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MINISTRY OF EDUCATION AND TRAINING CAN THO UNIVERSITY LE NHI BAO NGOC SUPPLY RESPONSE FUNCTION OF BLACK TIGER SHRIMP IN MEKONG DELTA DISSERTATION (ABSTRACT) Major: Agricultural Economics Major code: 62 62 01 15 2019 The research has been finished at Can Tho University, Can Tho City, Vietnam Supervisors: - Dr Le Quang Thong - Dr Thai Anh Hoa Discussant 1: Discussant 2: Discussant 3: The dissertation will be defended at the council of the school level at: On:…………hour…… date……… … month…… year……… Citing of this the dissertation is available at following the libraries: - Learning Resource Center-Can Tho University, Can Tho City - Vietnam National Library, HCM City i LIST OF PUBLISHED PAPERS RELATED TO DISSERTATION Le Nhi Bao Ngoc, Le Quang Thong, Thai Anh Hoa, (2018) Modeling and Forecasting the Farm-Gate Price of Tiger Shrimp in the Mekong Delta, Science and Technology Journal of Agriculture & Rural Development, Ministry of Agriculture and Rural Development, Vietnam, volume 2, pp 11-17 Le Nhi Bao Ngoc, Le Quang Thong, Thai Anh Hoa, (2018) Price transmission in black tiger shrimp market, Journal of Science Ho Chi Minh City Open University, 59 (2), 113-124 Le Nhi Bao Ngoc, Le Quang Thong, Thai Anh Hoa, (2018) Forecasting model of export price of tiger shrimp in Viet Nam Can Tho University Journal of Science 54(6D): 188-195 Le Nhi Bao Ngoc, Le Quang Thong, Pham Le Thong, Thai Anh Hoa, (2019) Supply response function of black tiger shrimp in Mekong Dalta Economic studies, volume (489), pp 67-75 ii CHAPTER INTRODUCTION 1.1 The statement of problem 1.1.1 The necessity of theory The study of supply response and elasticity is an important scientific field that attracts economists and policy makers It soughts to quantify the effects of changes of government programs on prices and trade policies for inputs, outputs, and responses of producers However, in Vietnam in general and the Mekong Delta, particularly, the quantitative researches related to the supply of agricultural or aquatic products at the macro or micro level Studies on the supply response of agricultural products began to develop early In particular, the supply response of agricultural products such as cereals and food developed by Nerlove (1958), Askari & Cummings (1977) Nerlove (1958) developed a partial adjustment supply response function in accordance with supply theory Since then, Nerlove supply response function has been interest to many scientists and applied in experimental studies of food crops and non-food crops in some countries such as the US, India, Thailand, and Chile (Holt and Johnson, 1988), chicken supply in the United States (Chavas, 1982) and the catfish industry in the US (Nguyen Van Giap, 2010) Nerlove supply response function (1958) is a dynamic supply response model combined with the expected price set in the form of self-regression model Therefore, supply can be a function of delayed price and other factors (Tomek & Robinson, 1981) In addition, the feasibility of the experimental study of the Nerlove supply response functional depends on the structure of data and the selection of the estimation method (Baum & Christopher, 2006) Researchers need to determine the model of expected price and data structure to determine the appropriate function form A theoretical framework gives researchers a scientific basis for choosing an approach to conduct an experimental analysis of the supply of black tiger shrimp in the Mekong Delta 1.1.2 Practical relevance The study of regional main agricultural and aquatic supply response is generally a very important issue for the purpose of policy-making purpose needed for regional or national production The focus of the supply response analysis is to determine the model of the expected price and the expected hypothesis of the household Because it is very useful for policymakers to understand the link among the price, decision of farmers, and factors related to specific supply According to the evaluation of the Ministry of Agriculture and Rural Development (MARD) and functional sectors, brackish shrimp is the main aquaculture product; In 2017, the farming area is 705 thousand hectares and accounts for over 64% of the aquaculture area of the whole country (Directorate of Fisheries, 2017) In the period of 2010 - 2017, the value of shrimp export turnover of the whole country increased from 2.1 billion USD to 3.8 billion USD, accounting for 46.0% of the export value of the fishery sector (Agromonitor, 2018 and VASEP, 2018) Therefore, brackish shrimp is identified as a main and potential product with many advantages in development (MARD, 2015, 2017) Mekong Delta has advantages in farming, processing and exporting brackish shrimp Area and production of black tiger shrimp in the region account for over 90% and 80% compared to the whole country, respectively Mekong Delta has the strength in the field of processing and exporting, the number of factories accounts for over 60% compared to the whole country Total capacity is over million tons of products per year (MARD, 2015) The area and production of brackish water shrimp in the Mekong Delta during the