that such policies have a minimal impact on enhancing labour market performance. Nickell (1979) has also found that there exists only a very limited impact of the number of years of schooling from 13 years and above on unemployment rate. Acemoglu (1997a) has attempted to incorporate all the above aspects. He found that, subject to the extent of exogenous productivity increase, firms may or may not adopt better technology. If the former is carried out, the firm will thus help enhance the human capital of the workers. Such an outcome raises the proportion of skilled workers within the workforce and would also lead to a reduction in unemployment. The findings here seem to imply that increase in human capital is driven by technology adoption and that unemployment falls as a consequence. His finding differs significantly from ours in that we view the presence of human capital to be the driving force behind technology 9 adoption and that unemployment may or may not decrease depending on the strengths of the job creation and job destruction effects. To summarize, the above literature suggests that raising human capital level may or may not result in implementation of higher level of technology. Faster technological change or implementation of higher level of technology need not necessarily raise equilibrium unemployment. The relationship between human capital and unemployment cannot be clearly established. Our contribution is to integrate the aspects of human capital and global technological advancement into a framework of unemployment and technology adoption arising from changes in the former aspect, which is presently sorely lacking in existing literature. The rest of this chapter is organized as follows. Section 1.2 describes the various aspects of the model and the optimization process. Steady-state and comparative statics analysis of changes in human capital is carried out in section 1.3. We consider changes in other parameters in section 1.4. Section 1.5 provides a general discussion of the implications of the outcomes obtained. Section 1.6 concludes this chapter. 1.2 The Model The economy consists of a collection of identical firms indexed from 0 to 1 that are producing the final good. The population consists of economically active agents that can also be indexed from 0 to 1, with Lt of these employed. Each agent is assumed to possess an exogenous amount of human capital h, h∈(0,1], that is not technology-specific, 10 with the difference in level of human capital determining the degree of proficiency with a given technology.4 It is also assumed that agents would not be looking for another job when employed. Each firm produces a single, all-encompassing final good of unitary price that is identical across all firms, and operates within a perfectly competitive environment. Firm i employs Lit of workers, and adopts a unit level of technology Ati that is freely available for adoption, with Ati indexed from 0 to 1, at a cost of q units of final good per unit of technology. 1.2.1 The Production Process The firm requires a combination of technology, human capital and labour for final-good production. Each of the firms in the economy takes on the Cobb-Douglas production function which satisfies the usual Inada conditions: F i ( hAti , Lit ) = B ( hAti ) Lit β α (1) where α, β ∈(0, 1], and the superscript denotes the index associated with the firm. Here, α represents the share of efficiency units of technology adopted by firms whilst β denotes the production share attributed to the number of employed workers. No numerical restriction is imposed regarding the sum of these two exponents. Thus, human capital, 4 We assume that human capital, h, is a slow moving variable that takes time to be accumulated. Therefore, we have assumed it to be exogenous to allow us to focus on how changes to human capital will affect technology adoption and unemployment. 11 technology and labour are seen as complementary in the production process. 5 We augment human capital to technology rather than to labour in view of our assertion that technology can only be an effective component of production through the implementation of available knowledge. Rewriting the above production function to allow human capital to augment labour would suggest that the total amount of effective workers increases at a diminishing rate.6 B represents a productivity parameter that is exogenous to the firm. Each firm also faces an exogenous per unit cost of technology q/h, which includes the cost of the physical unit of that technology as well as training costs, with this cost component decreasing in the human capital level of the economically active. This suggests that the availability of a better-trained workforce will help lower the cost of adopting a particular level of technology. In the process, each infinitesimal improvement in human capital presents firms the opportunity to make changes to existing work practices and job scope of workers, which could lead to adjustments in employment, to take advantage of possible use of higher levels of technology. For simplicity, the total cost associated with technology implementation can be seen as a whole, rather than being subjected to depreciation, upon the assumption that firms actually rent their machines from an agency that supplies machines equipped with a given technology. ( q h ) Ati Thus, can be seen as the total cost of using machinery equipped with a certain technology per time period t. 5 Given the Cobb-Douglas structure, human capital, technology and workers are complements. We thus conjecture that the outcomes are likely to be the same if human capital is also endogenized. This issue can be explored in future studies. 6 ( ) ( ) ( h( We may also rewrite the above production function as F i Ati , hLit = B Ati α α β) Lit ) β , where effective labour increases at a diminishing rate with respect to an increase in human capital. 12 1.2.2 Employment Decisions Employment cost comprises of a recurring component and a one-off search cost. Firms encounter a wage rate of wti units of final good per worker that is considered as being exogenous to the firm. Each firm also incurs search costs associated with interviewing prospective applicants of job vacancies of b units of final good per interviewed applicant. We also assume that firms face search costs which are increasing in the number of interviews conducted.7 In the process, the firm thus also needs to decide on the number of candidates Dit to be considered for an interview. In this paper, we assume that the cost of selecting the candidates follows the specific quadratic form bDit2, where b>0. 1.2.3 Job Matching and Creative Destruction Dynamics The probability that the interviewee would be able to secure the job is dependent on the average human capital level within the economy and the economy’s unemployment level ut, which would be equivalent to (1-Lt). From the firm’s perspective, a higher unemployment rate would mean a higher probability of finding that suitable worker if there is a larger pool of unemployed workers to choose from. This can be seen as a measure of tightness of the labour market. The average level of human capital is included as it is in general easier for firms to find the suitable worker within an economy with more better-skilled workers. Thus, the number of successful job interviewees that 7 Search costs can increase at an increasing rate through the tasks that can be undertaken due to loss of working time in the process of interviewing prospective applicants, which can otherwise be used to raise output in a more than proportionate manner. For example, the time taken to interview five candidates consecutively to fill up extra vacancies can be used to do an amount of work that is more than five times that of the time taken for one candidate due to human factors. The availability of a choice of candidates also leads to increased time required to select the worker arising from the analytical process of selecting the right candidate. 13 are offered employment can be written as ς(h)utεDit, where ς(h) is a function that generates a probability attributed to the human capital component in the selection process, with ς’(h)>0 and ς’’(h) 0 ). The movement in the north-east direction suggests the presence of a complementary effect that is stronger than that of the substitution effect, thus raising the level of technology adopted and employment. With an anticipated change, a jump in the level of technology implemented that is lower than that of the instantaneous case occurs. We find that A&t and L&t will be positive and negative respectively. The economy actually experiences a fall in employment, whilst experiencing increasing levels of technology implemented along its adjustment trajectory until it reaches the saddle path, whereby the economy will experience increasing employment and level of technology adopted until it arrives at the equilibrium point. Here, firms make the adjustment to implement better technology and releasing existing workers prior to the increase in the average skill-profile workers since the overall higher cost of technology implementation makes it not optimal to employ the existing number of workers to work with the better technology as the net discounted future profit of having the additional worker is negative. Once the changes actually take effect, firms will, at this point, actually seek to hire workers to work with better technology as implementation costs fall and output increases, with positive net discounted future profits from employing additional workers, until arrival at saddle-path equilibrium. Again, the complementary effect is much stronger relative to the substitution effect, thus resulting in higher level of technology adoption and employment, the latter surpassing the previous level of employment. The net effects arising from the short run adjustment process under either type of change would thus be the positive effects of an increase in human capital on job creation outweighing the negative effects of the same increase on job destruction. 30 Figure 1.3: Effect of an increase in h when h is below the threshold level of human capital At New A&t = 0 Saddle -Path Old A&t = 0 New L&t = 0 Old L&t = 0 Lt In the second scenario and with an unanticipated increase in h, we have an immediate upward jump in the level of technology. This time, both A&t and L&t are negative at that point after the upward jump. The latter thus suggests that the costs associated with the technological and overall job loss impact of creative destruction through adoption of better technologies now outweigh that of the benefits associated with ease of finding workers and better use of existing technology. At the higher level of human capital, the technological impact of creative destruction is now sufficiently large enough and that acquiring more workers to work with better technology reduces undiscounted profits and that each additional worker reduces net future discounted profits 31 (i.e. λ&t < 0 ). From that point on, the firms should thus seek to lower both the level of technology adopted and the number of workers employed in view of the optimal solution lying along the demarcation curves. With the technological impact of creative destruction now sufficiently large, it would make sense for the firm to reduce employment since the presence of these surplus workers actually reduce the current and discounted future profits that the firm can enjoy. To elaborate further, on the one hand, whilst having better-educated workers enables the firm to be able to work better with existing technology, the advantage of ease of finding workers in an economy with bettereducated workers has diminished. Moreover, there is a slowdown in the increase of the sum of discounted future profits from employing an additional worker as h increases. On the other hand, the creative destruction impact of technology has become stronger such that raising the technology level slightly, at a given level of employment, can raise job loss rate very quickly. We thus have the situation where the substation effect outweighs the complementary effect, as seen from the south-west movement towards the saddlepoint equilibrium. The south-west movement suggests that firms immediately implement high levels of technology, but subsequently find that the costs of using that technology with the higher-skilled and more highly-paid workers exceeding the gains in output of using that technology. Thus, the large extent of shift in A&t = 0 can be seen as the presence of a relatively and increasingly larger extent of substitution away from labour and towards technology across all levels of employment. When the increase in the level of human capital is anticipated, the economy will witness a jump in the level of technology implemented that will be less than that of the instantaneous case. The extent of the jump will determine the point the economy will attain on the new saddle path upon 32 Figure 1.4: Effect of an increase in h when h is above the threshold level of human capital At New A&t = 0 Old A&t = 0 Saddle -Path New L&t = 0 Old L&t = 0 Lt the increase. If this change is set to occur very soon, the economy is likely to jump vertically upward to a point just below the new saddle path, with firms raising the level of technology implemented and reducing employment. Upon arriving at the new saddle path at the time the change takes effect, the economy will take on the same changes as that of the unanticipated change. However, should the increase in human capital take a longer time to take effect, the extent of the vertical jump is likely to be lower. The economy will nevertheless embark on an adjustment process similar to the situation 33 discussed earlier, with the subsequent adjustment process upon the change taking place similar to that of scenario 1, where once the change takes effect, the cumulative actions of all firms would be to increase the level of technology further whilst using more workers to work with the technology. Nevertheless, employment levels will not attain the same levels as before due to the substitution effect outweighing the complementary effect, with employment below its previous level prior to the increase in h. On the whole, in terms of the net effects, the positive effects of an increase in human capital on job creation are now outweighed by the negative effects of the same increase on job destruction during the short run adjustment process under either type of change. One implicit indication of the slowdown in equilibrium employment that subsequently leads to a fall in employment arises from a decreasing rate of increase in the equilibrium value of λt for any given increasing value of h at the saddle-path stable equilibrium values of At and Lt. This is an indication that, beyond the threshold value of h, keeping employment unchanged or raising employment when implementing higher levels of technology would not be optimal as the additional output generated by having the extra worker would only lead to a reduction in the firm’s profit since the net discounted future profit is negative. The fact that the intersection point on the new L&t = 0 curve is to the left of the previous intersection suggests that firms are more than willing to employ less workers in favour of using better technology, which indicates greater dominance of the technology mechanism of creative destruction. This would also implicitly suggest that the firm’s profitability would be compromised if employment is not reduced since the additional output generated by having the additional worker over and above the optimal number of workers would not be sufficient to cover the costs of 34 keeping that worker. By employing fewer workers, firms do seek to suppress the overall job loss, which would aim to soften the increase in costs associated with creative destruction. Nevertheless, the creative destructive impact of technology arising from relatively cheaper implementation costs based on a continually falling share of total costs does continue to increase even beyond the threshold level of human capital, indicating that firms increasingly use technology to replace workers in production. We briefly discuss the impact of an increase in h on other variables. An increase in h would raise the equilibrium value of λt throughout. Note that the availability of better-skilled workers raises the marginal product of technology while reducing the marginal cost counterpart. Subject to the technological impact of creative destruction, optimal behaviour by all firms would require consideration of the labour-technology mix such that there is an incentive in using these higher-skilled workers in the form of net discounted future profit from employing that additional worker. However, this equilibrium net discounted future profit increases at a decreasing rate owing to the increasing creative destruction impact arising from increasing levels of technology adopted in the presence of higher-skilled workers. We also note that the increase in h would lead to an increase in wages. The extent of increase is higher than proportionate prior to the threshold owing to the improved bargaining power arising from higher employment. Firms will need to pay more to hire workers owing both to the human capital aspect as well as a premium attributed to the higher probability of a worker being able to find an alternative job to encourage the worker to take up the job. Beyond the threshold, an increase in h would still lead to 35 higher wages but the wages now increase in a lower than proportionate manner due to reduced bargaining power arising from lower employment. The firms can actually reduce the premium paid to the worker to fill the job since it is now harder to find a job from the viewpoint of the worker and easier from that of the firm. An increase in h would also raise the economy’s interview rate. This can be attributed to the fact that having more skilled workers in the economy raises the probability of finding a suitable worker. Indirectly, there is also an increased need to replace workers arising from greater job destruction. For levels of human capital below the threshold level, the pace of increase is slower owing to the opposing force arising from reduced unemployment, which shrinks the pool of workers available for hire. The pace of increase picks up when h is beyond the threshold since the pool of workers available for hire increases. The following summarizes the above findings concerning employment and level of technology adopted: Proposition 2: For levels of human capital below the threshold level, an increase in human capital would raise the level of technology implemented and employment. For levels of human capital above the threshold level, an increase in human capital would raise the level of technology implemented but reduces employment. Proof: See 1.7.2. 