Đang tải... (xem toàn văn)
Macro econom i c Measurem ent 5 1.1 GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.1 The three approaches to measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Real vs. Nominal GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Other important macroeconomic gauges: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 GNP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 PPPbased GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2 The Long Run Macro economy 9 2.1 The Solow Growth Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.1 The capital intensive form of the SGM . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 The dynamics of labor and technology . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.3 The dynamics of the capital stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.4 Some steady state results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1.5 The golden rule of saving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.6 Problemset exercises on the SGM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.7 Problem 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1.8 Problem 1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.1.9 Problem 1.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.10 Problem 1.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.1.11 Problem 1.8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3 The Short Run Macro economy 29 3.1 A Simple Theory of Household Consumption C(YT,r) . . . . . . . . . . . . . . . . . . . . . 29 3.2 A Simple Theory of Firm’s Investment I(r) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3 Government Spending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 The Trade Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.1 The Interest Rate Parity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.2 The Balance of Trade Function Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.6 The IS Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.6.1 Exercises on the IS curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.7 ISTR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.7.1 Monetary Policy Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.7.2 The lending rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.7.3 The TR curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.7.4 The ISTR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.7.5 Quantitative analysis of the ISTR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.8 Exercises on the ISTR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.8.1 Problem 3.14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.8.2 Problem 3.15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.8.3 Problem 3.16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.8.4 Problem 3.17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.9 The Extended ISTR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.9.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.9.2 Problemset Exercises on the Extended ISTR Model . . . . . . . . . . . . . . . . . . . 53 3 Downloaded by EBOOKBKMT VMTC (nguyenphihung1009gmail.com) lOMoARcPSD|2935381 4 CONTENTS 4 The Macro economy i n t he Medi um Run 57 4.1 The Supply Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.1.1 The Firm’s Pricing Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.1.2 Wage bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.1.3 The Supply Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2 The Demand Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 The ADAS model in the normal time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.4 Problemset Exercise on the Normal Time Medium Run . . . . . . . . . . . . . . . . . . . . . 61 4.4.1 Problem 4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.5 The ADAS Model During Deep Crisis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.5.1 Problem 4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.5.2 The Nonconditioned π Z L B . . . . . . . . . . . . . . . . . . .
lOMoARcPSD|2935381 Vietnamese - German University Faculty of Economics and Management Lecture Summary and Problem Set Manual Prepared for FA2015 Students Basic Macroeconomics - BMAK A qualification course for FA and BA students at the Vietnamese - German University By Dr Le Van Ha Vietnamese - German University Binh Duong, Vietnam April 2018 Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 This is a preliminary version which will be updated continuously Strictly meant to be used within FA2015 BMAK Class • Issues thoroughly discussed in the lecture slides will not be repeated in this note • Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 Contents Macroeconomic Measurement 1.1 GDP 1.1.1 The three approaches to measurement 1.1.2 Real vs Nominal GDP 1.2 Other important macroeconomic gauges: 1.2.1 GNP 1.2.2 PPP-based GDP 5 5 6 The Long Run Macroeconomy 2.1 The Solow Growth Model 2.1.1 The capital intensive form of the SGM 2.1.2 The dynamics of labor and technology 2.1.3 The dynamics of the capital stock 2.1.4 Some steady state results 2.1.5 The golden rule of saving 2.1.6 Problemset exercises on the SGM 2.1.7 Problem 1.5 2.1.8 Problem 1.5 2.1.9 Problem 1.6 2.1.10 Problem 1.7 2.1.11 Problem 1.8 10 11 11 11 12 13 14 19 23 26 27 27 Short Run Macroeconomy A Simple Theory of Household Consumption - C(Y-T,r) A Simple Theory of Firm’s Investment - I(r) Government Spending The Trade Balance 3.4.1 The Interest Rate Parity Theory 3.4.2 The Balance of Trade Function Form Exercises The IS Curve 3.6.1 Exercises on the IS