period of 2015-2017 is presented in Table 1.1, showing that the area and production of black tiger shrimp and white leg shrimp are always fluctuating Although the area and production of white leg shrimp in recent years tend to increase faster than black tiger shrimp, black tiger shrimp is still the main farming target In the Mekong Delta, black tiger shrimps are cultured in coastal provinces, including Long An, Tien Giang, Ben Tre, Tra Vinh, Soc Trang, Bac Lieu, Kien Giang, and Ca Mau (VASEP, 2016; Agromonitor, 2017) Table 1.1 Brackish shrimp development in the Mekong Delta in the period of 2015-2017 Percentage for the Quantity whole nation (%) Items/year 2015 2016 2017 2015 2016 2017 Area of black tiger shrimp (ha) 559,222 569,500 578,819 90.6 89.8 88.4 Area of white leg shrimp (ha) 57,781 64,440 75,994 9.4 10.2 11.6 Production of black tiger shrimp (tons) 245,873 253,528 253,738 52.9 50.0 45.3 Production of white leg shrimp (tons) 218,930 253,100 305,775 47.1 50.0 54.7 Source: Ministry of Agriculture and Rural Development, 2015, 2017 However, the area and output production of the region fluctuate continuously along with the fluctuation of prices in the domestic and export market When the export price of black tiger shrimp increases, processing and exporting enterprises increase export production and stimulate more businesses to join the industry Export prices also increase, and at the same time, impact on farm gate prices, creating an incentive to increase production and expand farmers' production When export prices fall, exporters reduce production levels or may close factories As a result, the decrease in farm gate prices leads to farmers reducing production or switching to other farming objects such as white leg shrimp, sea crabs and vice versa (VASEP, 2014, 2015 and 2017) In 2015, when white leg shrimp price dropped sharply 1; many households switched to raising black tiger shrimp as a traditional object of high value Some provinces have a large area and the output of black tiger shrimp increased sharply In particular, Kien Giang province increased by 11.2% in area and 15.7% in production, and Soc Trang increased by 2.8% in area and 48, 1% in production This leads to an The price of white leg shrimp in the first week of June increased by 10,000-15,000 VND /kg; The second week continued to increase by 3,000-5,000 VND/kg At the same time, applying the model of raising black tiger shrimp with other aquatic products such as crab and perch has relatively good efficiency, increasing the ability to fight diseases increase of 4.0% in the area and production of black tiger shrimp in the Mekong Delta compared to 2014 (VASEP, 2015) By at the end of June 2016, in Ca Mau province, the price of black tiger shrimp dropped sharply due to the abundant supply of black tiger shrimp in the province, but the seafood processing enterprises in the province reduced the production of processing shrimps Meanwhile, in Bac Lieu province, the harvested shrimp production was low but the seafood processing enterprises in the province stabilize the production, leading to a shortage of raw materials Therefore, the price of raw black tiger shrimp increased sharply from 50,000 to 60,000 VND/kg; with black tiger shrimp of 30 individuals/kg, ranging from 180,000 to 210,000 VND/kg, 40 individuals/kg from 140,000-155,000VND/kg (VASEP, 2017 and SCAP, 2017) When prices fluctuate, farmers will adjust supply in the next production season Deriving from the theoretical urgency and practice mentioned above, it is essential to conduct the dissertation of " Supply response function of black tiger shrimp in Mekong Delta" to analyze the dependence of black tiger shrimp supply on its own prices, input element prices, competitive product prices and other non-price factors affecting the supply in Mekong Delta provinces in the context of the interaction among prices in different market segments in the marketing channel and among prices over time in the market 1.2 Research objectives The study is designed to estimate a response model of tiger shrimp in the Mekong Delta Specifically, the objectives are: (1) To evaluate the production and consumption situation and analyze the relationship of the black tiger shrimp selling price among markets to determine commercial factors and the estimation method in accordance with the existing data set of the study; (2) To estimate the expected price model of farm households as a basis for selecting the expected price variable for the black tiger shrimp supply response function in Mekong Delta and calculating the elasticity coefficient of black tiger shrimp supply in the short and long run and; (3) To determine the black tiger shrimp production trend in Mekong Delta in the future and suggesting solutions from research results 1.3 Scope of the Study 1.3.1 Studied of the subjects Research object of the thesis is the black tiger shrimp supply response function in Mekong Delta based on the table data of the regional provinces in the period of the 1st quarter of 2014 to the 4th quarter of 2017 The process of doing this research goes through the following steps First, the price analysis of black tiger shrimp is