36 1.4 Changes in Other Parameters This section provides a brief account and intuition of the effects of various parameter changes on employment, technology adoption, threshold level of human capital, future marginal discounted revenue of an additional worker, interviews and wages. For all cases, we find that the behaviour of the system as h increases remains the same as the discussion above with respect to the transition that the slopes of the demarcation curves undergo. Tables 1.5 to 1.13 provide a numerical summary of the changes to various variables as the values of the exogenous parameters changes. A 5% increase is considered in most cases, with the exception of selected parameters such as overall collective wage bargaining parameter, cost per unit vacancy and interest rate. For ease of discussion, we consider only an increase in the relevant parameters unless otherwise indicated. The opposite outcome prevails when the direction of change is reversed. Table 1.4 summarizes the outcomes. Table 1.4: Summary of outcomes of comparative statics exercise of an increase in respective parameters in 1.4.1 to 1.4.5 Matching parameters Wage parameters Global tech progress Productivity parameter Cost parameters Interest rate Parameter Lt At λt wt Dt ε δ χ - + + + - + + + - γ + + + - + ψ z B b q r + + + - + + + + + - + + - + + + - Thresh-old h + + no change + + + + Current Profit + + + 37 1.4.1 Matching Parameters Increases in either the human capital matching function parameter ε or the matching parameter associated with unemployed workers δ results in a reduction in both the level of employment and technology adopted. However, such an increase actually raises the sum of discounted future profits of an additional worker and threshold level of human capital. Looking at (8’), increased marginal product of technology together with a reduction in the marginal creative destruction attributed to technology has resulted in the increase in the sum of discounted future profits of an additional worker. This allows the job creation effect to continue to dominate the job destruction effect, which had been reduced by the fall in employment and technology level, at higher levels of human capital resulting in a higher threshold level. In addition, it is more difficult to find workers when ε or δ increases since the probability of finding the suitable worker falls, thus leading to lower employment. Firms would therefore be better off to reduce technology level as well to ensure no net discounted future profits of an additional worker. Reduced employment results in a fall in wages. The fall in wages together with an increase in the sum of discounted future profits of an additional worker leads to an increase in the interview rate. 1.4.2 Wage Setting Parameters When the overall collective wage bargaining power has become stronger (i.e. increase in χ), this leads to an upward shift of only the locus of A&t = 0 . This encourages 38 Table 1.5: Simulation results for (a) ε = 0.2 and (b) ε = 0.3 (a) ε = 0.2 h 0.4000 0.5000 0.6000 0.6300 0.6375 0.6400 0.6425 0.6500 0.7000 0.8000 0.9000 0.9500 Lt 0.930855 0.937213 0.939603 0.939773 0.939782 0.939783 0.939781 0.939769 0.939384 0.937207 0.93342 0.930995 At 0.180144 0.280378 0.399243 0.438122 0.448052 0.451381 0.454718 0.464784 0.533824 0.680329 0.834042 0.911900 λt 0.233733 0.253985 0.269985 0.274078 0.275054 0.275375 0.275694 0.276640 0.282494 0.292016 0.298925 0.301495 h 0.4000 0.5000 0.6000 0.6700 0.6725 0.6750 0.6775 0.6800 0.7000 0.8000 0.9000 0.9500 Lt 0.925035 0.933304 0.936901 0.937603 0.937606 0.937608 0.937608 0.937606 0.937546 0.936056 0.932867 0.930722 At 0.178037 0.277888 0.396496 0.489207 0.492648 0.496098 0.499556 0.503022 0.531044 0.677878 0.832456 0.911006 λt 0.252015 0.269019 0.281741 0.288582 0.288798 0.289012 0.289225 0.289436 0.291056 0.297532 0.301579 0.302794 wt 0.057891 0.073057 0.087982 0.092404 0.093139 0.093506 0.093872 0.094239 0.095337 0.102612 0.116891 0.130759 Dt 0.195866 0.210036 0.226229 0.231518 0.232872 0.233327 0.233782 0.235158 0.244653 0.265303 0.287997 0.300001 zAth 0.035265 0.037066 0.040350 0.041620 0.041959 0.042073 0.042189 0.042541 0.045110 0.051437 0.059452 0.064128 zAthLt 0.032827 0.034738 0.037913 0.039113 0.039432 0.039540 0.039648 0.039979 0.042376 0.048207 0.055494 0.059703 Profit 0.077583 0.097365 0.116952 0.122782 0.123752 0.124236 0.124721 0.125205 0.126656 0.136291 0.155311 0.173922 Dt 0.202269 0.215231 0.230292 0.242191 0.242637 0.243084 0.243533 0.243983 0.247636 0.267247 0.288939 0.300463 zAth 0.035100 0.036901 0.040183 0.043357 0.043484 0.043612 0.043741 0.043871 0.044946 0.051288 0.059350 0.064068 zAthLt 0.032468 0.034439 0.037647 0.040652 0.040771 0.040891 0.041012 0.041134 0.042139 0.048009 0.055366 0.059630 Profit 0.077270 0.097096 0.116722 0.130317 0.130800 0.131283 0.131766 0.132248 0.136101 0.155169 0.173841 0.182996 (b) ε = 0.3 wt 0.057385 0.072631 0.087628 0.097954 0.098320 0.098685 0.099051 0.099416 0.102331 0.116690 0.130650 0.137465 Table 1.6: Simulation results for (a) δ = 0.5 and (b) δ = 0.7 (a) δ = 0.5 h 0.4000 0.5000 0.6000 0.6075 0.6100 0.6125 0.6200 0.7000 0.8000 0.9000 0.9500 Lt 0.952738 0.956937 0.958207 0.958216 0.958216 0.958215 0.958206 0.957504 0.955249 0.951643 0.949370 At 0.186798 0.290551 0.414020 0.424004 0.427354 0.430713 0.440854 0.554451 0.708111 0.870166 0.952536 λt 0.189896 0.206456 0.220423 0.221382 0.221700 0.222016 0.222956 0.232323 0.242437 0.250908 0.254549 wt 0.059806 0.075219 0.090430 0.091562 0.091939 0.092315 0.093445 0.105394 0.120053 0.134346 0.141336 Dt 0.179909 0.193061 0.208688 0.209667 0.210397 0.210828 0.212131 0.226988 0.247989 0.271550 0.284188 zAth 0.035781 0.037732 0.041239 0.041565 0.041675 0.041787 0.042127 0.046324 0.053110 0.061765 0.066840 zAthLt 0.034089 0.036107 0.039516 0.039828 0.039934 0.040041 0.040366 0.044355 0.050734 0.058778 0.063456 Profit 0.078311 0.098183 0.117882 0.119363 0.119840 0.120329 0.121796 0.137353 0.156528 0.175314 0.184526 39 (b) δ = 0.7 h 0.4000 0.5000 0.6000 0.6200 0.6275 0.6300 0.6325 0.6400 0.7000 0.8000 0.9000 0.9500 Lt 0.913233 0.919936 0.922356 0.922466 0.922480 0.922481 0.922481 0.922470 0.921904 0.919294 0.914941 0.912204 At 0.175558 0.272753 0.387501 0.412299 0.421742 0.424906 0.428080 0.437649 0.516706 0.656457 0.802051 0.875392 λt 0.257136 0.283969 0.305068 0.308678 0.309983 0.310411 0.310837 0.312098 0.321273 0.333238 0.341526 0.344452 wt 0.056363 0.071179 0.085729 0.088602 0.089675 0.090033 0.090390 0.091460 0.099949 0.113775 0.127149 0.133651 Dt 0.202437 0.218520 0.236137 0.239871 0.241290 0.241765 0.242242 0.243678 0.255534 0.276708 0.299456 0.311308 zAth 0.034903 0.036558 0.039633 0.040414 0.040721 0.040825 0.040930 0.041249 0.044093 0.049988 0.057396 0.061687 zAthLt 0.031875 0.033631 0.036556 0.037280 0.037564 0.037660 0.037757 0.038051 0.040649 0.045953 0.052514 0.056271 Profit 0.077155 0.096812 0.116259 0.120118 0.121562 0.122043 0.122524 0.123965 0.135434 0.154263 0.172650 0.181642 firms to reduce the employment of workers and increase the level of technology used, as it is now more costly to make use of the former. The sum of discounted future profits of an additional worker, number of interviews and threshold level of human capital have all decreased as a result. Since it now costs more to employ workers, firms would seek to try to replace the use of workers with technology where possible, which subsequently raises the job loss rate. Looking at (8’), the sum of discounted future profits of an additional worker would fall due to the greater impact of creative destruction relative to the marginal product of technology. The fall in the sum of discounted future profits of an additional worker plays a crucial role here in the determination of the threshold level of human capital. The overall effect of job creation, as a result of the preceding decrease, has been weakened as firms are reluctant to hire workers due to lower per-worker contribution to discounted future profits. The technology impact of job destruction is now stronger due to the higher level of technology implemented. This increase in technological implementation motivates greater substitution away from labour towards technology across all levels of employment, which will raise the job destruction effect. Weakened job creation together with stronger job destruction would result in the pace of shift of L&t = 0 being relatively slower to that of A&t = 0 at a lower value of h, 40 subsequently lowering the new threshold level. The fall in employment is the main factor behind the fall in wages. A relatively larger fall in the sum of discounted future profits of an additional worker compared to the fall in employment pushes the interview rate down. Increases in either the values of ψ and γ will result in an increase in the level of employment but a fall in the level of technology adopted. The sum of discounted future profits of an additional worker has also increased. However, the threshold value of human capital remains unchanged for the latter case and increases in the former. An increase in ψ in this context can be seen as a reduction in emphasis of the human capital factor in wage bargaining. This lowers the wage costs, hence providing firms with the incentive to use more workers and reduce the level of technology used. A similar analogy can be used for an increase in γ, the employment level factor in wage bargaining. The increase in threshold level with respect to an increase in ψ can be seen in light of the reduced job loss from creative destruction effect attributed to lower technology levels being adopted across all values of h relative to job creation. In the case of γ, it is likely that the effect of lower wage costs of employing workers is exactly matched by the effect of overall job loss from increased employment, hence no change in threshold level of human capital. The sum of discounted future profits of an additional worker increases in both cases and this is likely to be due to the impact of higher marginal product of technology relative to the creative destruction impact from (8’). The interview rate increases as the advantage of increased total discounted future profits of an additional worker exceeds the disadvantage of a reduced pool of workers to choose from. 41 Table 1.7: Simulation results for (a) 10% fall in χ (=0.144) and (b) 10% rise in χ (=0.176) (a) 10% fall in χ (=0.144) h 0.4000 0.5000 0.6000 0.6150 0.6200 0.6225 0.6250 0.6300 0.7000 0.8000 0.9000 0.9500 Lt 0.935573 0.940940 0.942746 0.942793 0.942797 0.942797 0.942796 0.942789 0.942168 0.939773 0.935869 0.933418 At 0.181028 0.281221 0.399828 0.419032 0.425509 0.428761 0.432023 0.438573 0.533830 0.679298 0.831360 0.908116 h 0.4000 0.5000 0.6000 0.6100 0.6150 0.6175 0.6200 0.6250 0.7000 0.8000 0.9000 0.9500 Lt 0.931449 0.937061 0.938914 0.938947 0.938954 0.938956 0.938955 0.938951 0.938232 0.935601 0.931334 0.928652 At 0.181243 0.281906 0.401296 0.414160 0.420651 0.423911 0.427180 0.433747 0.536505 0.683736 0.838252 0.916527 λt 0.233777 0.256430 0.274682 0.277090 0.277875 0.278264 0.278651 0.279418 0.289271 0.300692 0.309316 0.312675 wt 0.052472 0.066118 0.079555 0.081549 0.082213 0.082544 0.082876 0.083538 0.092734 0.105605 0.118115 0.124220 Dt 0.196573 0.211622 0.228670 0.231416 0.232343 0.232808 0.233275 0.234213 0.247937 0.269420 0.292919 0.305306 (b) 10% rise in χ (=0.176) λt 0.216151 0.236893 0.253662 0.255148 0.255879 0.256241 0.256601 0.257316 0.267113 0.277685 0.285699 0.288830 wt 0.063738 0.080345 0.096681 0.098297 0.099104 0.099507 0.099910 0.100715 0.112680 0.128271 0.143385 0.150741 Dt 0.188644 0.203105 0.219540 0.221303 0.222193 0.222639 0.223088 0.223988 0.238170 0.259007 0.281877 0.293968 zAth 0.035334 0.037121 0.040385 0.041000 0.041212 0.041319 0.041428 0.041647 0.045111 0.051374 0.059280 0.063875 zAthLt 0.033058 0.034929 0.038073 0.038654 0.038854 0.038956 0.039058 0.039264 0.042502 0.048280 0.055478 0.059622 Profit 0.083038 0.104228 0.125182 0.128301 0.129339 0.129858 0.130376 0.131413 0.145832 0.166093 0.185858 0.195515 zAth 0.035351 0.037166 0.040474 0.040886 0.041097 0.041204 0.041312 0.041531 0.045269 0.051643 0.059722 0.064437 zAthLt 0.032928 0.034827 0.038002 0.038389 0.038588 0.038689 0.038790 0.038995 0.042473 0.048317 0.055621 0.059840 Profit 0.072484 0.090829 0.109028 0.110838 0.111742 0.112194 0.112646 0.113550 0.127035 0.144789 0.162210 0.170765 Table 1.8: Simulation results for (a) γ = 1.1 and (b) γ = 1.7 (a) γ = 1.1 h 0.4000 0.5000 0.6000 0.6100 0.6175 0.6200 0.6225 0.6300 0.7000 0.8000 0.9000 0.9500 Lt 0.933163 0.938711 0.940556 0.940590 0.940601 0.940602 0.940601 0.940590 0.939913 0.937364 0.933216 0.930608 At 0.181171 0.281646 0.400719 0.413543 0.423262 0.426521 0.429789 0.439649 0.535442 0.681977 0.835553 0.913263 λt 0.223196 0.244884 0.262323 0.263864 0.264996 0.265369 0.265739 0.266839 0.276218 0.287036 0.295128 0.298242 wt 0.059311 0.074623 0.089742 0.091241 0.092364 0.092738 0.093112 0.094233 0.104620 0.119209 0.133458 0.140439 Dt 0.191855 0.206636 0.223355 0.225145 0.226502 0.226957 0.227413 0.228790 0.242244 0.263308 0.286364 0.298528 zAth 0.035345 0.037149 0.040439 0.040848 0.041165 0.041273 0.041381 0.041711 0.045206 0.051536 0.059549 0.064219 zAthLt 0.032983 0.034872 0.038035 0.038422 0.038720 0.038821 0.038923 0.039233 0.042490 0.048308 0.055572 0.059763 Profit 0.076626 0.096211 0.115566 0.117486 0.118924 0.119403 0.119882 0.121317 0.134621 0.153296 0.171487 0.180365 42 (b) γ = 1.7 h 0.4000 0.5000 0.6000 0.6100 0.6175 0.6200 0.6225 0.6300 0.7000 0.8000 0.9000 0.9500 Lt 0.934012 0.939441 0.941255 0.941290 0.941301 0.941302 0.941301 0.941292 0.940639 0.938167 0.934149 0.931627 At 0.181126 0.281516 0.400450 0.413256 0.422961 0.426215 0.429478 0.439323 0.534947 0.681121 0.834133 0.911460 λt 0.226830 0.248569 0.266166 0.267726 0.268875 0.269253 0.269630 0.270747 0.280311 0.291472 0.299991 0.303349 wt 0.056987 0.071940 0.086611 0.088060 0.089145 0.089506 0.089867 0.090948 0.100934 0.114838 0.128254 0.134758 Dt 0.193489 0.208242 0.225024 0.226824 0.228189 0.228646 0.229105 0.230492 0.244048 0.265315 0.288637 0.300955 zAth 0.035342 0.037141 0.040423 0.040831 0.041147 0.041254 0.041362 0.041692 0.045177 0.051485 0.059458 0.064099 zAthLt 0.033010 0.034891 0.038048 0.038434 0.038732 0.038833 0.038934 0.039244 0.042495 0.048301 0.055543 0.059716 Profit 0.078803 0.098739 0.118519 0.120486 0.121961 0.122452 0.122943 0.124416 0.138095 0.157404 0.176357 0.185666 Table 1.9: Simulation results for (a) 5% fall in ψ (=0.95) and (b) 5% rise in ψ (=1.05) (a) 5% fall in ψ (=0.95) h 0.4000 0.5000 0.6000 0.6200 0.6250 0.6275 0.6300 0.6350 0.7000 0.8000 0.9000 0.9500 Lt 0.932614 0.938392 0.940413 0.940491 0.940496 0.940496 0.940495 0.940489 0.939929 0.937541 0.933575 0.931070 At 0.181196 0.281699 0.400772 0.426567 0.433111 0.436397 0.439692 0.446309 0.535432 0.681792 0.835014 0.912454 h 0.4000 0.5000 0.6000 0.6100 0.6125 0.6150 0.6175 0.6200 0.7000 0.8000 0.9000 0.9500 Lt 0.934503 0.939735 0.941390 0.941411 0.941412 0.941412 0.941411 0.941408 0.940629 0.938005 0.933813 0.931192 At 0.181098 0.281462 0.400396 0.413205 0.416431 0.419667 0.422913 0.426167 0.534954 0.681296 0.834651 0.912238 λt 0.220898 0.243302 0.261551 0.264765 0.265547 0.265935 0.266321 0.267086 0.276303 0.288002 0.296982 0.300541 wt 0.060766 0.075767 0.090367 0.093237 0.093952 0.094309 0.094666 0.095378 0.104543 0.118261 0.131480 0.137890 Dt 0.190814 0.205942 0.223019 0.226693 0.227625 0.228093 0.228563 0.229507 0.242282 0.263747 0.287234 0.299624 (b) 5% rise in ψ (=1.05) λt 0.228977 0.250074 0.266920 0.268402 0.268768 0.269131 0.269491 0.26985 0.280254 0.290569 0.298227 0.301152 wt 0.055603 0.070835 0.085992 0.087500 0.087877 0.088253 0.088630 0.089006 0.100985 0.115732 0.130148 0.137210 Dt 0.194448 0.208894 0.225350 0.227116 0.227561 0.228007 0.228455 0.228904 0.244023 0.264908 0.287816 0.299915 zAth 0.035347 0.037153 0.040442 0.041275 0.041493 0.041603 0.041714 0.041939 0.045205 0.051525 0.059514 0.064165 zAthLt 0.032966 0.034864 0.038032 0.038819 0.039024 0.039127 0.039232 0.039443 0.042490 0.048307 0.055561 0.059742 Profit 0.075264 0.095135 0.114976 0.118933 0.119921 0.120415 0.120909 0.121896 0.134694 0.154186 0.173337 0.182743 zAth 0.035340 0.037137 0.040420 0.040828 0.040933 0.041038 0.041144 0.041251 0.045177 0.051495 0.059491 0.064151 zAthLt 0.033025 0.034899 0.038051 0.038436 0.038534 0.038634 0.038734 0.038834 0.042495 