curve IS-TR 3.7.1 Monetary Policy Rate 3.7.2 The lending rate 3.7.3 The TR curve 3.7.4 The IS-TR model 3.7.5 Quantitative analysis of the IS-TR Exercises on the IS-TR model 3.8.1 Problem 3.14 3.8.2 Problem 3.15 3.8.3 Problem 3.16 3.8.4 Problem 3.17 The Extended IS-TR Model 3.9.1 The Model 3.9.2 Problemset Exercises on the Extended IS-TR Model 29 29 31 33 33 33 34 34 39 42 45 45 45 45 46 47 47 47 48 48 51 51 51 53 The 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 CONTENTS The Macroeconomy in the Medium Run 4.1 The Supply Curve 4.1.1 The Firm’s Pricing Problem 4.1.2 Wage bargaining 4.1.3 The Supply Curve 4.2 The Demand Curve 4.3 The AD-AS model in the normal time 4.4 Problemset Exercise on the Normal Time Medium Run 4.4.1 Problem 4.1 4.5 The AD-AS Model During Deep Crisis 4.5.1 Problem 4.2 4.5.2 The Non-conditioned π ZLB Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) 57 57 58 58 59 59 60 61 61 63 63 67 lOMoARcPSD|2935381 Chapter Macroeconomic Measurement The measurement of economic performance is the prelude to sensible economic analysis which provides us with the understanding of how the economy works Understanding how the economy works helps business leaders (I mean you!) making the right decisions given the changes in major macroeconomic variables such as unemployment, inflation, economic growth, stock market indexes, and the exchange rate of the domestic currency against major trade partner currencies Good measurement of the development of main economic indicators is also of vital importance for the government to make good policy responses to the ailments of the economy, thus avoiding painful and prolonged periods of economic downturns For politicians, having a good team of economic advisers is also the key to keep the economy’s performance at an acceptable level, thus raising their chance of being in power 1.1 1.1.1 GDP The three approaches to measurement Gross domestic product, or GDP, is the market value of all final goods and services produced within a country in a given period of time (recall your OVWL discussions) Although GDP is not a perfect measure of economic well being1 , higher GDP is strongly correlated with higher living standards, longer longevity, better health care, more quality education as well as a larger number of other services that people enjoy Three approaches to measuring GDP are: Product approach (measuring the contribution of each stage of the production process, answering the question What is being produced); Income approach (how the profit of the production process is divided among owners of the factors of production in the economy, answering the question (Who gets the income generated by the production mentioned in the product approach); and Expenditure approach answering the question Who buys the goods/services created in the production process mentioned in the product approach Regardless of which approached being employed, the same value of GDP should be obtained In practice, however, there often exist the differences between these approaches due to the problem of statistical discrepancies Talking of GDP, two salient features arise: 1) In most if not all countries, GDP increases over a long period of time (increasing trend); however, 2) the development of GDP is far from smooth, meaning that actual GDP fluctuates around this trend These observations give rise to the study of the economy in the long run, and the short run, as we will proceed in this courses 1.1.2 Real vs Nominal GDP In the year 1985, a lunch portion similar to that at the VGU canteen cost about VND Now you pay about 20,000 VND In the same year 1985, the lunch would cost 0.4 USD Now you pay roughly 0.78 USD X · qit , (Nominal GDP)t = p } | {z } | it{z t price of good/service i in year t quantity of good/service i in year t When comparing values of nominal GDP across different years, this generally involves both changes in quantities and prices, and thus does not allow to infer about changes in the standard of living To allow for such inference, real GDP adjusts for price changes and reflects the sum of the value added produced by all Suffers from such limitations as excluding home production, disregarding environmental degradation, not taking income distribution and other indicators of happiness into account Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 CHAPTER MACROECONOMIC MEASUREMENT firms in the country in terms of only one set of prices, namely those of the so-called base year • The Laspeyres approach to computing real GDP involves using initial year prices as the base-year prices: N X Laspeyres Laspeyres pi0 × qit , t = 0, 1, , T, = Yt = (Real GDP)t i=1 implying the growth rate of real GDP: 1+ gYLaspeyres t = N P pi0 × qit i=1 N P , t = 0, 1, , T, pi0 × qi,t−1 i=1 The main problem with the Laspeyres approach is that as one moves from the initial year (t = 0) to the final year (t = T), Laspeyres-based real GDP over-states more and more the contribution to GDP of goods and services that are becoming less and less expensive • The Paasche approach to computing real GDP involves using final year prices as the base-year prices: (Real GDP)Laspeyres = YtLaspeyres = t N X piT × qit , t = 0, 1, , T, i=1 implying the growth rate of real GDP: + gYLaspeyres = t N P piT × qit i=1 N P , t = 0, 1, , T, piT × qi,t−1 i=1 The main problem with the Paasche approach is that as, starting in the final year (t = T), one moves back in time towards the initial year (t = 0), Paasche-based real GDP over-states more and more the contribution to GDP of goods and services for which the price is continuously rising from