conducted to determine the price relationship between the consuming markets and the farm gate price in order to select the estimation method Next, the expected price model of shrimp farmers is estimated to determine the formation of the expected price variable used for estimating the black tiger shrimp supply response function Since then, the author identifies the marginal effect of factors on production adjustment Based on the analysis results, the author proposes solutions for the black tiger shrimp industry in the future 1.3.2 Spatial scope The two criteria of area and production are used as a basis for selecting research sites According to the data of the General Statistics Office and MARD in the period of 2014-2017, Ca Mau, Kien Giang, Bac Lieu and Soc Trang are the provinces with the largest area and production of black tiger shrimp in the Mekong Delta, averagely accounting for over 90.0% and 75.0% respectively compared to the area and production of the whole Mekong Delta Therefore, four provinces of Ca Mau, Kien Giang, Bac Lieu, and Soc Trang were selected to represent the research site in the Mekong Delta 1.3.3 Temporal scope Various secondary and primary data sets are used by the author to analyze the objectives of the thesis Time series from September 2011 to April 2017 (5 years and months) with 68 observations were used to analyze the relationship among the selling prices of black tiger shrimp in intermediate markets in the distribution channel Direct interview data for 97 farmers were used to estimate the expected price model of Ca Mau shrimp farmers Data from the 1st quarter of 2014 to the 4th quarter of 2017 (T = 16 terms) in provinces of Ca Mau, Bac Lieu, Soc Trang, and Kien Giang in the Mekong Delta (n = 4); with 64 observations, used for analyzing the black tiger shrimp supply response in the Mekong Delta CHAPTER THEORETICAL FRAMEWORK AND RESEARCH METHODOLOGY This chapter presents an approach to the transmission of prices between factors and the expected price model of farm households, the theoretical basis of the partial adjustment supply response analysis; and propose an analytical framework, research model, and corresponding analysis methods for each objective of the thesis 2.1 Theoretical framework 2.1.1 Price transmission approaches in the market The relationship between world prices and domestic prices is first discussed by Mundlak & Larson (1992) in the study of agricultural prices According to Fackler & Goodwin (2001), product price i of market is different from product price i in market because of the cost incurred in distribution c The relationship between price of goods i between separate markets especially P1i = P2i + c (Enke, 1951) (2.1) The research analyzed price differences among different stages in the distribution channel due to market forces Because people having market power are the ones who value the product and the price difference between the two markets (McCorriston et al., 2000) In addition, the factors of transportation costs, transaction costs, increased profits according to production scale, and product differentiation and etc give rise to additional costs and are related to price among the factors in the value chain (Thompson et al., 2002) The series of price data is said to be transmitted when price changes in a market are transferred to the other market at all times In fact, price transmission does not always have immediate or post-impact effects but also occurs in the long term (Balcombe & Morisson, 2002) Normally, there is a relationship of price data series with the latency of past data series and product prices in markets Since time series not guarantee stationary attribute, the OLS (Ordinary Least Squares) estimation method on the relationship between prices on market periods does not give reliable results due to regression fake (Granger & Newbold, 1974) Cointegration theory developed by Granger (1981) and perfected by Engle & Granger (1987) was used to overcome nonstationary series At that time, the appropriate estimation method is the error correction vector (Vector Error Correction Mechanism) for long data series and Error Correction Mechanism for short data series (Barrett, 1996) 2.1.2 Approaches to expected prices in agricultural production Nerlove (1956) was the first person to put expectations on the analysis of supply dynamics Next, Muth (1961) put expectations on analyzing price fluctuations and then economists like Lucas & Sargent (1981) were pioneers to put expectations on economic theory system According to economists, there are two types of expected hypotheses These are the Adaptive Expectations hypothesis (AE) and the Rational Expectations hypothesis (RE) The AE hypothesis implies that people think of tomorrow based on what happened today and yesterday and learn more from the reality to adjust expectations (Phillips, 1958) By 1961, the RE hypothesis of Muth suggested that people expected the efficiency when information was available at the time of expected formation with deep knowledge, understanding of market mechanisms, and macro policies (price policies, production planning, and etc,) The expected price is considered the basis of