0.048303 0.055554 0.059737 Profit 0.080101 0.099780 0.119103 0.121015 0.121493 0.121970 0.122447 0.122924 0.138047 0.156564 0.174583 0.183378 43 1.4.3 Rate of Global Technological Progress As discussed earlier, the economies in question here depend very much on the extent of global technological advancement. A higher rate of progress, i.e. higher z, actually encourages the use of lower levels of technology and reduces employment in our model. However, the threshold level of human capital increases when z is higher. The direction of change in the level of technology and employment can be accounted by the fact that an increase in z would affect the sum of discounted future profits of an additional worker and changes the rate of creative destruction and thus job loss rate. With an increase in z, the reduction in total discounted future profits and higher costs associated with job loss and creative destruction result, which leads to a reduction in employment and also technology level. It is somewhat ironic that the threshold level of human capital increases when z increases and vice-versa. However, this can be seen in view of the fact that a higher rate of technological progress would make firms more conservative in technology usage due to the higher rate of creative destruction and job loss and the higher share of costs spent on conducting interviews to fill up the vacancies. Thus it is more cost optimal to hold on to the use of workers until their human capital level is sufficiently high (i.e. at a higher threshold), where it would then be relatively more cost efficient to make use of technology rather than workers. The increase in z reduces the sum of discounted future profits of an additional worker and wages and increases the number of interviews conducted. The reduction in the sum of discounted future profits arises due to the increased creative destruction effect whilst the fall in wages can be attributed to reduced employment. The interview rate increases because the effect of a fall in employment exceeds that of a fall in the sum of discounted future profits of employing an 44 additional worker. As indicated in our introduction, this overall increase in creative destruction does lead to reduced undiscounted profits in our model since the lifetime of the technology is reduced and this is supported by our simulation outcomes. Thus, the firms’ technology adoption behaviour when z increases indicates that they are seeking to extend the use of technology for as long as possible in order to attain sufficiently high profitability, thus they do not have the room to upgrade their technologies too often. Table 1.10: Simulation results for (a) 5% fall in z (=0.0665) and (b) 5% rise in z (=0.0735) (a) 5% fall in z (=0.0665) h 0.4000 0.5000 0.6000 0.6100 0.6150 0.6175 0.6200 0.6250 0.7000 0.8000 0.9000 0.9500 Lt 0.936392 0.941631 0.943352 0.943382 0.943388 0.943389 0.943389 0.943384 0.942704 0.940231 0.936222 0.933702 At 0.182243 0.283331 0.403251 0.416175 0.422696 0.425971 0.429256 0.435854 0.539116 0.687138 0.842574 0.921349 h 0.4000 0.5000 0.6000 0.6150 0.6200 0.6225 0.6250 0.6300 0.7000 0.8000 0.9000 0.9500 Lt 0.930837 0.936569 0.938506 0.938558 0.938563 0.938563 0.938562 0.938556 0.937901 0.935361 0.931215 0.928612 At 0.180069 0.279856 0.397959 0.417077 0.423525 0.426763 0.430009 0.436530 0.531340 0.676066 0.827279 0.903580 λt 0.226328 0.248182 0.265832 0.267395 0.268163 0.268544 0.268923 0.269675 0.279976 0.291085 0.299504 0.302793 wt 0.058374 0.073540 0.088474 0.089952 0.090690 0.091059 0.091428 0.092165 0.103120 0.117419 0.131309 0.138081 Dt 0.188853 0.203374 0.219892 0.221664 0.222559 0.223008 0.223459 0.224365 0.238634 0.259622 0.282690 0.294900 (b) 5% rise in z (=0.0735) λt 0.223822 0.245398 0.262792 0.265087 0.265835 0.266206 0.266574 0.267305 0.276698 0.287583 0.295795 0.298988 wt 0.057890 0.072987 0.087838 0.090041 0.090774 0.091140 0.091506 0.092237 0.102385 0.116568 0.130326 0.137029 Dt 0.196383 0.211382 0.228352 0.231084 0.232006 0.232469 0.232933 0.233866 0.247509 0.268841 0.292141 0.304409 zAth 0.033658 0.035397 0.038563 0.038957 0.039159 0.039261 0.039365 0.039574 0.043152 0.049256 0.056999 0.061521 zAthLt 0.031517 0.033331 0.036378 0.036751 0.036942 0.037039 0.037136 0.037333 0.040679 0.046312 0.053364 0.057442 Profit 0.077902 0.097690 0.117293 0.119242 0.120215 0.120701 0.121187 0.122159 0.136657 0.155711 0.174362 0.183503 zAth 0.037022 0.038883 0.042285 0.042926 0.043147 0.043259 0.043372 0.043601 0.047212 0.053738 0.061969 0.066751 zAthLt 0.034462 0.036416 0.039685 0.040289 0.040496 0.040601 0.040707 0.040922 0.044280 0.050264 0.057706 0.061985 Profit 0.077562 0.097298 0.116835 0.119745 0.120713 0.121197 0.121681 0.122648 0.136112 0.155054 0.173566 0.182624 45 1.4.4 Productivity Parameter An increase in the productivity parameter B would lead to an increase in both the level of technology implemented and employment, and vice-versa. However, the increase in productivity would actually lower the threshold level of human capital. The sum of discounted future profits of an additional worker is raised when B increases as the effect of increased productivity raises the marginal product of technology from (8’) relative to the creative destruction effect at all levels of At. It is likely that the subsequent effect of an increase in job creation is not as strong as that of creative destruction, as an increase in productivity can be seen to be dampening the significance of human capital in production. Subsequently, the demarcation curve for L&t = 0 can thus be considered to shift less quickly relative to the demarcation curve for A&t = 0 at a lower level of human capital, thus resulting in the lower threshold level of human capital. Wages increase due to the higher probability of workers finding employment. The economy’s interview rate increases as the effect of increased total discounted future profits of an additional worker overwhelms the fall in number of unemployed workers to choose from. Table 1.11: Simulation results for (a) 5% fall in B (=0.475) and (b) 5% rise in B (=0.525) (a) 5% fall in B (=0.475) h 0.4000 0.5000 0.6000 0.6300 0.6325 0.6350 0.6375 0.6400 0.7000 0.8000 0.9000 0.9500 Lt 0.931327 0.937374 0.939616 0.939758 0.939761 0.939762 0.939761 0.939759 0.939324 0.937112 0.933306 0.930872 At 0.167656 0.260987 0.371852 0.408165 0.411250 0.414343 0.417445 0.420556 0.497677 0.635103 0.779936 0.853606 λt 0.209042 0.229380 0.245892 0.250202 0.250549 0.250893 0.251236 0.251577 0.259214 0.269766 0.277861 0.281067 wt 0.057933 0.073075 0.087984 0.092402 0.092769 0.093136 0.093503 0.093869 0.102603 0.116874 0.130736 0.137496 Dt 0.182636 0.196075 0.211345 0.216322 0.216745 0.217170 0.217595 0.218023 0.228667 0.248063 0.269393 0.280693 zAth 0.034266 0.035761 0.038665 0.039804 0.039904 0.040006 0.040108 0.040211 0.042950 0.048683 0.055969 0.060227 zAthLt 0.031913 0.033521 0.036330 0.037406 0.037501 0.037596 0.037692 0.037789 0.040344 0.045621 0.052237 0.056064 Profit 0.068075 0.085343 0.102473 0.107580 0.108005 0.108429 0.108854 0.109278 0.119426 0.136145 0.152562 0.160629 46 (b) 5% rise in B (=0.525) h 0.4000 0.5000 0.6000 0.6025 0.6050 0.6075 0.6100 0.7000 0.8000 0.9000 0.9500 Lt 0.935517 0.940501 0.941954 0.941956 0.941957 0.941957 0.941955 0.941012 0.938220 0.933874 0.931183 At 0.194978 0.302672 0.429973 0.433380 0.436796 0.440223 0.443660 0.573500 0.728849 0.890568 0.971868 λt 0.240559 0.263553 0.281998 0.282408 0.282816 0.283222 0.283625 0.296655 0.308034 0.316156 0.319771 wt 0.058298 0.073416 0.088290 0.088658 0.089026 0.089394 0.089762 0.102861 0.117068 0.130848 0.137560 Dt 0.202380 0.218469 0.236703 0.237189 0.237676 0.238165 0.238656 0.257303 0.280247 0.305300 0.318481 zAth 0.036399 0.038511 0.042185 0.042297 0.042410 0.042524 0.042638 0.047432 0.054351 0.063066 0.068128 zAthLt 0.034052 0.036220 0.039737 0.039842 0.039948 0.040055 0.040163 0.044634 0.050993 0.058896 0.063440 Profit 0.087680 0.109994 0.132056 0.132604 0.133151 0.133699 0.134246 0.153792 0.175107 0.195882 0.206024 1.4.5 Cost Parameters An increase in the interview cost per interviewee, b, which raises production costs, will lead to a reduction in both the level of technology implemented and the employment of workers. Since this cost component is a one-off cost, such an increase does not, in a sense, have an impact on the total discounted future profits of an additional worker directly, thus we do not see the outcome as in the increase in χ. The increase in the sum of discounted future profits of an additional worker is likely to be due to the fact that with reduced employment, the marginal product of each additional worker will thus increase, with this effect being sufficiently strong enough to bring about this result. We also find that the threshold level of human capital has increased. This case is somewhat complicated by the finding that there is an increase in the equilibrium sum of discounted future profits of an additional worker. One way to reconcile this is simply that as the number of workers employed falls, the marginal product of each worker actually increases and thus the contribution of each worker to the discounted future profits increases. Also, the overall job creation impact is still stronger relative to the job loss, aided by the reduced technological impact of creative destruction. Looking at (8’), the 47 adjustment due to the latter effect is likely to be relatively weaker than the change in marginal product of technology, hence the increase in the sum of discounted future profits of an additional worker. Lower equilibrium employment drives wages down, whilst the effect of higher per interviewee cost is the dominant factor in reducing the economy’s interview rate. An increase in q also results in a fall in the level of technology implemented but an increase in the employment of workers. In this situation, this reduction in technology level implemented actually reduces the productivity of a worker at every level of employment, which thus leads to a decrease in the sum of discounted future profits attributed to an additional worker. We also find that the threshold level of human capital has risen. The intuition is fairly similar to that for the case of an increase in b, except that the extent of increase in the threshold level of h is larger, since this cost has a direct impact on technology adoption. Higher employment thus drives wages up whilst the decrease in total discounted future profits of an additional worker plays a dominant role in the fall in interview rate of the economy as it discourages creation of jobs. Table 1.12: Simulation results for (a) 10% fall in b (=0.09) and (b) 10% rise in b (=0.11) (a) 10% fall in b (=0.09) h 0.4000 0.5000 0.6000 0.6100 0.6150 0.6175 0.6200 0.6250 0.7000 0.8000 0.9000 0.9500 Lt 0.936624 0.941828 0.943531 0.943559 0.943565 0.943565 0.943565 0.943560 0.942873 0.940398 0.936392 0.933874 At 0.182264 0.283354 0.403278 0.416203 0.422724 0.425999 0.429284 0.435882 0.539148 0.687177 0.842623 0.921405 λt 0.215421 0.236134 0.252853 0.254333 0.255060 0.255421 0.255781 0.256492 0.266245 0.276755 0.284714 0.287820 wt 0.058394 0.073561 0.088497 0.089976 0.090714 0.091083 0.091452 0.092189 0.103146 0.117448 0.131342 0.138117 Dt 0.199287 0.214566 0.231956 0.233822 0.234764 0.235238 0.235713 0.236667 0.251697 0.273807 0.298113 0.310979 zAth 0.035431 0.037262 0.040594 0.041009 0.041221 0.041329 0.041438 0.041659 0.045425 0.051851 0.060002 0.064763 zAthLt 0.033185 0.035094 0.038302 0.038694 0.038895 0.038997 0.039100 0.039307 0.042830 0.048760 0.056186 0.060480 Profit 0.077895 0.097683 0.117287 0.119235 0.120208 0.120694 0.121181 0.122153 0.136651 0.155704 0.174355 0.183496 48 (b) 10% rise in b (=0.11) h 0.4000 0.5000 0.6000 0.6150 0.6200 0.6225 0.6250 0.6300 0.7000 0.8000 0.9000 0.9500 Lt 0.930742 0.936497 0.938447 0.938501 0.938506 0.938507 0.938506 0.938500 0.937850 0.935314 0.931170 0.928567 At 0.180103 0.279920 0.398065 0.417191 0.423641 0.426880 0.430128 0.436651 0.531504 0.676305 0.827613 0.903969 λt 0.234088 0.256744 0.275018 0.277430 0.278216 0.278606 0.278993 0.279762 0.289637 0.301087 0.309734 0.313100 wt 0.057882 0.072979 0.087830 0.090033 0.090766 0.091132 0.091498 0.092229 0.102378 0.116560 0.130318 0.137019 Dt 0.186873 0.201187 0.217375 0.219981 0.220860 0.221301 0.221744 0.222634 0.235645 0.255988 0.278207 0.289907 zAth 0.035262 0.037035 0.040278 0.040889 0.041100 0.041206 0.041314 0.041532 0.044973 0.051193 0.059039 0.063598 zAthLt 0.032820 0.034683 0.037799 0.038374 0.038572 0.038672 0.038773 0.038978 0.042178 0.047882 0.054976 0.059055 Profit 0.077577 0.097315 0.116853 0.119763 0.120732 0.121216 0.121700 0.122667 0.136133 0.155078 0.173593 0.182653 Table 1.13: Simulation results for (a) 5% fall in q (=0.133) and (b) 5% rise in q (=0.147) (a) 5% fall in q (=0.133) h 0.4000 0.5000 0.6000 0.6025 0.6050 0.6075 0.6100 0.7000 0.8000 0.9000 0.9500 Lt 0.933157 0.938301 0.939797 0.939800 0.939801 0.939800 0.939798 0.938819 0.935930 0.931437 0.928658 At 0.195179 0.303026 0.430474 0.433883 0.437303 0.440733 0.444173 0.574106 0.729485 0.891130 0.972348 λt 0.229917 0.251874 0.269492 0.269884 0.270273 0.270660 0.271045 0.283491 0.294356 0.302448 0.305550 wt 0.058092 0.073176 0.088007 0.088374 0.088741 0.089108 0.089474 0.102526 0.116668 0.130370 0.137038 Dt 0.197644 0.213386 0.231211 0.231685 0.232161 0.232639 0.233118 0.251329 0.273715 0.298133 0.310970 (b) 5% rise in q (=0.147) h 0.4000 0.5000 0.6000 0.6300 0.6325 0.6350 0.6375 0.6400 0.7000 0.8000 0.9000 0.9500 Lt 0.933994 0.939801 0.941937 0.942067 0.942069 0.942069 0.942068 0.942066 0.500523 0.939470 0.935769 0.933404 At 0.168733 0.262571 0.374030 0.410537 0.413638 0.416748 0.419866 0.422994 0.941631 0.638670 0.784243 0.858277 λt 0.220412 0.241875 0.259282 0.263822 0.264187 0.264550 0.264911 0.265270 0.273309 0.284407 0.292909 0.296272 wt 0.058165 0.073340 0.088288 0.092720 0.093089 0.093457 0.093824 0.094192 0.042502 0.117286 0.131219 0.138020 Dt 0.188046 0.201911 0.217672 0.222811 0.223248 0.223686 0.224126 0.224567 0.235559 0.255597 0.277644 0.289326 zAth 0.036414 0.038533 0.042215 0.042327 0.042440 0.042553 0.042668 0.047467 0.054389 0.063102 0.068160 zAthLt 0.033980 0.036156 0.039673 0.039779 0.039885 0.039992 0.040100 0.044563 0.050904 0.058776 0.063297 Profit 0.081054 0.101655 0.122033 0.122539 0.123045 0.123551 0.124056 0.142120 0.161831 0.181055 0.190446 zAth 0.034354 0.035869 0.038801 0.039949 0.040051 0.040153 0.040256 0.040360 0.067114 0.048901 0.056248 0.060540 zAthLt 0.032086 0.033710 0.036548 0.037635 0.037731 0.037827 0.037924 0.038022 0.033592 0.045941 0.052635 0.056509 Profit 0.074644 0.093621 0.112432 0.118036 0.118502 0.118968 0.119434 0.119900 0.049748 0.149350 0.167313 0.176129 The findings for the increase in interest rate or discounting factor appear puzzling. The increase reduces employment but actually increases the level of technology 49 implemented, which resulted from an upward shift of only the locus of A&t = 0 . However, the impact of the increase in r is only minimal. An increase in r will actually lead to a higher discounting of the sum of discounted future profits of an additional worker at all levels of employment. This will thus discourage the use of workers, hence the reduced employment and greater use of technology. Another factor that would have influenced the fall in the sum of discounted future profits of an additional worker would be that the marginal creative destruction impact is greater than the change in net marginal product of technology adoption in the process of replacing labour with technology, based on (8’). The threshold level of human capital is found to have increased though. This outcome can be seen in view of the fact that the fall in the sum of discounted future profits of an additional worker is not sufficiently large enough to encourage a greater substitution of labour with technology and that the marginal product of each worker would have increased when employment falls. Wages and interview rate have decreased. The former is due to lower employment, but this factor is overwhelmed by the reduction in the total discounted future profits of an additional worker in determining the outcome of the latter. Table 1.14: Simulation results for (a) 25% fall in r (=0.03) and (b) 25% rise in r (=0.05) (a) 25% fall in r (=0.03) h 0.4000 0.5000 0.6000 0.6100 0.6150 0.6175 0.6200 0.6250 0.7000 0.8000 0.9000 0.9500 Lt 0.934393 0.939735 0.941485 0.941515 0.941521 0.941522 0.941521 0.941516 0.940816 0.938289 0.934209 0.931651 At 0.181104 0.281461 0.400358 0.413161 0.419619 0.422863 0.426116 0.432650 0.534824 0.680987 0.834039 0.911417 λt 0.228494 0.250078 0.267453 0.268989 0.269743 0.270118 0.270490 0.271228 0.281322 0.292158 0.300310 0.303470 wt 0.058200 0.073333 0.088229 0.089703 0.090439 0.090807 0.091175 0.091909 0.102831 0.117080 0.130913 0.137657 Dt 0.194232 0.208896 0.225579 0.227369 0.228272 0.228726 0.229181 0.230095 0.244491 0.265624 0.288785 0.301012 zAth 0.03534 0.037137 0.040417 0.040825 0.041035 0.041141 0.041248 0.041465 0.045170 0.051477 0.059452 0.064096 zAthLt 0.033022 0.034899 0.038052 0.038438 0.038635 0.038735 0.038836 0.039040 0.042496 0.048300 0.055541 0.059715 Profit 0.077673 0.097433 0.116998 0.118942 0.119913 0.120398 0.120883 0.121853 0.136312 0.155302 0.173873 0.182966 50 (b) 25% rise in r (=0.05) h 0.4000 0.5000 0.6000 0.6150 0.6200 0.6225 0.6250 0.6300 0.7000 0.8000 0.9000 0.9500 1.5 Lt 0.932800 0.938431 0.940339 0.940391 0.940396 0.940397 0.940396 0.940390 0.939752 0.937260 0.933179 0.930610 At 0.181188 0.281693 0.400799 0.420098 0.426607 0.429876 0.433155 0.439739 0.535549 0.682086 0.835609 0.913258 λt 0.221670 0.243498 0.261152 0.263486 0.264247 0.264625 0.265000 0.265744 0.275321 0.286469 0.294937 0.298255 wt 0.058061 0.073190 0.088078 0.090287 0.091022 0.091389 0.091756 0.092489 0.102668 0.116900 0.130711 0.137442 Dt 0.191165 0.206028 0.222844 0.225552 0.226466 0.226926 0.227386 0.228311 0.241847 0.263050 0.286274 0.298534 zAth 0.035347 0.037152 0.040444 0.041064 0.041278 0.041386 0.041495 0.041717 0.045212 0.051543 0.059553 0.064219 zAthLt 0.032971 0.034865 0.038031 0.038616 0.038817 0.038919 0.039022 0.039230 0.042488 0.048309 0.055573 0.059763 Profit 0.077788 0.097553 0.117127 0.120044 0.121015 0.121500 0.121985 0.122954 0.136454 0.155459 0.174049 0.183154 General Discussion The above comparative statics analysis has yielded some interesting outcomes with respect to changes in various parameters. We attempt to provide a general discussion on the implications of some issues and policy implications associated with the existence of a threshold level of human capital. The key point to note is that in general, it is beneficial for a country with very low levels of human capital to undertake efforts to raise the skill level of the economically active through training courses and to provide more higher education opportunities for the schooling population. Such a move can raise both employment and earnings. However, over-emphasis on training and education such that human capital level is beyond the threshold level can lead to higher unemployment arising from creative destruction effect attributed to technology and reduced profitability in the use of workers. An empirical study carried out by Ho and Tan (2005) has revealed such a phenomenon occurring in Singapore. 