the initial year to the final year • The Annual Chain Weight approach aims to overcome these (opposing) biases of the Laspeyres and Paasche approaches and computes real GDP using the geometric average of results for the Laspeyres and Paasche approaches, with annually updated base years: v u N N P u P u pi,t × qit p × q i,t−1 it u i=1 i=1 Chain Weight u × , = + gYAnnual uP t N P u N pi,t−1 × qi,t−1 pi,t × qi,t−1 u u i=1 i=1 u| | {z } {z } t Annual Annual Paasche Laspeyres t = 0, 1, , T Annual Chain Weight (Real GDP)0 = Y0Annual Chain Weight = N X pi0 × qi0 i=1 and, Annual Chain Weight Chain Weight ) × Yt−1 YtAnnual Chain Weight = (1 + gYAnnual t 1.2 1.2.1 Other important macroeconomic gauges: GNP GNP = GDP + Net Factor Income From Abroad (NFIA) • NFIA = Values of (exports - imports) of factor services Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 1.2 OTHER IMPORTANT MACROECONOMIC GAUGES: • Export of factor services: – A Vietnamese person working in Japan on a labor export contract for years who earns an annual income of 10,000 USD – Viettel Group invests in Myanmar and made a profit of 10 million USD in 2017 • Import of factor services: – Dr Michel Toulouse, a Canadian, working at VGU as the coordinator of the Computer Science program His income is an example of the import of labor (a factor of production of education service) – Samsung Vietnam posted billion USD in profit from their smart phone business in Vietnam in 2017 1.2.2 PPP-based GDP How to compare the levels of GDP per capita across countries, which are measured in different currencies? This task is complicated by the fact that prices of traded goods relative to those of non-traded goods tend to be sizably higher in "poor" countries than in "rich" countries, and that pricing of market exchange rates is more closely related to the pricing of traded than of non-traded goods Purchasing power parity (PPP) exchange rates use a standardized basket of traded and non-traded goods and services across the countries in question, estimating the market value of the basket in the rich countries currency, Vrich , using the rich country’s currency; and the market value of the same basket in the poor country using the poor country’s V currency, Vpoor The PPP-based exchange rate is computed as: EXppp = Vpoor rich The PPP-based GDP is calculated using the EXppp instead of the market exchange rate As illustrated in the class, using market exchange rate the GDP per capita in Vietnam is about 2,200 USD However, using the PPP-based exchange rate, it’s about 7,000 USD The idea of the purchasing power parity is to ask: to live like a typical Vietnamese, how much would an American has to pay? Normally, the prices of non-tradable goods and services in Vietnam are lower than in the US, thus PPP-based GDP per capita in Vietnam is higher than the GDP per capita in current GDP The story will be reversed if we compare a country like Qatar and the USA In Qatar, most services are more expensive than in the USA, thus PPP-based GDP per capita for Qatar is lower than the GDP per capita in current USD Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 CHAPTER MACROECONOMIC MEASUREMENT Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 Chapter The Long Run Macroeconomy Figure 2.1: Long-run Economic Growth • Figure (1.1) presents the graph of GDP per capita (measured in purchasing power parity dollar) from the year 0001 to 2010 for some countries, including Vietnam1 Of course with such critical VGU minds, you all may simultaneously utter some objection: how they measure income from such a far distance in history? I can’t tell you All I know is that some prestigious professors have spent all of their life devising methods to estimate the mankind’s living standards over the last two millennia Still, they may have made some gross mistakes and all the data created are nothing more than the guesswork True! It is hard to accept but most of what we know about our own history is guesswork (and the rest is pure prejudice) So if we all for this moment contend with what we have at hand, Figure (1.1) tells some interesting story Figure 2.2: Vietnam’s GDP Per Capita Since 1820 We, mankind as one, have lived most our life in the last two thousand years around the subsistence level, i.e we just had barely enough to eat and hardly enough to cover our body In developed countries, the living standard only experienced a sustainable pick up sometime at the middle of the 18th century Yeah, if you happen to like the history subject during the high-school time, you may also recall that mid-18th The data can be downloaded from here: http://www.ggdc.net/maddison/oriindex.htm Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 10 CHAPTER THE LONG RUN MACROECONOMY century also marked the introduction of new technologies that had never existed before, namely the steam engines, and together with its, came the steamships, steam spinning, steam trains and many other ensuing inventions These newly invented technologies lifted people’s lives above the subsistence level People in some Western countries suddenly found themselves unable of eating everything they had made So they saved those redundant products for future use The future life, thus, became better thanks to the fact that people would be able to consume both the saving now with the production of the future As the story goes, humankind has become richer and richer over the last two centuries • Figure (1.2) in combination with Figure (1.1) tells the story of Vietnam Like the rest of the world, our ancestors spent all of their lives living at the subsistence level