the supply analysis theory This approach is based on the hypotheses about price model with expectation theory and time series The Cobweb model with adaptive expectations explains the volatility of the previous selling price along with the past adjustment, leading to the adjustment decisions of farmers (Nerlove, 1956) For the Cobweb model with the expectation of adaptation, Nerlove (1958) studied experimental analysis by time data Fisher & Tanner (1978) suggested that expected prices should be estimated by survey data From there, it is possible to understand how farmers expect future selling prices, personal capacity, and their expectation adjustment Scholars have confirmed that Cobweb model with adaptive expectations is appropriate in the context of uncertain market conditions limited forecasting capacity of farmers 2.1.3 Dynamic supply response models 2.1.3.1 Approaches to the dynamic supply response with output price According to Shephard (1953), solving the problem which maximizes the profit corresponding to the constrained condition of cost and production function will shows that optimal amount of the input and the output is the function of the input and output price.output Since then, we can build the supply function of manufacturers The goal of the manufacturers is the highest profit through adjusting the production of the ith manufacturer, the production function takes the form: Q   f ( p, c i , Z k ) (2.1) Where Q is the optimal production (tons); p is the product price (thousand dongs); c i is the price vector of the inputs; Z k is a fixed input vector In agricultural production, due to the biological characteristics of plants and animals, the supply cannot immediately respond to price changes Manufacturers often rely on the past prices to form the expected price for the current production and thus make decisions on the production Therefore, supply can be a function of the delayed price and other factors (Tomek & Robinson, 1981) The dynamic supply response model combined with the expected price is set in the self-regression model of Nerlove (1958), presented in the following system of equations: Supply function: Qt*    1 Pt *   Z t   3T  ut (2.2) Expected price: Pt *  Pt*1   ( Pt 1  Pt*1 ) (2.3) Manufacturing adjustment: Qt  Qt 1   (Qt*  Qt 1 ) (2.4) * * Where: Qt is the expected production (ton); Pt is the expected price of the product in the period t (thousand dongs); Pt*1 is the expected price of the product in the period t-1 (thousand dongs); Pt is the price of the product in the period t (thousand dongs); Qt – Qt-1 is the real change (ton); Qt* - Qt-1 is the expected change (ton); Qt is the production in the period t (ton); Qt-1 is the production in the period t-1 (ton); Zt is the factors affecting the production of the product in period t; T is a variable that reflects the time effect; ut is random disturbance; i are the intercept and slope coefficients;  is the coefficient adjusting the expected price;  is the coefficient adjusting the production; With  ) 71,75 Hausman statistic (  value) Level of significance (p-value) 0,00 5,48 Modified Wald test (  value) 0,24 Level of significance (Prob>  ) Lagrange Multiplier Test 6,42 Level of significance (Prob>F) 0,09 Note: *, *** corresponds to statistical significance of 5% and 1% respectively Source: Summarized of estimated results in the researched provinces The estimated results of the supply response model in terms of the output and farming area have an impact on black tiger shrimp output in the current quarter The estimated results show that the supply adjustment is affected by the prices of black tiger shrimp, of the competitive products, and input elements in accordance with supply law This proves that commercialization has a greater positive impact on the 21 expansion of area than on the increase of the output of black tiger shrimp in the researched provinces in the Mekong Delta 4.3.4 Coefficient of supply elasticity in output and farming area The results presented in Table 4.11 and Table 4.12 shows that all the elasticity coefficients of supply based on output and farming area with farm gate price of black tiger shrimp are positive, while the elasticity coefficients of supply based on output and farming area with farm-gate price of competitive products are negative, conforming with the expectation of the theory Therefore, we accept hypothesis 1: "The elasticity coefficients of supply based on output and farming area with expected selling price is positive." and hypothesis 4: "The supply curve of black tiger shrimp shifts under the impact input element prices and competitive product prices.” This implies that black tiger shrimp farming in the researched provinces in the Mekong Delta is being adjusted by farmers based on the selling prices of the product itself and of the competitive products However, the elasticity coefficient of these factors in the short-run is greater than in the long-run Analysis results showed that black tiger shrimp farming in the researched provinces in the Mekong Delta is not yet stable Based on the data in Table 4.11, the coefficient of supply elasticity of output subject to the farm gate price of