51 As the economy matures, the level of human capital within the workforce is likely to reach an apex. If this apex be beyond the threshold level of human capital, a solution needs to be found to help workers, who are likely to have spent a fairly large amount to attain the level of human capital, gain employment to help them recoup the investment in education. Policies that target the wage parameters and employment cost parameter can be implemented to help to boost the employment level and thus, in our model, reduce unemployment. 1.6 Conclusion In this paper, we have studied the interaction between technology adoption and employment (unemployment), with an emphasis on how changes in human capital influence the technology-employment mix of firms within the economy. Whilst the increasing skill level of the labour force has enabled the use of higher levels of technology, as found in several empirical studies, we observe also that workers have become increasingly replaceable by technology. We have shown that higher levels of human capital promote the use of higher levels of technology throughout. Also, such increases raise employment (lower unemployment) at lower levels of human capital and that, beyond a certain threshold, further increases in the level of human capital lead to lower employment (higher unemployment). A corresponding relationship that is similar in nature between employment and technology adoption can be obtained. Comparative statics analysis was carried out for various parameters, with the effects of increased pace of global technological advancement, increase in subsidy to technology adoption and 52 decreases in wage rate per unit of human capital being studied. Some implications on the above findings are discussed. 53 1.7 Appendices 1.7.1 Proof of Proposition 1 We first differentiate (15) and (16) with respect to h but keeping Lt fixed to obtain the vertical shift of the demarcation loci. The results are as follows: Differentiation of A&t = 0 with respect to h: ∂L&t ∂h ⎧ A − h ⎡αβ BhL β −1 ( hA )α ⎤ ⎫ t t ⎪ t ⎣ ⎦ − λt ⎪ + ⎨ ⎬ h 2 zLt Lt ⎪ ⎪⎩ ⎭ ⎧⎧ ⎫ ⎡ −h ⎛ 2 α +1 β −1 α −1 ∂At α β −1 α ⎞ ⎤ ⎫ + + − α β α α β A Bh L A Bh L A 1 ( ) ⎪⎪ t t t t ⎟ ⎥ ⎪ ⎪ ⎢ t ⎜ ∂h ⎝ ⎠ ⎥ ⎪ ⎪ ⎪ ⎪h 2 zL ⎢ − t ⎪ ⎪⎨ ⎢⎛ − h −1 ∂At ⎥ ⎪⎬ ⎪ α ⎞ β −1 −h + At ln At ⎟ αβ BhLt ( hAt ) ⎪⎪ ⎢⎜ hAt ⎥ ⎪ ⎪ ∂h ⎠ ⎣⎝ ⎦ ⎪⎪ ⎪ ⎪⎪ α ⎪ ⎪ −h β −1 ⎪⎭ ⎪ ⎪ ⎩ At αβ BhLt ( hAt ) ( 2hzLt ) − 2 ⎪ ⎪ 2 h zL ( ) t ⎪ ⎪ L&t ⎨ ⎬= ⎡⎛ ⎤ α ⎞⎡ − h −1 ∂At −h β ⎪ ⎪ −hAt − At ln At ⎟ α BhLt ( hAt ) − qAt ⎤ + ⎥ ⎣ ⎦ ⎪ 2 2 ⎢⎜⎝ ⎪ ∂h ⎠ ⎥− ⎪ h zLt ⎢ ⎪ ⎢ ⎥ A A ∂ ∂ −h ⎛ 2 α +1 β α −1 α β α ⎪ ⎪ t t ⎞ ⎢ At ⎜ α Bh Lt At ∂h + α (α + 1) Bh Lt At − q ∂h ⎟ ⎥ ⎪ ⎪ ⎝ ⎠⎦ ⎣ ⎪ ⎪ α ⎪ ⎪ At − h ⎡α BhLt β ( hAt ) − qAt ⎤ ( 2hzLt 2 ) ⎣ ⎦ ⎪ ⎪ 2 2 2 ⎪ ⎪ h zL ( t) ⎪⎩ ⎭⎪ ( ) 2δ −1 2ε ⎫⎪ ∂At ∂λt ⎧⎪ δ h (1 − Lt ) β −1 α −1 α ψ −1 γ λt + zAt h ⎬ + −αβ BLt h At − αβ BLt h At +ψχ h Lt + ⎨r + ∂h ∂h ⎪⎩ 2b ⎭⎪ ⎧⎪ ⎡ 2δε h 2ε −1 (1 − L )2δ −1 ⎤ δ h 2ε (1 − L )2δ −1 ∂λ ⎛ ∂A ⎞ ⎫⎪ t t t λt ⎨λt ⎢ + ⎜ hzAt h −1 t + zAt h ln At ⎟ ⎬ ⎥+ 2b 2b ∂h ⎝ ∂h ⎠ ⎭⎪ ⎥⎦ ⎩⎪ ⎢⎣ β −1 α α −1 (A1) 54 Differentiation of L&t = 0 with respect to h: 2ε h 2ε −1 (1 − Lt ) 2b 2δ h 2ε (1 − Lt ) λt + 2b 2δ ∂λt ∂A ⎡ ⎤ − zLt ⎢ hAt h −1 t + At h ln At ⎥ = 0 ∂h ∂h ⎣ ⎦ (A2) where: ∂λt 1 = ∂h ( h 2 zL )2 t and ⎧ ⎧⎛ ⎫ ⎫ α ⎞ − h −1 ∂At − At − h ln At ⎟ ⎡ − qA + α BhLt β ( hAt ) ⎤ + ⎪ ⎪⎜ −hAt ⎪ ⎪ ⎦ ∂h ⎠⎣ ⎪ ⎪ ⎪h 2 zL ⎨⎪⎝ ⎬ −⎪ t ⎪ ∂ ∂ A A ⎡ ⎤ ⎪ A − h − q t + α 2 Bhα +1 L β A α −1 t + α (α + 1) Bhα L β A α ⎪ ⎬ ⎨ t t t t ⎥ ⎪⎩ t ⎢⎣ ∂h ⎪ ∂h ⎦ ⎭⎪ ⎪ ⎪ ⎪ α ⎪ At − h ⎡ −qAt + α BhLt β ( hAt ) ⎤ ( 2hzLt ) ⎪ ⎣ ⎦ ⎩ ⎭ ∂L&t would be equal to the left-hand side of (A2). ∂h Note that the derivatives of At with respect to h are not equal in both (A1) and (A2) in general. However, at the threshold level of human capital, both derivatives would be the same. In addition, the extent of vertical shift would be the same at the threshold level of human capital, thus this point would correspond to the situation where both A&t and L&t would be zero. Solving the equation formed by (A1) and (A2) at the threshold level of human capital (i.e. eliminating the derivatives of At with respect to h) together with (15) and (16) would yield the solutions for the threshold h, the level of technology implemented at the threshold and the maximum level of employment (minimum level of unemployment) attainable within the economy. 55 1.7.2 Mathematical Intuition of Proposition 2 The outcomes associated with result 1 can be obtained by re-examining the equations in section 1.7.1. First, substitute the left-hand side of (A2) into (A1) and rewrite both (A1) and (A2) such that the terms associated with the derivative of At with respect to h are brought together. Assume that the final form is as follows: From (A1), i.e., locus of A&t = 0 : Ω1 ∂At = Ω2 ∂h (B1) From (A2), i.e., locus of L&t = 0 : Ω3 ∂At = Ω4 ∂h (B2) Thus, for values of h beyond the threshold level, Ω2Ω3 – Ω1Ω4 > 0, with Ω2Ω3 – Ω1Ω4 < 0 being the outcome for values of h below the threshold level. The former corresponds to the case where the locus of A&t = 0 shifts by a larger extent than that of L&t = 0 , with the opposite occurring for the latter case. The case where Ω2Ω3 – Ω1Ω4 = 0 will correspond to the situation where the derivatives of At with respect to h are eliminated as in Appendix A, that is, both graphs shift by the same extent. The following table presents a numerical simulation of the baseline case. 56 Table 1.15: Simulation results for baseline case on the shift of demarcation loci h 0.3000 0.3170 0.3500 0.4000 0.5000 0.6000 0.6100 0.6175 0.6200 0.6225 0.6300 0.7000 0.8000 0.9000 0.9500 (Ω2/Ω1) -0.597485 0.464564 0.682390 0.837116 1.070960 1.268620 1.286660 1.299970 1.304400 1.318010 1.321740 1.433310 1.557800 1.632670 1.648630 (Ω4/Ω3) 0.686148 0.725035 0.799214 0.907800 1.107400 1.275520 1.290180 1.300880 1.304370 1.307880 1.318160 1.400880 1.471380 1.476350 1.452180 (Ω2/Ω1)- (Ω4/Ω3) -1.28363 -0.26047 -0.11682 -0.07068 -0.03644 -0.00690 -0.00352 -0.00091 3E-05 0.01013 0.00358 0.03243 0.08642 0.15632 0.19645 Remarks 0 , and δ ∈ ( 0,1) . The cost decreases with an increase in the economy’s human capital HN, H N ∈ ( 0,1) , and increases exponentially with an increase in the quality required from the supplier. The cost is considered to be decreasing in HN because human capital improves the reliability of the manual component being produced. Though better-trained workers are assumed to be more efficient in supplying the manual good, but such efficiency diminishes with further increases in human capital through the parameter δ , which would reflect the similar characteristic as encountered by the integrated firm in producing the manual component. The per-unit cost of quality is assumed to increase exponentially to indicate that higher quality will require greater customization and hence increased costs, which are passed down to the firm. Here, ρ can be seen as an indexing parameter that represents the base cost of outsourcing. A lower ρ would also represent cost savings from the supplier being passed down to the user of the manual component. Under the domestic outsourcing scenario, one unit of the final good of quality level VNO can be produced based on the following production function: VNO = λ (VM ) 1− β ( H N LNO ) β (1) where β and 1 − β denote respectively the production shares attributed to the manual and organizational components. Note that β ∈ ( 0,1) . λ is an indexation parameter for overall production, with λ > 0 . LNO denotes the number of workers employed for each unit of service good produced under the case of outsourcing the manual component. In this case, the manager is assumed to be able to devote all his time into the production of 69 the organizational component and that there is perfect coordination between the firm and the supplier. Workers employed by the firm enter into the production of the organizational component of the good only, and thus it can be said that there exists diminishing marginal quality of per-unit employment. Under integrated production, the manager has one unit of time that is equally divided between supervising the production of the two components.16 One unit of the final good of quality level VN can be produced based on the following production function: 1− β ⎛ H ηL ⎞ VNI = λ ⎜ N NI ⎟ ⎝ 2 ⎠ ⎛ H N LNI ⎞ ⎜ 2 ⎟ ⎝ ⎠ β (1’) where LNI denotes the total number of workers required in the integrated firm to produce one unit of the final service good of quality VN. η is a parameter that indicates the effectiveness of the human capital component, with η ∈ ( 0,1) .17 Given that the manual component does not involve a high level of skill utilization, thus further increases in the level of human capital will only have a diminishing positive impact on the quality of the manual component. From the above forms of production function for quality, it is possible that the quality of the manual component under the fragmented form of production would be 16 We have assumed the time allocation to be exogenous and equally divided for simplicity, to concentrate on the firm’s decision on the mode of production to undertake as human capital increases. The time allocation is likely to be closely related to the productivity of human capital in each of the components. 17 Here, η does not take the value of 1 as this would then result in no differentiation of the human capital element in producing the manual and organizational component. 70 lower than that under the integrated mode. However, overall quality of its service or infrastructural good can be higher under the fragmented mode of production as the firm concentrates on raising the quality of the organizational component. While outsourcing the manual component allows the firm to pursue a differentiated cost strategy leading to cost reduction, it also provides a potential avenue for the firm to improve the overall quality of its infrastructural or service good. Firms face a wage cost that is the outcome of negotiations between the firm and an agency that oversees the setting of wages. Employment can thus be considered to be demand-determined. 18 The firm thus faces a per worker wage rate of wH N ε , where ε > 0 determines the extent of change in wages per unit change in human capital. w can be considered as the base wage before adjusting for the human capital level of the worker. The firm faces two different profit functions, depending on the choice of production favoured by the firm. The profit functions can be written as follows, with π NO and π NI denoting the profit of the firm under outsourcing and integration respectively: Outsourcing : π NO = PN QNO − wH N ε QNO LNO − No outsourcing : π NI = PNI QNI − wH N ε QNI LNI ρ HN δ eVM QNO 18 Such an assumption can be taken where the government plays a major role in setting general guidelines on the determination of wages. 71 where QNk, where k={O, I}, is the quantity of the service good sold by the Northern firm. Note that with the above definition of the production function, the total number of workers employed by the firm is denoted by QNOLNO or QNILNI, which differs from the conventional setup since in this case the output is determined by demand from consumers. The above can be re-expressed as follows for ease of interpretation: ⎡ Outsourcing : π NO = QNO ⎢ PNO − wH N ε LNO − No outsourcing : π NI = QNI ⎡⎣ PNI − wH N ε LNI ⎤⎦ ⎣ ρ HN δ ⎤ eVM ⎥ ⎦ (2) (2’) where the term in square brackets denotes the profit made for each unit of the service good of quality VNk sold, or in short, the per-unit profit.19 2.2.2 Preferences We make a slight modification to the standard model of product quality differentiation by Mussa and Rosen (1978), Shaked and Sutton (1982), Tirole (1988), Motta (1993) and others. In this context, though each firm is a monopolist within its own economy, the nature of the good is such that they compete within a global context since domestic demand is insignificant. The utility of a consumer i when he consumes product j is denoted by the following: 19 In the above model, whilst the direct cost of the organizational component increases as human capital increases via the wage bill, this cost can decrease indirectly via reduction in per-unit employment. This is because as human capital increases, each worker is now more capable of producing a higher quality of the organizational component, and thus fewer workers will be needed to produce a given level of this component. 72 U ij = θi log (V jk ) − χ Pjk (3) In the above, j={NI, NO, S} and θi denotes consumer i’s taste parameter or willingness to pay for quality, θ ∈ ⎡⎣θ , θ ⎤⎦ . A higher value of θ indicates a greater willingness to pay for quality. χ is a common parameter indicating the consumer’s responsiveness to price changes. We consider the natural logarithmic formulation here based on the assumption of diminishing utility of quality. All consumers here are assumed to have either zero or unitary demand for the service good. The above utility can be seen as the surplus that consumer i derives from consuming the service good. 2.3 Equilibrium and Changes in Human Capital Level The equilibrium is attained based on a sequential process akin to a three-stage game, starting with the determination of employment per unit of service good produced within the Northern firm and, if the firm outsource the manual component, the quality required from the supplier. This is followed by the choice of price and finally the overall quantity demanded of the service good from the consumers. We segregate the firm optimization process into two stages for ease of analysis as this will not change the solution. We make use of backward induction to obtain the equilibrium. The solutions obtained will allow us subsequently to determine the quality of the final service good provided, total employment and profits made by the Northern firm. 73 2.3.1 Analytical Solution Based on the above consumer preferences, there exists the marginal consumer with taste θ = θ * who is indifferent between buying the service good from the North or South such that θ * log (VNk ) − χ PNk = θ * log (VS ) − χ PS , which yields the taste parameter of the marginal consumer as: θ* = χ ( PNk − PS ) (4) log (VNk ) − log (VS ) Therefore, all consumers with taste parameter in excess of θ * will buy the service good from the North. Hence, the quantity demanded from the Northern firm will be: QNk = θ − θ * = θ − χ ( PNk − PS ) (5) log (VNk ) − log (VS ) At the second stage, the Northern firm caries out the optimization with respect to price, taking into account the quantity demanded of its service good. We first consider the case where the firm carries out outsourcing (hence k=O subsequently), noting that similar results can be obtained for the other case by omitting the term corresponding to the cost of outsourcing. Substituting the quantity demanded from (5) into the profit function (2) and maximizing with respect to PNO yields: PNO = 1 2χ ⎡ ⎛ ρ VM ε e ⎢θ ( log (VNO ) − log (VS ) ) + χ ⎜ PS + wLNO H N + δ H N ⎝ ⎣ ⎞⎤ ⎟⎥ ⎠⎦ (6) 74 At this juncture, the solutions of PNO and QNO are functions of LNO and VM (function of LNI only, where LNI replaces LNO, if we consider the case under no outsourcing). On solving, the solution of QNO is as follows: QNO ⎡ ⎛ ⎞⎤ ρ χ ⎜ wLNO H N ε + δ eVM − PS ⎟ ⎥ ⎢ HN 1 ⎠⎥ = ⎢θ − ⎝ ⎥ 2⎢ log (VNO ) − log (VS ) ⎢ ⎥ ⎢⎣ ⎥⎦ (7) The price charged by the Northern firm in equation (6) is positively related to the net difference in utility derived from consuming both goods, the responsiveness to price changes, price charged by the Southern firm, employment, the economy’s human capital level, cost of purchasing and quality of the manual component. The opposite holds for all items in terms of its relationship with quantity demanded except for the net difference in utility derived from consuming both goods and price charged by the Southern firm. For (7) to hold, the following condition must be fulfilled: 0 < wLNO H N ε + ρ HN η eVM − PS < θ ( log (VNO ) − log (VS ) ) χ The left-hand inequality indicates that the total per unit cost incurred by the Northern firm should be less than the price charged by the Southern firm. This is to ensure that the demand does not exceed θ . The right-hand inequality indicates that quantity demanded cannot be negative. 