Things only started to look a little bit brighter in the 1990s Before that, we suffered decades of wars, war against the US, war against China, and war against ourselves Each war was followed by a sharp drop in our parents’ and grandparents’ hard-earned standard of living • It’s beyond the scope of this manual, to say anything less superficial than that when it comes to the history of economic development However, this manual as part of the great BMAK course, will equip you with the models so that once mastering them, you are able to tell a much deeper story in your own way Before we start, let’s send our special thank to Nobel Laureate Robert Solow, who put up such a powerful analytical framework we know as the Solow Growth Model 2.1 The Solow Growth Model The Solow model is powerful in explaining why humankind has, over the last two centuries, and Vietnam has, over the last three decades, experienced unprecedented improvement in our living standards In our world today, it seems that production and distribution of goods and services involves a lot of things: human minds, human hands, machines, tools, equipments, factories, roads, ports, know-hows, recipes, and so on Solow suggested that we bundle them into three categories only, namely labor, capital and technology These three ingredients combine available inputs in certain way to produce all the goods and services we enjoy in our daily life A simple, but yet, powerfully way some summarizing this process is to define a production function as: Yt = F (Kt , At , Lt ) = Ktα (At Lt )1−α where Kt , Lt , and At are capital, labor, and technological progress, respectively At any point in time, ∂Y = αKt1−α (At Lt)1−α is defined we have Kt units of capital, Lt of labor, and At units of know-hows ∂K t as the marginal product of capital This is also the share of goods and services that we pay to capital owner per unit of capital they own Capital owners own Kt units of capital at time t, and their income is: ∂Y = Kt · αKt1−α (At Lt)1−α or α · Ktα (At Lt)1−α = α · Yt Kt · ∂K t • You may wonder why we need to bundle labor and technology into one and call this composite factor as effective units of labor For the sake of exposition, imagine that each worker is a capsule of two things, their labor (L), and their skills (A) that are embodied within them So an ALRonaldo = 1000·ALCongP huong at the market price as of 2013 As individual human beings, there is no meaning, and we have no right to compare Cristiano Ronaldo with Nguyen Cong Phuong However, as effective workers in the football industry the market valued Ronaldo 1000 times more than Cong Phuong • This is the very point I reiterated during the lectures, students are workers working so hard to increase the A factor within themselves If you not read the text by Burda and Wyplosz, and other accompanying documents, not to mention dozing over during the lectures, blame yourself for the fact that Vietnam is poorer than Germany even though the two countries are comparable in terms of the number of human beings Let us dream of a day when one Vietnamese worker is valued as 15 Chinese, and we will forever escape the agonizing feeling of living next to a giant and cruel neighbor • Similar to the case of capital, the salary paid to an effective unit of labor is its marginal product, ∂Y α −α , and so the total wages and salaries paid to workers are At Lt·(1−α)Ktα (At Lt)−α = ∂AL = (1−α)Kt (At Lt) α 1−α (1 − α) · Kt (At Lt) = (1 − α) · Yt In other words, if α = 0.3 and Vietnam’s GDP is USD 240 billion, USD 80 billion will be paid to capital owners in the form of rent and depreciation, while USD 160 billion will be paid to the workers (and their effectiveness factors) in the form of wages and salaries Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 54 CHAPTER THE SHORT RUN MACROECONOMY value of φy , the steeper, that is, the more positive the slope of the extended TR-curve in the range Y > Y ZLB • Case 2: Y < Y ZLB When Y < Y ZLB , the slope depends only on the parameter ry reflecting how sharply the endogenous risk premium changes once output changes The larger the magnitude of ry , the steeper, that is, the more negative the slope of the extended TR-curve in the range Y < Y ZLB b) What is the value of output in the short-run macroeconomic outcome? Answer: The IS equation is (you have to derive it yourself!) Y = A C r + I r + Gr + T B ǫ · ǫ r − · r − Cy + T Bim − Cy + T Bim (3.17) Where A = C0 + I0 + G0 + T B0 + T Bex · (Y ∗ − T ∗ ) + T Bǫ · (ǫ0 + ǫr r∗ ) − Cy · T + T Bim · T Rewrite the IS in a more compact form as: Y = IS0 − IS1 · r The definition of IS0 and IS1 should be clear from the context First, we need to compute the zero-lower bound output: r¯M P + φy Y ZLB −Y¯ Y¯ Y ZLB = − MP r¯ φy Y ZLB = 14.70 =0 Y¯ How to proceed from here? We not really know if the level of actual output is below or above the Y ZLB The strategy here is to assume that initially Y < Y ZLB , using the extended TR-curve: r = r¯RP − ry · Y − Y ZLB Plugging r into the IS curve to get: Y = IS0 − IS1 r¯RP − ry · Y − Y ZLB Y = IS0 − IS1 r¯RP + ry · Y ZLB + IS1 ry · Y (1 − IS1 ry ) · Y = IS0 − IS1 r¯RP + ry · Y ZLB IS0 − IS1 r¯RP + ry · Y ZLB Y = − IS1 ry (3.18) Plugging the parameters, IS0 = 13.97; IS1 = 33.33; and Y ZLB = 14.70 into (2.133), the short run outcomes are: • Y = 13.42 The results indeed show that the economy is in a deep crisis The short run interest rate is computed as: • r = r¯RP − ry · Y − Y ZLB = 0.0164 c) Calculate the effects on domestic short-run output of a simultaneous increase of the exogenous component of the risk premium, r¯RP , by 