black tiger shrimp, of black tiger shrimp seeds, and of competitive products (whiteleg shrimp) are inelastic, while the coefficient of supply elasticity of area subject to the farm gate price of the products, of black tiger shrimp seeds, and of competitive products are elastic The result shows that there were differences when adjusting the supply of black tiger shrimp amongst farmers Table 4.11 Coefficient of supply elasticity in short-run Variable name Variable Output Black tiger shrimp price in the quarter t-1 0,57 Pit 1 Black tiger shrimp price in the quarter t-2 -0,20 Pit  Whiteleg shrimp price in the quarter t-1 Pmit Whiteleg shrimp price in the quarter t-2 -1,17 Pmit  Mud crab price in the quarter t-2 0,49 Pcit  Black tiger shrimp seed price in the quarter t Psit Black tiger shrimp seed price in the quarter t-2 0,27 Psit  Source: Summarized and calculated in the researched provinces Table 4.12 Coefficient of supply elasticity in long-run Variable name Variable Output Area Black tiger shrimp price 0,21 2,68 Pit Whiteleg shrimp price -0,61 -0,15 Pmit Mud crab price -0,27 -1,40 Pcit Black tiger shrimp seed price 0,15 -0,85 Psit Source: Summarized and calculated in the researched provinces Area 2,72 2,65 -3,81 3,50 -2,82 1,32 -3,04 22 The calculation results of long-run elasticity coefficients are presented in Table 4.12, showing the elasticity of supply of output by product price; the price of black tiger shrimp is less than and smaller than the supply elasticity coefficient in area by product price and price of tiger shrimp seeds However, the elasticity coefficient based on the farm gate price of black tiger shrimp with the black tiger shrimp farming area is 2.68 This implies that the farm gate price of black tiger shrimp is a factor that positively affects the area rather than the production of black tiger shrimp in the surveyed provinces in the Mekong Delta This result shows that black tiger shrimp farming technology is too backward and lack of investment so farm households decided to expand the production area to increase production and increase the supply of black tiger shrimp in the market 4.4 Conclusion This chapter has presented and discussed empirical research results CHAPTER CONCLUSION AND SOLUTION 5.1 Conclusion With the content of the thesis after research, it is possible to draw some conclusions as all the research objectives of the thesis are achieved The hypotheses set after test are accepted The results of the research contents are as follows:  A price transmission model of black tiger shrimp in the market Estimation results showed that the prices of black tiger shrimp between markets have a causal relationship In the long run, the price of black tiger shrimp at the farm gate and retail and export prices were co-integrated and positively correlated In the short run, retail price was likely to have a significant effect on farm-gate one but the export price was not It was also found that the disequilibrium of the market in a month was corrected in the subsequent month through the error-correction mechanism  The expected prices model of the shrimp farming households The estimation results show that Cobweb model with adaptive expectation is a price model consistent with the most observable data Accordingly, the expected price of the farm households is determined based on the delayed price of a period and the expected adjustment compared to the actual price of the farm households in the previous period This proves that the farm gate price of the previous crop was used by shrimp farmers for the expectation of the future price of black tiger shrimp This is the basis for farm households to decide on the area of stocking shrimps and corresponding technical measures to achieve the expected production of black tiger shrimp The research results also indicate that the expected price of the farm households is not effective in production decisions  The supply response model of black tiger shrimp in Mekong Delta Based on the results of the expected price model of farmers, the author used the expected price of Cobweb function with a delay in the Nerlove supply response model The estimated results of the supply response function by FEM show that the laged 23 price of the previous season plays an important role in the process of deciding to adjust the output and area of black tiger shrimp farming Especially, prices are considered as an important factor determining the area of black tiger shrimp farming in the short and long run In the short and long run, the coefficient of supply elasticity of output at the farm-gate price of the product, the farm-gate price of input elements and of competitive products (mud crabs) are inelastic However, the coefficient of supply elasticity of output with the farm-gate price of competitive products (whiteleg shrimp) is elastic Meanwhile, the coefficient of supply elasticity of area at the farm-gate price of the product, the farm-gate price of input elements and of competitive products are elastic This shows that the area of black tiger shrimp farming is very sensitive to the fluctuations in selling prices but the output of black tiger shrimp is not The supply curve