75 At the first stage, the Northern firm chooses the number of workers to hire per unit of service good produced as well as the quality required from the supplier. Substituting the above solutions for PNO and QNO and the per-unit production function for quality represented by equation (1’), the optimization problem yields two first order conditions that implicitly solve for the optimal levels of LNO and VM as follows: ⎡ 1 ⎛ βθ ⎤ ⎞ ⎡ ρ VM ⎤ + χ wH N ε ⎟ − wH N ε ⎥ QNO + ⎢ PNO − wLNO H N ε − e ⎥ ⎢ ⎜ δ 2 L H χ NO N ⎝ ⎠ ⎣ ⎦ ⎣ ⎦ ⎡ χβ ⎢ ⎢ LNO ⎢ ⎢ ⎣⎢ ⎤ ⎛ ⎞ ρ VM ε e − PS ⎟ − χ wH N ε ( log (VNO ) − log (VS ) ) ⎥ ⎜ wH N LNO + δ HN ⎝ ⎠ ⎥=0 2 ⎥ ( log (VNO ) − log (VS ) ) ⎥ ⎥⎦ (8) ⎡ 1 ⎛ (1 − β ) θ ⎡ χρ VM ⎞ ρ VM ⎤ ρ VM ⎤ e ⎟− e ⎥ QNO + ⎢ PNO − wLNO H N ε − e ⎥ + ⎢ ⎜ δ δ HN H Nδ ⎥⎦ ⎣ ⎦ ⎠ HN ⎣⎢ 2 χ ⎝ VM ⎡ (1 − β ) ⎛ ⎤ ⎞ ρ VM ρ eVM ε wH L e P χ χ log (VNO ) − log (VS ) ) ⎥ + − − ⎢ ⎜ N NO S ⎟ δ δ ( VM ⎝ HN HN ⎠ ⎢ ⎥=0 2 ⎢ ⎥ ( log (VNO ) − log (VS ) ) ⎢ ⎥ ⎣⎢ ⎦⎥ (9) The above can be expressed as the following: 76 ⎡ 1 ⎛ βθ ⎞⎤ ⎡ ρ VM ⎤ + χ wH N ε ⎟ ⎥ QNO + ⎢ PNO − wLNO H N ε − e ⎥× ⎢ ⎜ H Nδ ⎠⎦ ⎣ ⎦ ⎣ 2 χ ⎝ LNO ⎡ χβ ⎛ ⎞⎤ ρ VM ε e − PS ⎟ ⎥ ⎢ ⎜ wH N LNO + δ HN ⎠ ⎥ = wH ε Q + ⎢ LNO ⎝ N NO 2 ⎢ ⎥ log (VNO ) − log (VS ) ) ( ⎢ ⎥ ⎢⎣ ⎥⎦ ⎤ ⎡ χ wH N ε ρ VM ⎤ ⎡ ε e ⎢ ⎥ ⎢ PNO − wLNO H N − ⎥ H Nδ ⎣ ⎦ ⎣⎢ ( log (VNO ) − log (VS ) ) ⎦⎥ (8a) ⎡ 1 ⎛ (1 − β ) θ ⎡ χρ VM ⎞ ⎤ ρ VM ⎤ ε + e Q + P − wL H − e ⎥× ⎢ ⎜ ⎥ ⎟ NO NO NO N ⎢ H Nδ H Nδ ⎣ ⎦ ⎠ ⎥⎦ ⎣⎢ 2 χ ⎝ VM ⎡ (1 − β ) ⎛ ⎞⎤ ρ VM ε e − PS ⎟ ⎥ ⎢χ ⎜ wH N LNO + δ VM ⎝ HN ⎠ ⎥ = ρ eVM Q + ⎢ NO 2 ⎢ ⎥ H Nδ log (VNO ) − log (VS ) ) ( ⎢ ⎥ ⎣⎢ ⎦⎥ ⎤ ⎡ ρ VM ⎤ ⎡ χρ eVM ε − − P wL H e ⎢ ⎥ ⎢ NO ⎥ NO N δ δ HN ⎣ ⎦ ⎢⎣ H N ( log (VNO ) − log (VS ) ) ⎥⎦ (9a) The above first-order conditions (8a) and (9a), obtained from (8) and (9) respectively, can be easily interpreted as follows. For (8a), the left-hand side terms denote the overall benefit of having an additional worker, which comprises respectively of the overall marginal revenue product of having an additional worker and the additional positive contribution to profit that can be obtained from the additional demand that can be generated as a result of employing the additional worker (recall that the employment of an additional worker raises the quality of the service good, which can affect quantity demanded). The right-hand side terms denote the overall marginal cost of having the 77 additional worker. These terms respectively denote the total additional remuneration required in employing an additional worker for every unit of service good produced and the negative contribution to profit arising from the additional demand that has to be fulfilled as a result from employing the additional worker. In a similar fashion, the left-hand side terms in (9a) denote the overall marginal benefit of a unitary increase in the quality of the manual component from the supplier. These comprise respectively of the overall marginal revenue product of a unitary increase in the quality of the manual component from the supplier and the additional positive contribution to profit that can be obtained from that unitary increase. The right-hand side of (9a) would denote the overall marginal cost of a unitary increase in the quality of the manual component from the supplier. These comprise respectively of the total additional cost of the unitary increase in the quality of the manual component from the supplier and the negative contribution to profit arising from the additional demand that has to be fulfilled due to that unitary increase. We also list the corresponding results for the price and quality of the service good and the first-order condition for per-unit employment for the case where the firm does not outsource the manual component: PNI = 1 ⎡θ ( log (VNI ) − log (VS ) ) + χ ( PS + wLNI H N ε ) ⎤ ⎦ 2χ ⎣ χ ( wLNI H N ε − PS ) ⎤ 1⎡ ⎥ QNI = ⎢θ − 2⎢ log (VNI ) − log (VS ) ⎥ ⎣ ⎦ (6’) (7’) 78 ⎤ ⎞ 1⎡ 1 ⎛ θ 1 + χ wH N ε ⎟ − wH N ε ⎥ QN + ⎡⎣ PNI − wLNI H N ε ⎤⎦ ⎢ ⎜ 2 ⎣ 2 χ ⎝ LNI 2 ⎠ ⎦ ⎡ χ ⎤ ε ε ⎢ L ( wH N LNI − PS ) − χ wH N ( log (VNI ) − log (VS ) ) ⎥ ⎢ NI ⎥=0 2 ⎢ ⎥ log log − V V ( S )) ( ( NI ) ⎢⎣ ⎥⎦ (8’) Given the non-linear nature of the above solutions, it is not possible to obtain analytical solutions for LNO or LNI and VM as well as for PNk, QNk, VNk, and profits. In addition, we may have multiple equilibria for LNO or LNI and VM. Nevertheless, a unique solution for LNk and VM such that profits are globally maximized will emerge. We will thus proceed to use numerical methods for further analysis. 2.3.2 Numerical Example We will be using a numerical example here to study the solutions obtained in this model. We will not attempt to calibrate the base model as many of the above parameters do not have real-world counterparts, but will instead choose sensible parameter values that would enable us to gain some insights and policy implications arising from changes in human capital of the Northern economy as well as competitiveness of the Southern economy. Table 2.1 shows the parameter values used in the base case, with HN=0.5 to demonstrate the nature of the solution. We have allowed the production share attributed to the organizational component to be larger, indicating the greater role of this component towards the per-unit overall quality of the service good. For simplicity, we impose the condition that θ − θ = 1 , with θ = 1 . 79 Table 2.1: Parameter values used for initial numerical analysis Production share of organizational component, β Human capital of Northern economy, HN Effectiveness of human capital in manual component, η Indexing parameter for quality production, λ Indexing parameter for wages, w Wage behaviour parameter, ε Base cost of outsourcing, ρ Outsourcing cost parameter associated with human capital, δ Per-unit price charged by Southern firm, PS Quality of service good of Southern firm, VS Consumer taste for quality, θi Consumer responsiveness to price, χ 0.67 0.5 0.8 1.5 0.24 0.67 0.075 0.75 0.3 0.5 uniformally distributed between 0 to 1 1 Multiple roots can be found in the case where no outsourcing is undertaken whereas multiple equilibria exist under the case of outsourcing of the manual component. Under the latter case, we find infinitely many solutions where the graphs overlap each other as well as a couple of points of intersection between the two graphs. All solutions that are classified under the former observation are not optimal to the firm as they earn no profits and thus optimal output level is zero. This would directly suggest that the graph depicting the overlapping portions to correspond to either a plot of QN=0 or per-unit profit being zero in both (8) and (9), which can be attained by the combination of LNI and VM depicted by the overlapping portions of the graph. Unique solutions can be found for each of the intersection points. However, one of the points, where the per unit of service good employment and required quality of the outsourced manual component are low, would require the quality of the Northern firm’s service good to be fairly similar in quality to that of the Southern firm’s. Under such a 80 product differentiation model, it is actually not optimal for the firms to produce goods of similar quality as these goods then become close substitutes, which would suggest a higher degree of competition between the two firms. Profit in this case is also found to be not a global maximum. As for the other intersection point, where per unit of service good employment and required quality of the outsourced manual component are higher, the Northern firm’s service good is now vastly superior to that of the Southern firm’s in terms of quality, which suggests a high degree of product differentiation, and we find that profits are higher under this equilibrium than in the previous one. The above explanation applies when the firm takes on an integrated form of production. We find three roots, out of which one root has properties similar to the case of overlapping graphs, whilst out of the other two roots, the root with higher employment per service good yields higher quality and profit. Table 2.2 provides a numerical summary of the discussion of the solutions for a particular value of HN. Table 2.2: Comparison of roots obtained with HN = 0.5 Integrated production Local max Global max LNI VNI QNI PNI πNI 1.5895 4.1977 0.6242 1.6486 0.7697 0.3918 0.4011 1.0756 0.1315 0.1831 Employment (QNI LNI) 1.2234 1.6446 Fragmented production Local max Global max LNO VM VNO QMO PNO πNO 0.7808 2.9493 0.3159 0.7630 0.5457 1.7758 0.8303 0.3590 0.3648 1.1624 0.0602 0.1633 Employment (QNO LNO) 0.6483 1.0588 81 2.3.3 Changes in the Human Capital Level of the Northern Economy In this section, we will be analysing how the form of production taken on by the firm, price and quality of the Northern good, the Northern firm’s profits and the quantity demanded will be affected by changes in the economy’s human capital level. Consider the progression of the human capital level within the Northern economy HN. We allow HN to vary between 0.15 and 0.9 and compare between the profits of the firm under both the cases of integrated production and outsourcing of the manual component, with the results shown in Table 2.3. As the human capital level of the Northern economy increases, the benefits come in the form of improved quality of the service good and, if outsourcing is undertaken, reduced prices for the outsourced manual component. However, higher levels of human capital translate into higher wages per worker. For the case of integrated production, employment per unit of service good produced falls as human capital rises. This is likely to be due to the fact that for a given level of per-unit employment, the marginal cost of using the same number of workers to produce one unit of the good exceeds the marginal benefit from the increase in human capital, thus the reduction. In the case where outsourcing is carried out, in terms of the graphs surrounding the global maximum, the graph of the first-order condition corresponding to (8) shifts to the left whilst that of (9) shifts upwards and becomes steeper, leading to a decrease in employment per unit of service good and an increase in the quality level of the outsourced manual component required from the supplier. A similar explanation holds in this case in terms of the effect 82 Table 2.3: Numerical results under both forms of production for different values of HN Integrated production HN 0.15 0.20 0.30 0.40 0.50 0.60 0.61 0.62 0.63 0.64 0.65 0.70 0.80 0.90 LNI 10.4471 8.38926 6.18747 5.00070 4.24594 3.71807 3.67373 3.63065 3.58877 3.54805 3.50842 3.32529 3.02002 2.77493 VNI 1.33375 1.40092 1.50853 1.59471 1.66753 1.73109 1.73704 1.74292 1.74874 1.75449 1.76019 1.78779 1.83917 1.88628 QNI 0.29216 0.31142 0.33451 0.34845 0.35805 0.36521 0.36583 0.36644 0.36703 0.36761 0.36817 0.37082 0.37538 0.37919 PNI 0.99449 1.00943 1.03488 1.05570 1.07322 1.08834 1.08975 1.09114 1.09251 1.09386 1.09520 1.10165 1.11354 1.12428 πNI 0.08375 0.09992 0.12357 0.14082 0.15442 0.16564 0.16667 0.16767 0.16866 0.16964 0.17060 0.17520 0.18353 0.19091 QNI LNI 3.05224 2.61258 2.06980 1.74249 1.52028 1.35788 1.34396 1.33040 1.31718 1.30429 1.29170 1.23309 1.13366 1.05223 PNI/ VNI 0.74563 0.72055 0.68602 0.66200 0.64360 0.62870 0.62736 0.62604 0.62474 0.62346 0.62221 0.61621 0.60546 0.59603 Fragmented production HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 8.70591 0.54796 1.46649 0.11520 1.25206 0.01428 1.00294 0.85378 0.20 6.60848 0.59594 1.52024 0.18638 1.20476 0.03863 1.23166 0.79248 0.30 4.55785 0.67471 1.62075 0.26468 1.16477 0.08239 1.20637 0.71866 0.40 3.54392 0.73926 1.71154 0.30738 1.15229 0.11627 1.08934 0.67325 0.50 2.93447 0.79455 1.79390 0.33450 1.15020 0.14295 0.98159 0.64117 0.60 2.52497 0.84316 1.86924 0.35337 1.15271 0.16466 0.89224 0.61667 0.61 2.49120 0.84772 1.87644 0.35494 1.15310 0.16662 0.88424 0.61452 0.62 2.45849 0.85223 1.88358 0.35648 1.15352 0.16854 0.87639 0.61241 0.63 2.42678 0.85669 1.89066 0.35796 1.15395 0.17043 0.86870 0.61034 0.64 2.39602 0.86111 1.89768 0.35941 1.15441 0.17229 0.86116 0.60832 0.65 2.36617 0.86548 1.90466 0.36082 1.15487 0.17412 0.85376 0.60634 0.70 2.22926 0.88667 1.93873 0.36730 1.15742 0.18283 0.81882 0.59700 0.80 2.00470 0.92612 2.00327 0.37807 1.16320 0.19838 0.75791 0.58065 0.90 1.82772 0.96227 2.06360 0.38665 1.16948 0.21193 0.70669 0.56672 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) on per-unit employment whilst for a given level of quality of the manual component from the supplier, the effect of a lower marginal cost of outsourcing is likely to dominate in the shifting of the graph associated with (9). The graph below compares the cases between HN=0.7 and HN=0.72, with dashed lines denoting the latter case. 83 In both cases, we see a fall in per unit employment as the presence of bettertrained workers would reduce the labour requirement across all quality levels of the service good produced, without compromising on the quality. Quantity demanded and quality of the service good and the quality of the manual component from the supplier under the fragmented form of production all increase. Overall employment increases slightly for a not-too-low level of human capital under the fragmented form of production and decreases for subsequent increases in the level of human capital, whereas the latter holds throughout under the integrated form of production. The fall in overall employment can be explained by the fact that despite the improvement in quality, the response on quantity demanded is insufficient to overcome the fall in per-unit worker requirement. However, unlike the integrated form of production where the price of the Figure 2.1: Graphs of the first-order conditions around the intersection point for HN=0.7 and HN=0.72 (dashed lines denote latter) VM Shift of graph associated with equation (8) 0.91 LN O 2.15 0.89 2.2 2.25 2.3 Shift of graph associated with equation (9) 0.88 0.87 84 good increases as human capital increases, the price under the fragmented form of production somewhat falls throughout until it increases when human capital exceeds a particular level. The above findings indicate that the Northern firm’s profits are higher when the integrated form of production of the service good is undertaken at low levels of human capital. However, profits under the fragmented form of production increase fairly quickly and will eventually catch up and subsequently overtake that of the integrated form of production. This suggests the existence of a threshold level of human capital HN* whereby below the threshold level, the Northern firm undertakes the integrated form of production. For levels of human capital beyond the threshold level, the Northern firm outsources the manual component and concentrates on the organizational component. This threshold level will enable us to obtain the threshold employment per unit of service good under integrated and under fragmented production and the required quality of the manual component. Our numerical solution yields a threshold level of HN* that falls between 0.61 and 0.62. The following proposition summarizes the above observation. Proposition 3: There exists a threshold level of human capital in the Northern economy, HN*, such that the profits under either form of production would be equal, which yields the threshold level of employment per unit of service good under integrated production, LNI*, the threshold level of employment per unit of service good under fragmented production, LNO*, and the required quality of the manual component from the supplier, VM*. 