0.02, and of the foreign real interest rate, r∗ , by 0.01? Decompose the overall output effects into its components (that is, the Keynesian multiplier induced effect and the domestic interest rate induced crowding out/in effects) Make sure to provide, in addition to numerical results, a detailed Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 3.9 THE EXTENDED IS-TR MODEL 55 economic rationale as to how the various effects arise Answer: From question b), we know that the economy’s short run output is below Y ZLB The simultaneous shocks from r¯RP and r∗ are negative and positive, respectively Again, using the extended IS-TR system to get: Y = IS0 − IS1 · r¯RP − IS1 · ry · Y ZLB − IS1 · ry (3.19) Plugging the parameter values into (2.134) to get: Y = 12.64 Using this value in (2.136) yields the value of the new even deeper crisis interest rate as: r = 0.0403 Now we need to decompose the impact of the composite shock that hit the economy To decompose the overall output effects into its components, first notice that: ∆Y = ∂Y ∂A ∆A + ∂Y ∂r ∆r, ∂A ∗ where ∆A = ∂r = T Bǫ ǫr ∆r∗ and ∆r = ∆¯ rRP − ry ∆Y Further, we could compute the change in A, ∗ ∆r and r using the available information as: ∆A = 1.1.0.01 = 0.01 ∆r = 0.02 − 0.005(12.64 − 13.42) = 0.0239 The overall effect can now be decomposed as • The autonomous components, the KM effects: ∂Y ∂A ∆A = KM · ∆A = 1.666666667 · 0.01 = 0.1666666667 where the value of KM is taken from Problem (3.7) • Crowding-out of consumption: r − 1−CyC+T Bim ∆r = −0.1195 • Crowding-out of investment: r − 1−Cy I+T Bim ∆r = −0.5975 • crowding-out of government spending r − 1−CyG+T Bim ∆r = −0.039833333 • crowding-out of trade balance 1−Cy +T Bim · T Bǫ ǫr ∆r = −0.039833333 Economic Rationale: There is a notably rich set of adjustments An increase of the foreign interest rate results in a right shift of the IS-curve, reflecting the spot depreciation of the domestic currency, and the resultant improvement of the trade balance However, at the same time there is an increase in the exogenous component of the domestic risk premium, that is, a parallel shift of the extended TR-curve upwards, which (from the calculations above) more than offsets the effects induced by the increase of the foreign interest rate As the economy is already in a crisis and output is below the Y ZLB threshold the central bank cannot mitigate the negative effect of the increase in the risk premium As the interest rate at which households, firms and the government can borrow increases a crowding-out will occur through the consumption, investment, government expenditure and the exchange rate/trade balance channels In addition, due to the decrease in output the endogenous component of the risk premium rises as well which exacerbates the overall negative output effect Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 56 CHAPTER THE SHORT RUN MACROECONOMY Problem 3.19 On the Extended IS-TR model: Suppose an economy is in a deep contraction, and features a large current account deficit The costs of borrowing for households and firms in this economy are high due to a high overall risk premium The central bank of this economy operates at the zero lower bound, and the fiscal authorities of this economy have fiscal space The economy’s policy makers consider two options: (i) expansionary fiscal policy; (ii) unconventional monetary policy in the form of purchases of government bonds at all maturities Use an Extended IS-TR model of the form given in Problem (3.9) to contrast how the different policies will affect the economy’s short-run output and current account Make sure to provide, in addition to a graphical analysis, a detailed economic rationale as to how the output and current account effects under the different policy options arise Can the sign of the output and current account effects be predicted without knowledge of the numerical values of the model parameters? Explain your reasoning Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 Chapter The Macroeconomy in the Medium Run 4.1 The Supply Curve Figure 4.1: A Recall of the Economy in the Short-run In the previous chapter, we defined the short run as the short enough period so that price remain constant Firms not change their price, workers not bargain to change their wages, and suppliers not negotiate to change the price of inputs In this setting, supply responds to demand and firms provide what ever quantity demanded by driving down or building up their inventories • By the medium run, we consider the time frame long enough for firms to change their price, workers to demand higher wages, and supplier to negotiate a new deals When all prices and wages fully adjust, the economy fully recover from the shocks and settles at the potential (by potential we mean most comfortable output level That is also when the economy comes back to its long-run output level we are so familiar with in the Solow Growth Model • I feel imperative to put a note here on difference between macroeconomic analysis in the short and medium run, with the macroeconomic analysis in the long run Through out discussion, it seems to me that some of you are disappointed that after tireless rounds of adjustments, the economy comes back to the potential output, without any further progress There is no contradiction here Recall that the potential output is the most comfortable level of production and the economy should operate at that point In the short and medium runs, the economy is shocked by unexpected factors beyond our control and could enter costly rounds of bounce and busts and we need the insights from