black tiger shrimp shifts to the left because of the impact of rising prices of black tiger shrimp seeds and competitive products 5.2 Suggestions and solutions to develop the black tiger shrimp industry Based on the research results, the policies and suggestions are as follows: (1) The analysis result of the actual situation in chapter shows that the black tiger shrimp industry is facing large challenges such as poor quality shrimp seed, low labor productivity, and complicated epidemics Therefore, it is essential to standardize the infrastructure of shrimp disease testing laboratory systems and invest in researching shrimp seed, especially providing support in the technology of breeding black tiger shrimp with disease resistance and rapid growth capability (2) The results show that the Cobweb price model with adaptive expectations is used by farmers during the process of price forecasting for the next season Expected prices of the farmers often have latency compared to the actual prices, so the supply is also late compared to market demand Therefore, timely price forecasting and dissemination of price have positive meanings in timely supply adjustment (3) Short-run estimation of the supply response model shows that the late price of the previous season affects the decision to adjust the farming area positively and more strongly than the output element This is the evidence that the black tiger shrimp farming area and output in the provinces surveyed is very sensitive to the impact of the farm-gate price of the products in the season This implies that farmers quickly update information when establishing expected prices in the process of adjusting the supply of black tiger shrimp by expanding the shrimp farming area to increase the output of black tiger shrimp both in the short-run and long-run Therefore, it is necessary to have policies to improve the capacity and market access of the farmers based on each group of producers (4) The coefficients of supply elasticity by output with farm-gate price of the product, farm-gate prices of input elements, and farm-gate prices of competitive products are inelastic Low productivity and the application of science and technology 24 in black tiger shrimp farming are the causes of the insignificant adjustment of black tiger shrimp supply when facing the impact of its own farm-gate price, input element farm-gate prices and competitive product farm-gate price in short-run Therefore, it is necessary to have breakthrough policies on technical, scientific, and technological solutions in the improved extensive black tiger shrimp farming area (5) The coefficients of supply elasticity by farming area with farm-gate price of the product, farm gate prices of input elements, and farm gate prices of competitive products are elastic This implies that the farmers’ decision to join or to leave the industry is very sensitive to these elements Black tiger shrimp farmer over-exploited the natural environment Therefore, it is important to invest in the infrastructure of shrimp farming area, especially irrigation systems, science and technology and fishery extension in shrimp farming Most importantly, the proactive management of the production environment must be closely associated with the preservation of the natural environment (6) The supply curve of black tiger shrimp shifts to the left because of the impact of the black tiger shrimp seed price and competitive product prices (mud crabs and whiteleg shrimp) Farm-gate prices of sea crabs have a positive impact on the output while whiteleg shrimp farm gate prices have a negative impact on the output and farming area of black tiger shrimp Therefore, to encourage farmers to stabilize production and stabilize the market, the state should promulgate policies to encourage and support shrimp farmers to borrow capital and invest in technology, etc, 5.3 Further research directions Within the framework of the thesis, there are certain limitations that cannot be avoided Therefore, the next research directions developed from the limitations and the conclusions of the thesis can be implemented in the upcoming time Continue to collect data, supplement selling price variables in the markets Expand the research on supply response to the total supply of black tiger shrimp industry Expand the research on production surplus received by black tiger shrimp farmers Expand the research towards risk analysis and market strength of the black tiger shrimp industry in the market Continue to study Nerlovian supply response in other industries in Vietnam 25 ... Thong, Thai Anh Hoa, (2018) Price transmission in black tiger shrimp market, Journal of Science Ho Chi Minh City Open University, 59 (2), 113-124 Le Nhi Bao Ngoc, Le Quang Thong, Thai Anh Hoa, (2018)... transmitted when price changes in a market are transferred to the other market at all times In fact, price transmission does not always have immediate or post-impact effects but also occurs in the long. .. correction vector (Vector Error Correction Mechanism) for long data series and Error Correction Mechanism for short data series (Barrett, 1996) 2.1.2 Approaches to expected prices in agricultural