85 Proof. At HN*, we can equate the profit equations (2) and (2’) to obtain the following: ε QNO ⎡⎢ PNO − w ( H N * ) LNO − ρ eVM ⎣ (H ) * η N ⎤=Q NI ⎥⎦ ⎡ P − w ( H * )ε L ⎤ N NI ⎥ ⎢⎣ NI ⎦ (10) Equation (10), together with the first order conditions (8), (8’) and (9), where we replace HN with HN*, will provide us with a system of 4 equations with 4 unknowns, which implicitly allows us to solve for the solution set (HN*, LNI*, LNO*, VM*). ■ A likely reason to explain the existence of the threshold level of human capital is as follows. First, note that at low levels of human capital, profit will be lower if they make use of the outsourcing mode of production to produce the same product quality as in the fragmented mode, suggesting that it is not cost-effective to outsource the manual component. Moreover, with outsourcing costs being relatively higher at low levels of human capital relative to the use of workers, this mode of production does not enable the Northern firm to reduce the per unit employment sufficiently so as to allow the quality of the good to be of a sufficiently high level. This would subsequently lead to the firm incurring high wage and outsourcing costs and translates into high per-unit cost of production of a given quality and a high price-to-quality ratio, which results in relatively higher prices. Per unit profits are also lower in this case. To summarize, the strengths of the push factor, in the form of higher wages, and the pull factor, in the form of low outsourcing cost, are less prominent, thus the continued use of the integrated mode of production at low levels of human capital. From the preference side, the high price difference to difference in utility of quality ratio if the fragmented mode of production was used would thus raise the taste index required for indifference to occur, which 86 subsequently reduces overall demand from the Northern firm. On the whole, though the number of workers required per unit produced is higher, the cost of hiring more workers does not exceed the cost to outsource the manual component, which thus translates into a relatively lower price differential. Beyond the threshold level of human capital, the fragmented form of production is preferred by the firm. In this situation, the cost of outsourcing is now sufficiently relatively lower compared to pre-threshold levels of human capital. Whilst the increase in human capital allows the firm to reduce the per-unit labour requirement, the firm can also now reduce the number of workers they employ sufficiently and yet be able to produce a sufficiently high level of quality of the product. Moreover, the increase in wages arising from the increase in human capital results in such cost being relatively higher compared to the cost of outsourcing the manual component. Thus, it is relatively more cost-effective to undertake the fragmented form of production, which translates into the firm being able to price the service good relatively lower in a manner such that it reflects the benefits of a falling price-to-quality ratio. In addition, since human capital is less productive in the manual component and that the production share attributed to this component is low, there would be a higher divergence between the productivities of each of the two components, which would render the use of the same compensation strategy relatively more costly. As a result, the firm thus pursues a differentiated cost strategy here. In summary, the strengths of the push factor of relatively higher wage cost and pull factor of relatively lower cost of outsourcing are sufficiently strong such that the change in mode of production occurs. From the preference side, a lower price difference to difference of utility of quality ratio due to the relatively stronger effect arising from 87 greater product differentiation helps to reduce the taste index required for indifference to occur, which subsequently raises the overall demand from the Northern firm. Thus, regardless of the relevant form of production the firm will undertake based on the human capital level of the economy, we can conclude that quality of the service good, profits and quality of the manual component from the supplier all increase throughout whilst the per-unit employment and overall employment falls, starting from a not-too-low level of human capital. It is also useful to note that upon the firm changing to the fragmented form of production, there will be a sudden fall in quantity demanded and employment but an upward jump in the price of the service good as well as the quality of the service good sold. Intuitively, this suggests that it is more profitable for the firm to let go of some fringe customers in favour of higher-end customers who are willing to pay a higher price for a service good of higher quality. It turns out that product differentiation can be enhanced in our model. The sudden fall in employment by the Northern firm would reflect the reduced dependence of workers upon the firm outsourcing the manual component to the supplier, with the remaining workers in the firm now focussing on the organizational component. 2.4 Other Comparative Statics In this section, we consider the effects of external factors, such as a change in price charged by and quality of the Southern firm’s service good, and internal factors such as cost of outsourcing, wage cost and general productivity, on the various decision variables of the Northern firm as well as quantity demanded and overall employment. 88 The subsequent discussion centers only on the effect arising from a specified particular direction of change. The opposite outcomes apply for changes in the other direction. 2.4.1 Price Charged by the Southern Firm We now consider the effects of a change in the unit price of the service good from the South. The quality of the good from the Southern firm will be kept unchanged here. This analysis can be seen as an indication on how a change in the competitiveness of the Southern economy can affect the Northern economy. We consider the case of a 20% fall in the price charged by the Southern firm, which can be seen as the Northern firm’s service good becoming less competitive as it is now relatively more costly. The effects differ somewhat from the base case in 2.3.3, depending on the form of production undertaken. The numerical results are shown in Table 2.4. The manner in which the variables change as human capital increases is similar to that under the case in the preceding section. We next compare across the findings in this and the preceding section to evaluate the changes that have taken place for the different variables. Under integrated production, the quality and price of the service good as well as per unit employment has increased. However, the quantity demanded of the Northern good falls, with this fall sufficient to generate a fall in overall employment within the firm across all levels of human capital. Profits are also lower for all levels of human 89 Table 2.4: Numerical results under both forms of production for different values of HN with a 20% fall in price charged by the Southern firm Integrated production HN 0.15 0.20 0.30 0.40 0.50 0.59 0.60 0.61 0.62 0.63 0.64 0.70 0.80 0.90 LNI 10.9884 8.82055 6.49878 5.24697 4.45101 3.94266 3.89454 3.84781 3.80241 3.75828 3.71536 3.48067 3.15915 2.90113 VNI 1.40286 1.47294 1.58443 1.67324 1.74807 1.80709 1.81325 1.81935 1.82538 1.83134 1.83723 1.87132 1.92390 1.97207 QNI 0.25548 0.27602 0.30103 0.31636 0.32705 0.33437 0.33508 0.33578 0.33646 0.33713 0.33779 0.34142 0.34661 0.35096 PNI 1.00809 1.02219 1.04617 1.06578 1.08230 1.09525 1.09659 1.09792 1.09923 1.10053 1.10181 1.10919 1.12045 1.13064 πNI 0.06734 0.08231 0.10452 0.12089 0.13388 0.14365 0.14465 0.14563 0.14660 0.14755 0.14849 0.15385 0.16188 0.16902 QNI LNI 2.80736 2.43464 1.95634 1.65994 1.45570 1.31829 1.30499 1.29202 1.27937 1.26704 1.25499 1.18838 1.09498 1.01817 PNI/ VNI 0.71859 0.69398 0.66028 0.63695 0.61914 0.60608 0.60477 0.60347 0.60220 0.60094 0.59971 0.59273 0.58238 0.57333 Fragmented production HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 8.98952 0.55939 1.50851 0.08638 1.24888 0.00824 0.7765 0.82789 0.20 6.84355 0.60908 1.56744 0.15743 1.20271 0.02832 1.07741 0.76731 0.30 4.73526 0.69019 1.67517 0.23606 1.16365 0.06737 1.11779 0.69465 0.40 3.68743 0.75624 1.77079 0.27934 1.15133 0.09867 1.03003 0.65018 0.50 3.05542 0.81255 1.85667 0.30707 1.14907 0.12371 0.93824 0.61889 0.59 2.66604 0.85720 1.92722 0.32485 1.15093 0.14238 0.86605 0.59720 0.60 2.62976 0.86187 1.93471 0.32653 1.15128 0.14427 0.85869 0.59506 0.61 2.59462 0.86649 1.94215 0.32816 1.15164 0.14613 0.85146 0.59297 0.62 2.56057 0.87106 1.94952 0.32975 1.15202 0.14796 0.84436 0.59093 0.63 2.52757 0.87558 1.95682 0.33130 1.15242 0.14976 0.83738 0.58892 0.64 2.49555 0.88005 1.96407 0.33280 1.15284 0.15153 0.83052 0.58696 0.70 2.32187 0.90591 2.00636 0.34102 1.15563 0.16159 0.79180 0.57598 0.80 2.08779 0.94576 2.07270 0.35229 1.16105 0.17648 0.73550 0.56016 0.90 1.90317 0.98221 2.13455 0.36133 1.16696 0.18950 0.68768 0.54670 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) capital. Intuitively, the increase in quality of the service good helps the firm to exercise greater product differentiation in order to reduce the competition between the two firms. This can be seen from (4), where an increase in quality of the Northern good lowers the level of point of indifference in terms of taste for quality. Under this form of production, the only way to raise the quality of the service good is to employ more workers per unit of service good produced. Nevertheless, the effect of trying to differentiate their service 90 good is insufficient to overcome the increase in price differential and thus results in a fall in quantity demanded. The effect of the fall in quantity demanded exceeds that of the increase in per-unit employment and thus drives down employment by the Northern firm. In addition, in terms of per-unit profit, the increase in price is insufficient to cover the increased wage bill, which thus results in a fall in per-unit profit. This, together with a fall in quantity demanded, subsequently drives down overall profits of the Northern firm. Under the situation where the firm outsources the manual component, the graphs corresponding to (8) and (9) display a rightward and upward shift respectively at all levels of human capital. Our numerical results here indicate an increase in per unit employment and both the quality of the manual component from the supplier and that of the service good. However, the quantity of the service good sold across all levels of human capital falls, with this fall sufficient in leading to a reduction in overall employment as well. The price of the service good is actually lower than that in the base case across all levels of human capital compared to the base case, though they behave in a similar manner in terms of its changes as human capital changes.20 Given the nature of the production function, it is optimal to raise the inputs attributed to each of the components to raise the overall quality of the service good, which acts to increase the extent of product differentiation for similar reasons as documented above. Despite the increase in quality and fall in price of the Northern firm’s service good, the fall in quantity demanded would suggest that the price differential effect dominates the product differential effect, with this outcome dominating the per-unit increase in employment and thus decreasing overall employment. 20 We have also considered a different set of parameter values and found that it is possible for the price to be higher for some levels of human capital compared to the base case. Nevertheless, the mode of production undertaken by the Northern firm is based on profitability considerations. 91 One interesting point to note at this juncture is that by considering the relevant forms of production applicable, we find that whilst quality increases throughout, the price charged under this case is higher throughout prior to the threshold level of human capital and is minimally lower beyond the threshold level as compared to the base case. We also note that the increase in quality that is larger relative to that of price for the former, thus reducing the price-to-quality ratio. Conventionally, a decrease in the price charged by a competitor should trigger a similar reaction by other competing firms. However, our study suggests in fact that the firm, when facing increased competition, can actually raise the price of its good, depending on the mode of production adopted, while at the same time raising the quality. Supposing that we consider the two changes separately, the increase in the latter can be seen as reducing the competitive pressure faced by the Northern through further differentiation in its product, whilst the former can be considered as a response arising from a fall in competition. Our model of endogenous quality thus enables us to capture such an overall response which would otherwise not be possible under models where the quality cannot be varied in a continuous manner. It is also interesting to note that the threshold level of human capital has dropped slightly compared to the preceding section. Recall that the per-unit employment has increased. This increase in per-unit employment actually reduces the marginal product of an additional worker per unit of the service good produced and thus the integrated form of production can be considered to be less productive due to its greater use of workers. The fall in threshold level of human capital can be explained by the following. The above situation coupled with the form of production function used brings about the 92 situation where the fragmented mode can be seen as being a more productive form of production at a lower level of human capital relative to the integrated mode. An increase in product quality can be spread between the two distinct factors of production under the former compared to the latter, which will be more optimal. Subsequently, this may suggest that the cost of undertaking outsourcing may be seen by the Northern firm as being sufficiently low relative to that of employing workers at a lower level of human capital. Hence, we have a transition from the integrated to the fragmented form of production at a lower threshold level of human capital. Applying the relevant mode of production based on the level of human capital, the variables do change in a similar manner as that in the preceding section, with intuitions that can be applied in the same manner with respect to the transition from integrated to fragmented form of production. 2.4.2 Quality of the Southern Firm’s Service Good We consider the other factor in our model associated with the competitiveness of the Southern firm, a change in the quality of the Southern firm’s service good. In this analysis, we consider a 20% increase in the quality of the service good produced by the Southern firm, which in this framework can be considered as an attempt to reduce the degree of product differentiation and thus an increase in competition between each firm’s good. The numerical results for this case are displayed in Table 2.5. We compare this situation with the base case situation. Under integrated production by the Northern firm, there is an increase in the per-unit employment and the 93 Table 2.5: Numerical results under both forms of production for different values of HN with a 20% increase in the quality of the Southern firm’s service good Integrated production HN 0.15 0.20 0.30 0.40 0.50 0.59 0.60 0.61 0.62 0.63 0.64 0.70 0.80 0.90 LNI 11.2955 9.00272 6.57499 5.28038 4.46324 3.94404 3.89501 3.84741 3.80118 3.75626 3.71260 3.47411 3.14818 2.88733 VNI 1.44206 1.50336 1.60301 1.68390 1.75287 1.80772 1.81347 1.81916 1.82479 1.83035 1.83587 1.86780 1.91722 1.96269 QNI 0.23468 0.26107 0.29284 0.31201 0.32520 0.33413 0.33500 0.33585 0.33668 0.33749 0.33828 0.34266 0.34887 0.35404 PNI 0.97111 0.97873 0.99494 1.00996 1.02344 1.03438 1.03553 1.03667 1.03781 1.03892 1.04003 1.04646 1.05641 1.06555 πNI 0.04829 0.06260 0.08427 0.10046 0.11338 0.12313 0.12413 0.12511 0.12608 0.12703 0.12797 0.13334 0.14139 0.14855 QNI LNI 2.65081 2.35032 1.92539 1.64752 1.45145 1.31783 1.30484 1.29215 1.27978 1.26769 1.25589 1.19046 1.09832 1.02224 PNI/ VNI 0.67342 0.65103 0.62067 0.59978 0.58386 0.57220 0.57102 0.56986 0.56873 0.56761 0.56651 0.56026 0.55101 0.54290 Fragmented production HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 9.47711 0.57854 1.58021 0.03682 1.23272 0.00131 0.34898 0.78010 0.20 7.13399 0.62494 1.62534 0.12168 1.17529 0.01475 0.86803 0.72310 0.30 4.85847 0.70073 1.71273 0.21618 1.12216 0.04902 1.05031 0.65519 0.40 3.74389 0.76280 1.79398 0.26830 1.10140 0.07884 1.00449 0.61394 0.50 3.07952 0.81607 1.86911 0.30161 1.09357 0.10337 0.92881 0.58508 0.59 2.67395 0.85857 1.93205 0.32284 1.09188 0.12188 0.86326 0.56514 0.60 2.63632 0.86303 1.93880 0.32485 1.09188 0.12377 0.85640 0.56317 0.61 2.59991 0.86744 1.94549 0.32679 1.09192 0.12563 0.84964 0.56126 0.62 2.56466 0.87180 1.95214 0.32868 1.09199 0.12745 0.84296 0.55938 0.63 2.53051 0.87612 1.95875 0.33052 1.09208 0.12925 0.83638 0.55754 0.64 2.49740 0.88040 1.96530 0.33231 1.09220 0.13102 0.82990 0.55574 0.70 2.31825 0.90517 2.00373 0.34205 1.09338 0.14108 0.79295 0.54567 0.80 2.07798 0.94347 2.06453 0.35533 1.09664 0.15602 0.73837 0.53118 0.90 1.88948 0.97864 2.12173 0.36592 1.10087 0.16912 0.69141 0.51886 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) quality of the service good. However, the per-unit price, quantity demanded of the service good, overall profits and employment have all decreased. As indicated above, these findings reflect the presence of reduced product differentiation, which also suggests increased competition occurring between the two firms and thus can explain the decrease in the price of the service good. In view of the results obtained and looking at equation (4), the decrease in quantity demanded suggests that the product differentiation effect is 94 now weaker relative to the price difference effect. The increase in quality of the service good is not sufficient relative to that by the Southern firm, which explains the weaker effect. The increase in per-unit employment would correspond to the rise in quality arising from the increased competition. The effect of the decrease in quantity demanded exceeds that of a rise in per-unit employment, leading to the decrease in overall employment. Overall profits decrease due to the twin effects of a decrease in per-unit profit and quantity demanded. The graphs corresponding to (8) and (9) display a rightward and upward shift respectively under the case where the firm makes use of the outsourcing mode of production at all levels of human capital. Our numerical results indicate that the direction of change of the variables is similar to that under the case where the integrated form of production is undertaken. In addition, the Northern firm now purchases a higher quality of the manual component from the supplier. Intuitively, given the nature of the production function, a rise in the quality of the Southern firm’s service good (which does not affect the cost of outsourcing) leading to a increase in the Northern firm’s quality of the service good is best achieved by raising the quality of both components that constitute the service good. Combining the results of the two forms of production, the firm will now choose to outsource the manual component at a lower level of human capital compared to the benchmark case. This is because as the labour requirement per unit of service good produced is now higher, the marginal product of an additional worker would now be lower. Such an effect has a greater influence under the integrated mode of production 95 compared to the outsourcing mode, hence the choice of the former at lower levels of human capital. This may have also contributed towards the relatively lower cost of outsourcing the manual component compared to the costs of employing better-educated workers at all levels of human capital, thus the decrease in the threshold level of human capital. 