the short and medium run models to devise counter measures to keep the economy stable, to stay on the long-run potential path of development 57 Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 58 4.1.1 CHAPTER THE MACROECONOMY IN THE MEDIUM RUN The Firm’s Pricing Problem In the medium run, firms can adjust price and have to accept changes in wages So the firm’s maximization problem is: Π ≡ max P · Y = Y W |{z} ∂Π ∂Y ∂Π ∂Y L |{z} =P +Y · ∂P ∂Y −W · k · K} |r {z − , (4.1) Treated as fixed Given nomila wages Labor hours The F.O.C is: Setting · ∂L ∂Y = yields: ∂P ∂Y P +Y · P 1+ Y P ∂L − W · ∂Y =0 W ∂P = ∂Y · ∂Y ∂L Note that in this step we have used the property of the derivative of an inverse function W = P 1− η λ |{z} {z } | ∂y ∂x · ∂x ∂y = ∂x ∂x = (4.2) marginal cost marginal revenue where η = −(∂Y /∂P )/(Y /P ) is the price elasticity of aggregate demand and λ is the marginal product of labor Recall from the lecture that the degree of pricing power of the firms, that is, the extent to which they can charge mark-ups (which we will denote by θ) on their goods and services is inversely related to η From equation (3.2), we have: P− P η = MC P − MC | {z } = (Absolute)mark−up Denoting the mark-up as θ = P M Cη , P η (4.3) we obtain the following expression for the pricing of goods and services: P = (1 + θ) · M C = (1 + θ) · W λ (4.4) Again, taking the logarithm of both sides and take the total differentiation of the resulting equation to get: ∆P P or in terms of the inflation rate: π= 4.1.2 = ∆θ 1+θ + ∆W W − ∆λ λ ∆θ ∆W ∆λ + − 1+θ W λ (4.5) Wage bargaining Workers negotiate their wages based on their expectation of future inflation, labor productivity, and how tight the labor market is The situation of the labor market is determined by the state of the economy relative to the long-run potential output Thus: ∆λ Y − Y¯ ∆W e =π + + |{z} ω (4.6) W λ Y¯ ω>0 Substituting (3.6) into (3.5) yields: π= ∆θ 1+θ + πe + ∆λ λ + |{z} ω Y −Y¯ Y¯ − Y − Y¯ Y¯ ω>0 ∆θ + π e + |{z} ω π= 1+θ ω>0 ∆λ λ (4.7) Besides, the economy constantly faces supply shocks which can be formalized by including a term s into (3.6) as: ∆θ Y − Y¯ e π= +π +ω +s (4.8) 1+θ Y¯ Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 4.2 THE DEMAND CURVE 4.1.3 59 The Supply Curve Notice in equation (3.8) that price (π) still depends on two other unknowns One way to move forward is to work out how firms/workers form their inflation expectation In this context, we assume adaptive inflation expectation π e = πt−1 The supply curve in the medium run becomes: Y − Y¯ ∆θ +ω +s (4.9) π = πt−1 + 1+θ Y¯ Figure 4.2: The Medium Run Supply Curve 4.2 The Demand Curve The TR curve in the medium run is different from the TR curve in the short run by the inclusion of the inflation term: Y − Y¯ r = r¯M P + φy + φπ π − π T + r¯RP (4.10) ¯ Y And the IS curve is the same as the short run IS curve: Y = A (Cr + Ir + T Bǫ · ǫr ) + ·r − (Cy − T Bim − Gy ) − (Cy − T Bim − Gy ) | {z } | {z } = IS0 (4.11) = IS1 Combining (3.10) and (3.11) yields: MP Y = IS0 − IS1 · r¯ + φy Y − Y¯ RP + φπ (π − πT ) + r¯ Y¯ φ Y = IS0 − IS1 · r¯M P − φy − φπ πT + r¯RP − IS1 Y¯y · Y − IS1 φπ π φ IS1 φπ π = IS0 − IS1 · r¯M P − φy − φπ πT + r¯RP − (IS1 Y¯y + 1) · Y Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) (4.12) lOMoARcPSD|2935381 60 CHAPTER THE MACROECONOMY IN THE MEDIUM RUN IS1 · φy + φπ πT − r¯M P − r¯RP + IS0 Y¯ + φy IS1 πt = − · Yt IS1 φπ IS1 φπ Y¯ This is the demand curve of the economy in the medium run (4.13) Figure 4.3: The Demand Curve in the Medium Run Why is it the case that the medium run demand curve slope downward? As the rate of inflation increases, the central bank, following the Taylor rule, raises the monetary policy rate, in turn causing (for a given risk premium) the real interest rate at which households and firms can borrow to increase Through the consumption, investment and exchange rate channels, this lowers output Figure 4.4: The Reason Medium Run Demand Curve Slope Downward 4.3 The AD-AS model in the normal time So armed with the supply: π= ∆θ 1+θ + πe + ω Y −Y¯ Y¯ +s Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 4.3 THE AD-AS MODEL IN THE NORMAL TIME 61 and demand curves: π= IS1 ·[φy +φπ πT −¯ r M P −¯ r RP ]+IS0 IS1 φπ − Y¯ +φy IS1 IS1 φπ Y¯ ·Y We are in a very good position to discuss how the economy response to shocks and how the central bank behaves Let’s some problems: 4.3.1 Problem 4.1 On the AS-AD model: An economy with sticky prices (for which foreign variables are exogenous) is described by the following model: Yt = DDt = Ct + It + Gt + T Bt ; Ct = C0 + Cy · (Yt − T ) − Cr · rt ; I t = I − I r · rt ; G t = G − G r · rt ; T Bt = T B0 + T Bex · (Y ∗ − T ∗ ) − T Bim · (Yt − T ) + T Bǫ · ǫt ; ǫt = ǫ0 + ǫr · (r − r∗ ) Y¯ + φπ (πt − π T ); RtM P = r¯M P + π e + φy · Y Y− ¯ Y¯ rt = RtM P − π e + r¯RP ; πt = π e + ω · YtY− + s ¯ When numerical calculations are asked for, assume the following parameter values: C0 = 1.6; Cy = 0.55; Cr = 3; T = 2.5; I0 = 3.25; Ir = 15; G0 = 2.8; Gr = 1; T B0 = 0; T Bex = 0.1; Y ∗ = 10; T ∗ = 3; T Bim = 0.15; T Bǫ = 1; ǫ0 = 1; ǫr = 1; r∗ = 0.03; r¯M P = 0.02; φy = 1; Y¯ = 15; r¯RP = 0.01; π e = 0.02; φπ = 2; φy = 1; π T = 0.02; ω = 0.05; s = a) Derive the AD - curve Provide detailed economic reasoning for the AD - curve derived, namely, how an increase in the medium-run rate of inflation,πt , affects medium-run output, Yt Answer: Recall from Problem (3.7): Y = C r + I r + Gr + T Bǫ · ǫ r A − · r − Cy + T Bim − Cy + T Bim (4.14) Where A = C0 + I0 + G0 + T B0 + T Bex · (Y ∗ − T ∗ ) + T Bǫ · (ǫ0 + ǫr r∗ ) − Cy · T + T Bim · T However, it is more