2.4.3 Cost of Outsourcing Manual Component We now turn our attention to internal factors influencing the production process of the Northern firm. In this analysis, we consider the impact of a 10% decrease in the base cost of outsourcing the manual component to the supplier on the various variables. The other analysis deals with a 10% fall in δ (which also has the effect of reducing the cost of outsourcing), the parameter representing diminishing overall cost of outsourcing the manual component associated with human capital. It is useful to note that this change will have no impact on the Northern firm if it is undertaking the integrated form of production. The numerical results for this case are shown in Table 2.6. The actual effects and explanations associated with either of the above changes are similar and thus it suffices to account for the above changes together. Comparing the base case with this situation under the fragmented mode of production, the graphs corresponding to (8) and (9) around the intersection display a leftward and upward shift respectively at all levels of human capital. We find a fall in per-unit employment and price of the service good, the latter changing in a similar manner as human capital 96 Table 2.6: Numerical results under both forms of production for different values of HN with a decrease in the cost of outsourcing (10% fall in ρ and 10% fall in δ) Integrated production HN 0.15 0.20 0.30 0.40 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.70 0.80 0.90 LNI 10.4471 8.38926 6.18747 5.00070 4.24594 4.18499 4.12612 4.06921 4.01415 3.96087 3.90926 3.85926 3.81077 3.76373 3.71807 3.32529 3.02002 2.77493 VNI 1.33375 1.40092 1.50853 1.59471 1.66753 1.67426 1.68089 1.68744 1.69391 1.70029 1.70660 1.71283 1.71899 1.72508 1.73109 1.78779 1.83917 1.88628 QNI 0.29216 0.31142 0.33451 0.34845 0.35805 0.35886 0.35964 0.36041 0.36115 0.36187 0.36257 0.36326 0.36392 0.36458 0.36521 0.37082 0.37538 0.37919 PNI 0.99449 1.00943 1.03488 1.05570 1.07322 1.07483 1.07641 1.07798 1.07952 1.08104 1.08254 1.08402 1.08548 1.08692 1.08834 1.10165 1.11354 1.12428 πNI 0.08375 0.09992 0.12357 0.14082 0.15442 0.15563 0.15683 0.15800 0.15914 0.16027 0.16138 0.16248 0.16355 0.16460 0.16564 0.17520 0.18353 0.19091 QNI LNI 3.05224 2.61258 2.06980 1.74249 1.52028 1.50183 1.48393 1.46656 1.44970 1.43331 1.41739 1.40190 1.38683 1.37216 1.35788 1.23309 1.13366 1.05223 PNI/ VNI 0.74563 0.72055 0.68602 0.66200 0.64360 0.64197 0.64038 0.63882 0.63730 0.63580 0.63433 0.63288 0.63146 0.63007 0.62870 0.61621 0.60546 0.59603 QNO LNO 1.19024 1.33436 1.24984 1.11284 0.99617 0.98582 0.97569 0.96578 0.95609 0.94660 0.90213 0.82595 0.76330 0.71091 PNO/ VNO 0.83584 0.77745 0.70683 0.66316 0.63219 0.62955 0.62698 0.62447 0.62202 0.61963 0.60847 0.58938 0.57348 0.55992 Fragmented production (10% fall in base cost of outsourcing, ρ) HN 0.15 0.20 0.30 0.40 0.50 0.51 0.52 0.53 0.54 0.55 0.60 0.70 0.80 0.90 LNO 8.45416 6.43911 4.46237 3.48091 2.88900 2.84231 2.79737 2.75408 2.71234 2.67207 2.49018 2.20154 1.98193 1.80857 VM 0.57530 0.62605 0.70913 0.77695 0.83484 0.84020 0.84549 0.85071 0.85588 0.86097 0.88557 0.93087 0.97186 1.00934 VNO 1.46161 1.51891 1.62477 1.71946 1.80483 1.81292 1.82094 1.82889 1.83676 1.84457 1.88258 1.95406 2.02028 2.08204 QNO 0.14079 0.20723 0.28008 0.31970 0.34482 0.34684 0.34879 0.35067 0.35250 0.35426 0.36227 0.37517 0.38513 0.39308 PNO 1.22166 1.18088 1.14843 1.14028 1.14100 1.14133 1.14169 1.14208 1.14250 1.14295 1.14549 1.15168 1.15859 1.16577 πNI 0.02126 0.04772 0.09245 0.12624 0.15262 0.15495 0.15724 0.15948 0.16167 0.16383 0.17400 0.19185 0.20712 0.22041 97 Fragmented production (10% fall in the diminishing cost of outsourcing associated with human capital, δ) HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 8.37031 0.58520 1.46021 0.14931 1.21171 0.02389 1.24977 0.82982 0.20 6.41551 0.63055 1.51882 0.21013 1.17761 0.04906 1.34811 0.77534 0.30 4.47555 0.70412 1.62412 0.27796 1.15065 0.09102 1.24401 0.70848 0.40 3.50223 0.76367 1.71657 0.31553 1.14428 0.12280 1.10506 0.66661 0.50 2.91155 0.81423 1.79916 0.33970 1.14549 0.14776 0.98906 0.63668 0.55 2.69437 0.83700 1.83744 0.34887 1.14746 0.15841 0.93998 0.62449 0.56 2.65540 0.84138 1.84488 0.35053 1.14792 0.16042 0.93080 0.62222 0.57 2.61774 0.84571 1.85225 0.35214 1.14840 0.16239 0.92182 0.62000 0.58 2.58133 0.84999 1.85956 0.35370 1.14890 0.16433 0.91303 0.61783 0.59 2.54609 0.85422 1.86680 0.35522 1.14942 0.16623 0.90442 0.61571 0.60 2.51198 0.85840 1.87398 0.35669 1.14995 0.16810 0.89600 0.61364 0.70 2.22199 0.89774 1.94254 0.36937 1.15586 0.18516 0.82073 0.59503 0.80 2.00095 0.93329 2.00592 0.37923 1.16241 0.19979 0.75882 0.57949 0.90 1.82623 0.96575 2.06496 0.38715 1.16917 0.21258 0.70703 0.56620 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) increases as in the base case. Increases in the quality of the manual component, quantity demanded, profits and overall employment are observed in this case. The lower cost of purchasing the manual component from the supplier thus actually leads to the firm placing a higher emphasis in the manual component of its service good, since the fall in per-unit employment is tantamount to a fall in the quality of the organizational component. However, we find that the quality of the service good is lower at low levels of human capital, with this quality being higher than the base case beyond some level of human capital. Nevertheless, these observations associated with quality of service good and price occurs at levels of human capital below the threshold level of human capital where the form of production undertaken is changed. The change from integrated to fragmented form of production occurs at a much lower level of threshold level of human capital. This decrease can be solely attributed to an overall lower cost of outsourcing the manual component at every level of human capital relative to the wage cost of employing workers. The intuition for the transition 98 from the integrated to fragmented mode of production as human capital increases would be the same as in section 2.3.3. 2.4.4 Wage Cost We consider a 25% increase in the wage rate per worker before adjustments for the human capital level of the worker paid by the service good firm. Table 2.7 provides the numerical results obtained for this case. Under the integrated form of production, we find that there is a fall in per-unit employment, the quality and price of the service good, quantity demanded, overall profits and overall employment. In this case, the firm is faced with a higher cost of production that cannot be adjusted by use of other factors of production. The fall in the number of workers employed per unit of service good produced due to the higher wage cost would, based on the production function, subsequently lead to a fall in the quality of the service good. A fall in the quality of the service good would thus require a fall in the per unit price in order to ensure that this good is still competitively priced. The wages paid out for every unit produced has actually increased. This, together with a fall in price, lead to a fall in per unit profit and subsequently overall profit as the quantity demanded falls. The fall in quantity demanded is the result of the reduced product differential effect which dominates the fall in price differential, thus raising the level of point of indifference in terms of taste for quality from equation (4). 99 Table 2.7: Numerical results under both forms of production for different values of HN with a 15% increase in the base wage rate Integrated production HN 0.15 0.20 0.30 0.40 0.49 0.50 0.51 0.52 0.53 0.54 0.60 0.70 0.80 0.90 LNI 9.62886 7.68841 5.62882 4.52774 3.88958 3.83147 3.77540 3.72125 3.66893 3.61834 3.34661 2.98706 2.70838 2.48516 VNI 1.22929 1.28388 1.37233 1.44388 1.49904 1.50475 1.51039 1.51596 1.52145 1.52688 1.55814 1.60594 1.64938 1.68931 QNI 0.24974 0.27429 0.30379 0.32158 0.33277 0.33383 0.33485 0.33585 0.33682 0.33776 0.34293 0.35004 0.35581 0.36062 PNI 0.97492 0.98438 1.00293 1.01945 1.03260 1.03398 1.03533 1.03667 1.03800 1.03931 1.04686 1.05841 1.06887 1.07842 πNI 0.05611 0.07095 0.09318 0.10967 0.12158 0.12278 0.12396 0.12511 0.12624 0.12736 0.13367 0.14298 0.15111 0.15833 QNI LNI 2.40472 2.10882 1.70998 1.45604 1.29433 1.27904 1.26420 1.24978 1.23576 1.22214 1.14764 1.04560 0.96368 0.89620 PNI/ VNI 0.79308 0.76672 0.73083 0.70605 0.68884 0.68714 0.68547 0.68384 0.68224 0.68067 0.67186 0.65906 0.64804 0.63838 Fragmented production HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 7.89183 0.56281 1.38588 0.07763 1.24034 0.00614 0.61263 0.89498 0.20 5.96489 0.60997 1.43092 0.15545 1.18801 0.02541 0.92727 0.83024 0.30 4.08779 0.68723 1.51658 0.24159 1.14153 0.06476 0.98757 0.75270 0.40 3.16428 0.75056 1.59505 0.28882 1.12501 0.09677 0.91389 0.70531 0.49 2.65676 0.79975 1.66000 0.31638 1.12032 0.12011 0.84054 0.67489 0.50 2.61158 0.80486 1.66691 0.31889 1.12014 0.12245 0.83281 0.67198 0.51 2.56816 0.80990 1.67377 0.32131 1.12001 0.12474 0.82518 0.66915 0.52 2.52639 0.81488 1.68057 0.32365 1.11992 0.12699 0.81767 0.66639 0.53 2.48617 0.81980 1.68732 0.32591 1.11988 0.12919 0.81028 0.66370 0.54 2.44742 0.82466 1.69401 0.32810 1.11988 0.13136 0.80300 0.66108 0.60 2.24157 0.85266 1.73309 0.33983 1.12062 0.14356 0.76176 0.64660 0.70 1.97521 0.89551 1.79441 0.35532 1.12379 0.16133 0.70183 0.62627 0.80 1.77346 0.93441 1.85160 0.36727 1.12836 0.17660 0.65135 0.60940 0.90 1.61483 0.97009 1.90520 0.37681 1.13367 0.18994 0.60848 0.59504 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) The graphs around the intersection corresponding to equations (8) and (9) display a leftward and upward shift respectively under the fragmented form of production as compared to the base case at all levels of human capital. The effect of the increase in wage rate on the various variables is similar to that under the integrated form of production. In addition, the quality of the manual component purchased from the supplier by the firm is now higher. The increase in wage rate now makes the cost of 100 outsourcing the manual component relatively cheaper. Under this form of production and in view of the relatively lower outsourcing cost, the firm will, whilst reducing per unit employment, and thus the quality of the organizational component, replaces this with an increase in the quality of the manual component. This accounts for the relatively smaller drop in quality of the service good under fragmented production compared to the situation for integrated production. A smaller fall in quality would thus allow the firm to reduce the price charged by a smaller extent. The effect arising from reduced product differentiation is now less dominant compared to the fall in price differential, resulting in a smaller fall in quantity demanded compared to the integrated mode of production. By comparing the profits under the two types of production, we find that the threshold level of human capital has decreased by a large extent. The higher cost of employing workers at any level of human capital relative to the cost of outsourcing the manual component at a lower level of human capital would explain the large decrease in the threshold level. 2.4.5 General Productivity Level The final internal factor we will examine is the change in the general productivity level of the firm. We consider a 20% increase in the general productivity parameter, with Table 2.8 providing the numerical results for this case. 101 Table 2.8: Numerical results under both forms of production for different values of HN with a 20% increase in general per unit productivity Integrated production HN 0.15 0.20 0.30 0.40 0.50 0.60 0.61 0.62 0.63 0.64 0.65 0.70 0.80 0.90 LNI 9.82922 7.94334 5.90538 4.79638 4.08655 3.58777 3.54578 3.50497 3.46529 3.42668 3.38911 3.21529 2.92495 2.69128 VNI 1.50584 1.59175 1.72771 1.83546 1.92592 2.00451 2.01185 2.01911 2.02628 2.03337 2.04039 2.07438 2.13752 2.19531 QNI 0.33403 0.34802 0.36485 0.37507 0.38215 0.38746 0.38792 0.38837 0.38881 0.38924 0.38966 0.39164 0.39505 0.39790 PNI 1.03424 1.05498 1.08754 1.11269 1.13320 1.15055 1.15214 1.15372 1.15527 1.15680 1.15831 1.16559 1.17887 1.19078 πNI 0.12301 0.14025 0.16506 0.18294 0.19694 0.20845 0.20950 0.21053 0.21154 0.21254 0.21352 0.21823 0.22672 0.23424 QNI LNI 3.28321 2.76444 2.15460 1.79898 1.56168 1.39011 1.37547 1.36122 1.34733 1.33380 1.32060 1.25922 1.15549 1.07087 PNI/ VNI 0.68682 0.66278 0.62947 0.60622 0.58839 0.57398 0.57268 0.57140 0.57014 0.56891 0.56769 0.56190 0.55151 0.54242 Fragmented production HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 8.10650 0.52309 1.65227 0.17612 1.28478 0.03708 8.10650 0.77759 0.20 6.20438 0.57267 1.72607 0.23613 1.24644 0.06908 6.20438 0.72212 0.30 4.32958 0.65420 1.86017 0.30151 1.21769 0.11943 4.32958 0.65461 0.40 3.39292 0.72089 1.97842 0.33689 1.21206 0.15611 3.39292 0.61264 0.50 2.82515 0.77784 2.08406 0.35930 1.21458 0.18428 2.82515 0.58280 0.60 2.44104 0.82777 2.17968 0.37486 1.22041 0.20689 2.44104 0.55990 0.61 2.40926 0.83245 2.18877 0.37616 1.22109 0.20892 2.40926 0.55789 0.62 2.37845 0.83708 2.19778 0.37743 1.22178 0.21091 2.37845 0.55592 0.63 2.34857 0.84165 2.20671 0.37865 1.22248 0.21287 2.34857 0.55398 0.64 2.31958 0.84618 2.21557 0.37985 1.22319 0.21479 2.31958 0.55209 0.65 2.29143 0.85065 2.22435 0.38101 1.22391 0.21668 2.29143 0.55023 0.70 2.16211 0.87236 2.26718 0.38636 1.22763 0.22566 2.16211 0.54148 0.80 1.94930 0.91270 2.34798 0.39525 1.23537 0.24163 1.94930 0.52614 0.90 1.78094 0.94960 2.42315 0.40235 1.24322 0.25549 1.78094 0.51306 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) We find that there is a fall in the per unit employment level but an increase in the quality of the service good, the quantity demanded, price of the service good, profits and overall employment under the integrated mode of production. With a general increase in per-unit productivity, the endogenous factor used in production, which is labour in this case, is more productive and thus less workers per unit of output produced is required. The increase in quality of the service good suggests that the firm does not reduce the 102 employment level in a one-for-one manner. Here, a reduction in the number of workers used to produce each unit reduces the firm’s cost and yet raising the quality of the service good provides the firm with the opportunity to raise its price slightly. These changes result in a definite increase in per unit profit. Moreover, the increase in quantity demanded suggests that the quality differential effect is relatively stronger compared to the price differential effect, thus the increase in quantity demanded, with this subsequent effect being relatively stronger to drive the increase in overall employment. Profit increases unambiguously as a result of higher per unit profit and quantity demanded. Under the fragmented mode of production, the graphs associated with (8) and (9) have shifted to the left and shifted downwards respectively, at all levels of human capital. The effect on the various variables considered above is the same with similar intuitions. In addition, we also find that there is a decrease in the quality of the manual component being purchased from the supplier. The intuition for this decrease would be similar to that of the decrease in per unit employment. This additional avenue of cost reduction arising from higher per unit productivity would result in an unambiguous increase in per unit profit. We also note that the quantity demanded of the service good can be higher under the fragmented mode of production compared to the integrated mode of production. Interestingly, we note that there is no noticeable change in the threshold level of human capital. It may be that the impact brought about by a change in general productivity level does not differ between either mode of production, thus the unchanged threshold level of human capital. 