convenient to go one step further to rewrite the IS curve in the form: Yt = IS0 − IS1 · rt , (4.15) where the definition of IS0 and IS1 should be clear from the context • The TR curve in the medium run is the defined as: rt = RtM P − π e + r¯RP = r¯M P + φy Yt − Y¯ + φπ (πt − π T ) + r¯RP ffl Using the formula of r given by the TR curve in the IS curve yields: Y − Y¯ RP Y = IS0 − IS1 · r¯M P + φy + φ (π − π ) + r ¯ π T Y¯ φ Y = IS0 − IS1 · r¯M P − φy − φπ πT + r¯RP − IS1 Y¯y · Y − IS1 φπ π φ IS1 φπ π = IS0 − IS1 · r¯M P − φy − φπ πT + r¯RP − (IS1 Y¯y + 1) · Y IS1 · φy + φπ πT − r¯M P − r¯RP + IS0 Y¯ + φy IS1 π= − ·Y IS1 φπ IS φ Y¯ | {z } | 1{zπ } ≡ AD0 (4.16) (4.17) (4.18) ≡ AD1 Economic Rationale: The AD-curve features a negative slope An increase in inflation induces the central bank to set a higher nominal policy rate For given inflation expectation and risk premium, this raises the interest rate faced by households, firms and government, corresponding to crowding-out via consumption, investment, government and exchange rate channels This reduces aggregated demand and thus output There is a negative relationship between inflation and output Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 62 CHAPTER THE MACROECONOMY IN THE MEDIUM RUN • b) Obtain the medium-run macroeconomic outcome The AD curve is given by: π = AD0 − AD1 · Y And the AS curve is given by: ω Yt − Y¯ ω e + s = π e − ω + s + ¯ · Yt = π e − ω + s + ¯ ·Yt πt = π + ω · | {z } Y¯ Y Y |{z} ≡ AS0 (4.19) ≡ AS1 Combine both equations: AD0 − AD1 · Yt = AS0 + AS1 · Yt output is obtained as: Yt = AD0 −AS0 AD1 +AS1 The resulting value of output Yt is 14.40967742 Plugging this value in the AD equation to get the value of πt as: 0.018032258 c) Calculate the effects on medium-run output and inflation of a fiscal stimulus in the form of a decrease of (domestic) income taxes, T, by 0.25 Provide a detailed economic rationale as to how the medium-run output and inflation effects arise Answer: • The impact of a change in taxes on output is defined as: ∆Yt = is to compute ∂Y ∂T ∂Y ∂T · ∆T ∆T is given Our next task AD −AS ∂Y ∂T = = = = ∂AD0 ∂T ∂ AD0 +AS0 1 ∂T · AD1 +AS1 ∂IS0 ∂T φπ ·IS1 · AD1 +AS1 ∂A 1 ∂T 1−Cy +T Bim φπ ·IS1 · AD1 +AS1 1 = (T Bim − Cy ) 1−Cy +T Bim φπ ·IS1 · AD1 +AS1 Plugging in the relevant parameters yields ∂Y /∂T = −0.193548387 The change in out put is given by: ∆Y = ∂Y /∂T · dT = −0.193548387 · (−0.25) = 0.048387097 • The change in inflation due to the change in government spending is defines as ∂πt /∂T · ∆T ∂πt ∂T = ∂AS0 ∂T + ∂πt ∂T ∂AS1 ∂T · Yt + ∂Yt ∂T · AS1 = ∂Yt ∂T · AS1 Thus, the change in inflation due to a change in T is given by: ∆πt = 0.00016129 ∂πt ∂T ∆T = ∂Yt ∂T · AS1 · ∆T = Economic Rationale: Lower domestic income taxes increase disposable income of households This increases consumption and decreases the trade balance, enforced by the Keynesian multiplier In the short-run, the higher desired demand increases output The central bank increases interest rates, which leads to a partial crowding-out of consumption, investment, government expenditure and trade balance (movement from A to B) In the medium-run, the higher output translates into higher wage mark-up, increasing inflation The central bank increases interest rates even more, leading to a further crowding-out of aggregate demand (movement from B to C) Overall, we end up with higher output and inflation than before Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 4.4 THE AD-AS MODEL DURING DEEP CRISIS 63 Figure 4.5: The Impact of a Decrease in Income Taxes 4.4 The AD-AS Model During Deep Crisis The discussion is done during class sessions So we will focus on the problem set questions only 4.4.1 Problem 4.2 On the extended AS-AD model: An economy with sticky prices (for which foreign variables are exogenous) is described by the following model: Yt = DDt = Ct + It + Gt + T Bt ; Ct = C0 + Cy · (Yt − T ) − Cr · rt ; I t = I − I r · rt ; Gt = G − G r · rt ; T Bt = T B0 + T Bex · (Y ∗ − T ∗ ) − T Bim · (Yt − T ) + T Bǫ · ǫt ; ∗ ǫt = ǫ0 + ǫr · (r o n −r ) Y¯ T + φ (π − π ) ; RtM P = max 0, r¯M P + π e + φy · Y Y− π t ¯ MP RP ZLB ZLB rt = Rt − πt−1 + r ¯ − ry · Y t − Y t | πt · I Y t < Y t | πt ; Y¯ πt = π e + ω · YtY− + s ¯ When numerical calculations are asked for, assume the following parameter values: C0 = 1.6; Cy = 0.55; Cr = 3; T = 2.5; I0 = 3.25; Ir = 15; G0 = 2.8; Gr = 1; T B0 = 0; T Bex = 0.1; Y ∗ = 10; T ∗ = 3; T Bim = 0.15; T Bǫ = 1; ǫ0 = 1; ǫr = 1; r∗ = 0.03; r¯M P = 0.02; φy = 1; Y¯ = 15; r¯RP = 0.01; π e = 0.02; φπ = 2; φy = 1; π T = 0.02; ω = 0.05; s = 0; ry = 0.07 • a) Derive the Extended AD-curve Provide detailed economic reasoning for the Extended AD-curve derived, namely, how an increase in the medium-run rate of inflation, πt , affects medium-run output, Yt • Answer: Combine monetary policy rule (with zero lower bound) and the risk premium to obtain the Extended TR-curve: Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 64 CHAPTER THE MACROECONOMY IN THE MEDIUM RUN n = max −π e , r¯M P rt = RtM P − πte + rtRP o Y¯ + φy · Y Y− + φπ (πt − π T ) + r¯RP − ry · Yt − YtZLB |πt · I Yt < YtZLB |πt ¯ • Normal business cycle outcome, RM P > 0: The Extended TR-curve collapses to the standard TRcurve We obtain the same AD-curve as before: πt = AD0 − AD1 · Yt There is a negative relationship between output and inflation • During crisis time, central banks keep cutting the interest rate to encourage demand, thus pushing the economy back to the equilibrium, i.e potential ouput level However, when the crisis is too deep, RM P could be cut to, or close to At this point, the