103 2.5 Production Share Parameters Up to this point, our above analysis is based on the organizational component’s production share being larger than that of the manual component. It would be of interest to analyze the base case outcome by switching the relative production shares attributed to each component (i.e. setting β=1/3 and keeping all other parameter values unchanged). The results are shown in table 2.9. The key observation in this case arising from the change in production shares is the higher threshold level of human capital required before the Northern firm switches to the fragmented mode of production. A higher production share of the manual component would delay the need to pursue a differentiated cost strategy since the difference in productivity between the manual and organizational component would not be sufficiently large until higher levels of human capital are attained, following which the effect of a higher wage cost relative to the cost of outsourcing the manual component sets in. Note that upon the firm switching to the fragmented mode of production, the firm now purchases a higher quality of the manual component from the supplier and this can be attributed to the need to make up for the fall in contribution towards the quality of the service good from the organizational component arising from its reduced productive share. It is not cost optimal to retain the same level of per-unit employment compared to the base case due to the low marginal increase in quality from employing an additional worker to work on that unit of the good. Nevertheless, with the increasing cost of obtaining a higher quality of the manual component from the supplier for a given level of 104 Table 2.9: Numerical results under both forms of production for different values of HN with a change in the productive share of the organizational component (β=1/3) Integrated production HN 0.15 0.20 0.30 0.40 0.50 0.60 0.70 0.71 0.72 0.73 0.74 0.80 0.90 LNI 9.99795 8.10984 6.05233 4.92512 4.20086 3.69068 3.30904 3.27602 3.24379 3.21232 3.18158 3.01118 2.77124 VNI 1.44850 1.50765 1.59890 1.66954 1.72785 1.77787 1.82186 1.82599 1.83007 1.83411 1.83811 1.86127 1.89705 QNI 0.32259 0.33435 0.34905 0.35830 0.36487 0.36989 0.37390 0.37426 0.37461 0.37495 0.37529 0.37721 0.38002 PNI 1.02054 1.03467 1.05671 1.07370 1.08758 1.09934 1.10955 1.11051 1.11145 1.11238 1.11330 1.11860 1.12672 πNI 0.11069 0.12339 0.14163 0.15478 0.16508 0.17356 0.18076 0.18143 0.18208 0.18273 0.18336 0.18702 0.19257 QNI LNI 3.22527 2.71156 2.11256 1.76465 1.53277 1.36513 1.23724 1.22607 1.21515 1.20447 1.19403 1.13585 1.05312 PNI/ VNI 0.70455 0.68628 0.66090 0.64311 0.62944 0.61835 0.60902 0.60817 0.60732 0.60649 0.60567 0.60099 0.59393 Fragmented production HN LNO VM VNO QNO PNO πNI QNO LNO PNO/ VNO 0.15 4.55874 0.84921 1.18508 0.07337 1.09964 0.00465 0.33449 0.92790 0.20 3.37395 0.89891 1.22544 0.16921 1.04476 0.02567 0.57090 0.85256 0.30 2.25728 0.98249 1.30181 0.27166 0.99694 0.07062 0.61322 0.76582 0.40 1.72536 1.05249 1.37157 0.32560 0.98054 0.10698 0.56177 0.71490 0.50 1.41358 1.11321 1.43518 0.35884 0.97606 0.13578 0.50725 0.68010 0.60 1.20780 1.16700 1.49344 0.38137 0.97692 0.15915 0.46062 0.65414 0.70 1.06115 1.21534 1.54709 0.39766 0.98036 0.17862 0.42198 0.63368 0.71 1.04875 1.21992 1.55222 0.39904 0.98078 0.18039 0.41850 0.63186 0.72 1.03668 1.22445 1.55732 0.40039 0.98122 0.18213 0.41508 0.63007 0.73 1.02495 1.22894 1.56238 0.40170 0.98168 0.18385 0.41173 0.62832 0.74 1.01353 1.23340 1.56741 0.40298 0.98214 0.18555 0.40843 0.62660 0.80 0.95089 1.25928 1.59679 0.40999 0.98508 0.19518 0.38986 0.61691 0.90 0.86467 1.29958 1.64308 0.41967 0.99043 0.20953 0.36287 0.60279 (Note that numerical results in bold denote the lower and upper bound within which the threshold level of human capital lies) human capital, the firm is unable to make up fully for the lower quality from the organizational component, thus accounting for the lower quality of the service good under the fragmented mode of production. From the preference side, the loss in utility from consuming a lower quality of the service good upon the Northern firm switching to the fragmented mode of production is less than the utility gained from cost savings gained through paying a lower price for the service good, which would explain for the 105 increase in quantity demanded, even though the price-to-quality ratio has increased under this mode of production. 2.6 Modifying the Cost of Outsourcing The above model assumes that the cost of outsourcing decreases, albeit in a diminishing manner, as HN increases. In this section, we briefly mention and provide some intuition behind the actions of the firm under the situation where the overall base cost of outsourcing remains unchanged. Simply put, outsourcing cost is now specified as ρ eV instead of ( ρ H N δ ) eV .21 M M For sufficiently high values of ρ , as HN increases, the firm will choose to produce both components, thus remaining an integrated entity, since overall profits through integration remain higher than that of fragmentation.22 To account for this, we first observe that if the firm is under the outsourcing mode of production, it will reduce the quality of the manual component that it purchases and per-unit employment. As human capital increases, each worker is actually able to produce a higher quality of the organizational component. The exponential increase in the quality of the manual component is likely to have resulted in the cost of increasing the quality of the manual component purchased being more expensive than employing workers to raise the quality of the organizational component instead. In fact, the observation of the firm reducing the quality of the manual component purchased suggests that they would prefer to release 21 Numerical results for this case have not been included. These are available upon request. Depending on the parameter values, if ρ is sufficiently low, we can theoretically have a situation where the firm actually outsources the manual component at low values of HN and undertakes the integrated mode of production beyond a threshold level of HN. This would be the opposite of Proposition 3. 22 106 less workers to produce a higher quality of the organizational component to make up for the loss in the quality of the manual component. On the whole, if the element of reliability is absent (i.e. outsourcing cost doesn’t decrease as HN increases), then there is no avenue for the Northern firm to differentiate its costs. The Northern firm would thus continue with the integrated mode of production. 2.7 General Discussion Some interesting results have been obtained from the above comparative statics analysis. We attempt to provide a general discussion on the implications of selected outcomes and some possible policy implications by combining the various findings that have been obtained through the above analyses. In the above model, we find that increased competitive pressures arising from a fall in the Southern firm’s service good can have a negative impact on the Northern firm’s various decision variables as well as quantity demanded, overall employment and profits. We have also noted the attempt by the firm to try to further differentiate its product as a result of increased competition. The above studies of the effects of internal factors on the various variables provide some useful implications on the policies that can be formulated to deal with increased competition. Government measures targeted at lowering the cost faced by the supplier can be translated into lower cost of outsourcing faced by the Northern service good firm. This can then be translated into lower prices 107 and higher overall product quality, which reduces the competition level and thus raises the extent of product differentiation. In terms of policies that can be implemented to assist the firm directly, this may come in the form of reducing the firm’s social security contributions or subsidizing wage costs (by adjusting w). However, it is difficult to gauge the optimal level of assistance, either to the firm or to the supplier as mentioned above, that should be rendered as such assistance may result in deadweight losses that can potentially reduce the welfare of the society as a whole, which we do not model here. A non-intervention approach should be that the firm should strive to raise its productivity levels to cope with competition from foreign firms. This can come in the form of raising operational efficiency and streamlining and restructuring their operations. In Singapore, the Port of Singapore Authority and Singapore Airport Terminal Services have recently recorded improved bottom-lines despite intense foreign competition after having undertaken measures, sometimes painful ones in the form of retrenchments, to operate in a more efficient and effective manner. Also playing an important role in fending off foreign competition would be to upgrade the skills of workers in the firm continually to help workers working in such firms to be able to produce higher quality of the service good whilst keeping the price of its good competitive. Our study above also analysed the impact of an increase in product quality of the Southern firm on the Northern firm. Depending on the nature of the service good, the Southern firm may want to reduce the quality of its service good so as to further differentiate its product or, in other instances, to raise the quality of its service good so as 108 to compete with the Northern firm. It may be more likely that firms would try to raise service quality and yet try, at the very minimum, to keep price increases low. A richer model where the Southern firm’s decision-making process is endogenized will certainly provide a more comprehensive analysis of North-South competition in the service-link industry. 2.8 Conclusion and Future Research In this study, we have considered a simple two-country model with competition in the provision of service links. Our motivation arises from the fact that certain industries face limitations in terms of the locational aspect of outsourcing the lower-end tasks in that such firms can only either produce all the components of their product or outsource those components to a supplier located domestically. We have also studied the role of human capital in determining whether the integrated or fragmented mode of production would be adopted. Our findings indicate the existence of a threshold level of human capital where the integrated mode of production is adopted for human capital levels below the threshold level, with the fragmented mode of production implemented upon crossing that threshold. An interesting consequence pertaining to the transition from the integrated to outsourcing mode of production would be the jump in the extent of product differentiation, with the firm ceasing to serve her fringe customers as a result. Comparative statics analysis was carried out to determine the impact of external and internal factors on various variables associated with the Northern firm such as product quality and price, per unit employment, required quality of the outsourced component, profits, quantity demanded and overall employment. Table 2.10 provides a summary of 109 the various comparative statics analyses as well as the changes that occur upon transition from the integrated to the fragmented mode of production. Some implications regarding suitable initiatives to deal with competitive pressures were discussed. Whilst the above study provides some useful results on two-country competition in sectors where there are limitations on the location where components can be outsourced to, we note that there can be other factors that determine the consumer’s preference on where to acquire such services associated with these sectors. One interesting addition would be to study the role of distance and transport or communication costs required. In this model, we would expect that the consumer’s distance and such costs incurred would be inversely related to the quantity demanded. The Northern firm’s pricing decision would then have to be varied accordingly depending on such costs. Another improvement, as mentioned in the preceding section, would be to allow the various variables associated with the Southern firm to be endogenous. This would allow for a richer study of how changes in various factors can have an impact on both the Northern and Southern firm. Such a study will be more realistic as changes in the cost conditions faced by either firm will realistically have an impact on the pricing and quality decisions and thus profits on both firms. This can be further augmented by having the price variable faced by the supplier to be endogenous. Such improvements can be implemented in future studies on this area of research on domestic outsourcing and foreign competition. 110 Table 2.10: Summary of outcomes of comparative statics exercise of an increase in respective parameters in section 4 under the relevant production mode (b) Integrated mode (for a given level of human capital in Northern economy) Total CurrPNI / Parameter LNI VNI QNI PNI Empent VNI loyed Profit Price of service good PS + + + of Southern firm Quality of service VS + + good of Southern firm Base cost of ρ Not applicable under integrated mode outsourcing Outsourcing cost δ Not applicable under integrated mode parameter associated with h Base wage rate w + General per-unit λ + + + + + productivity (b) Fragmented mode (for a given level of human capital in Northern economy) Parameter LNO VNO VM QNO PNO PNO / VNO Total Employed Threshold h* Current Profit - - - - Price of service good of Southern firm PS + + + - + (h*) Quality of service good of Southern firm VS + + + - + - - - - Base cost of outsourcing ρ - + + - - + - + δ - + + - - + - + w - + - - + - Outsourcing cost parameter associated with h Base wage rate + (for h*) - no General per-unit λ + + + + + chanproductivity ge Note: “h*” denote respectively very low and very high levels of human capital that are much lower and much higher than the threshold level of human capital. (c) Changes in variables upon switch from integrated to fragmented mode upon instant of crossing threshold h* From LNI to LNO From VNI to VNO FromQNI to QNO From PNI to PNO Price to quality ratio Total Employed Current Profit - + - + - - + 111 Another interesting modification would be to consider a continuum of manual components where the firm gradually outsources each variety and concentrate increasingly on the organizational component. Under such a model, the so-called “threshold” level of human capital would then be considered to be a juncture where the firm then fully concentrates on the organizational component. 112 References Abraham, Katherine G. and Susan K. 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Empirical findings by Papageorgiou (2003) based on World Bank data revealed that post-primary education contributes significantly towards technology innovation and adoption whilst primary education contributes towards final output production Hollanders and Weel (2002) found a positive relationship between skill upgrading and R&D intensity in manufacturing based on an empirical study of six OECD countries... human capital is carried out in section 1.3 We consider changes in other parameters in section 1.4 Section 1.5 provides a general discussion of the implications of the outcomes obtained Section 1.6 concludes this chapter 1.2 The Model The economy consists of a collection of identical firms indexed from 0 to 1 that are producing the final good The population consists of economically active agents that can... may no longer require a cameraman to accompany them in news reporting should future technological developments result in improved versions of the videophone Thus, technological progress could potentially have destructive effects on employment, with serious repercussions on job creation within the economy as well The above discussion leads to the following question: does improved skill profile amongst... leading nations Eaton and Kortum (1996) did an empirical study to assess the proportion of a nation’s growth that can be attributed 2 to its own research efforts and found that such efforts within major economies, namely United States, Japan and Germany, form a significant proportion of their growth Nahuis and van de Ven (1999) further postulated that efforts that concentrate on the adaptation of technology... small nations based on the empirical outcomes from Eaton and Kortum (1996) Computations by Howitt and Mayer-Foulkes (2002) revealed that 80% of the global R&D expenditure can be attributed to 5 countries, this figure rising to 95% with the inclusion of another 6 countries, thus suggesting that most other nations are embarking on technology adoption rather than being at the forefront of the global technological. .. relationship between IT capital and labour and further indicated that the impact has increased during recent times Other writers have also studied the relationship between human capital and unemployment An increase in education capital is found to reduce unemployment by Davis and Reeve (2003), regardless of whether the economy is closed or open Empirical studies by Richardson and van der Berg (2001) and. .. proportion of skilled workers within the workforce and would also lead to a reduction in unemployment The findings here seem to imply that increase in human capital is driven by technology adoption and that unemployment falls as a consequence His finding differs significantly from ours in that we view the presence of human capital to be the driving force behind technology 9 adoption and that unemployment. .. technology adoption decisions of Italian manufacturing firms have revealed that the human capital level of a firm’s employees does play an important role towards the firm’s decision on whether to adopt a certain technology.3 2 Empirical evidence on the skill-biased nature of technological innovations can be found in Berman, Bound and Machin (1998), Machin and van Reenen (1998) and Morrison Paul and Siegel ... or reduction in the optimal level of employment amongst the firms Hence, we have this non-monotonic relationship between unemployment and technology adoption and also unemployment and human capital... presentation I conducted and the summer meeting of the North American Economics and Finance Association held at the 80th Western Economics Association conference I would also like to thank Mdm Foo and. .. graph consisting of the above demarcation curves in Figures and corresponding to situations and A brief explanation of the above observations will be given in the next sub-section The simulation