central runs out of ammunition, and cannot cut RM P further, at least too much below the zero level We face the problem of zero lower bound, the situation in which output falls below the threshold potential output level so much that below it, the Taylor rule dictates RM P ≤ We name this threshold as YtZLB |πt , which can be solved as: r¯tM P + πte + φy · YtZLB |πt −Y¯ Y¯ + φπ · (πt − π T ) = r¯tM P + πte − φy + φy · YtZLB |πt Y¯ + φπ · (πt − π T ) = r¯tM P + πte − φy + φy · YtZLB |πt Y¯ + φπ · (πt − π T ) = φy · YtZLB |πt Y¯ YtZLB |πt = = φy − r¯tM P − πte − φπ · (πt − π T ) Y¯ φy φy − r¯tM P − πte − φπ · (πt − π T ) Facing this situation, commercial banks become wary of the fact that their customers have become more risky and face a higher probability of default To compensate for this risk, commercial banks endogenize the risk premium rRP that they would charge their customer This risk premium increases as the actual level of out put falls deeper below the zero lower bound output level, YtZLB |πt This insight is formalized by specifying the risk premium as: rtRP = r¯RP − ry · Yt − YtZLB |πt where ry > The real interest rate facing banks’ customers is: rt = rM P + r¯RP − ry · Yt − YtZLB |πt rtM P = RtM P − πte = −πte because RM P = Therefore, rt = −πte + r¯RP − ry · Yt − YtZLB |πt In this exercise, taking the assumption that inflation expectation is adaptive, and current level of inflation expectation is equal to last period’s inflation, rt = −π t−1 + r¯RP − ry · Yt − YtZLB |πt This is the extended TR curve during crisis time in the medium run Plugging the expression of YtZLB |πt into the extended TR curve yields: n rt = −π t−1 + r¯RP − ry · Yt − rt = −π t−1 + r¯RP − ry · Yt + ry · Y¯ φy Y¯ φy (φy φy − r¯tM P − πt−1 − φπ · (πt − π T ) − r¯tM P − πt−1 + ·φπ · π T ) − ry · Plugging this result into the IS curve yields: Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) Y¯ φy o · φ π · πt lOMoARcPSD|2935381 4.4 THE AD-AS MODEL DURING DEEP CRISIS 65 n Yt = IS0 − IS1 · −πt−1 + r¯RP − ry · Yt + ry · n Yt = IS0 − IS1 · −πt−1 + r¯RP + ry · Y¯ φy Y¯ φy φy − r¯M P − πt−1 + φπ π T ) − ry · φy − r¯M P − πt−1 + φπ π T ) n Yt (1 − IS1 · ry ) = IS0 − IS1 · −πt−1 + r¯RP + ry · Y¯ φy o Y¯ φ y φ π πt o ¯ + IS1 · ry · Yt + IS1 · ry · φYy φπ πt φy − r¯M P − πt−1 + φπ π T ) o + IS1 · ry · Y¯ φ y φ π πt ¯ h n − IS0 − IS1 · −πt−1 + r¯RP πt = − IS1 · ry · φYy φπ πt = oi ¯ + Yt (1 − IS1 · ry ) + ry · φYy φy − r¯M P − πt−1 + φπ π T ) n IS0 − IS1 · −πt−1 + r¯RP + ry · | Y¯ φy IS1 · ry · {z φy − r¯M P − πt−1 + φπ π T ) Y¯ φy φ π ]0 ≡ AD o } + (1 − IS1 · ry ) IS1 · ry · {z | Y¯ φy φπ ]1 ≡ AD ·Yt } ]0 + AD ]1 · Yt πt = −AD Figure 4.6: The extended AD curve Economic Rationale: Technically in the deep crisis scenario, the AD-curve is upward-sloping A decrease in inflation increases the level of output at which the central bank hits the zero lower bound Thus, the endogenous risk premium matters at higher levels of output than before, and is higher for any given Y < YtZLB |πt This causes crowding-out of aggregate demand There is a positive relationship between in ation and output • Intuitively, inflation often falls during recessions when demand is low, firms cut their output, and therefore, employment Cuts in employment lead to the loss of income, thus lowering demand further Lower demand leads to lower price, i.e a further decrease in inflation When the economy has reached the trough of the business cycle, i.e the worst point, ineffective firms are driven out of the market due to bankruptcy, only efficient firms remain These efficient firms also cut their prices along the way ( due to lower costs as a result of wage cuts and decreases in input price) to the level that prices are considered as low, demand starts to pick up As we discuss in the short run, firms respond to short run Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 66 CHAPTER THE MACROECONOMY IN THE MEDIUM RUN increase in demand by changing their inventories However, as the increase in demand is sustained, they start to increase production, call back their former employees, and stop cutting prices, and perhaps they may also start to consider more investment to meet the future demand With higher employment, higher investment, demand continues to increase, leading to the first increase in price, i.e inflation • The message of this discussion is that during crisis time, further falls in prices (inflation) constitutes a signal of a worsening situation, thus raising the risk premium banks want to charge, and lowering demand In the reversed situation, increases in inflation signal the recovery from a deep recession/crisis, enticing banks to cut the risk premium, and therefore, the interest rate they charge, pushing the demand curve to the right The demand curve will keep shifting to the right until the economy is strong enough that the central bank decides to increase its RM P rate, marking the end of the deep crisis period and bringing the economy back to its normal AD-AS model Note that this is also in line with the explanation we have in the case of the Extended IS-TR, the only difference is now we are in the medium run, having a lot of short run periods (with different price levels) pieced together in a time line b) Obtain the values of output and inflation in the medium-run macroeconomic outcome (suppose that πt−1 = 0.02) ]0 + AD ]1 · Yt , combining with the supply curve given as • From a) the demand curve is given by πt = −AD πt = π e + ω · πt = π e + ω · Yt −Y¯ Y¯ Yt Y¯ +s −ω+s πt = π e − ω + s + ω Y¯ · Yt ω πt = π e − ω + s + ¯ ·Yt | {z } Y |{z} ≡ AS0 ≡ AS1 the medium run macroeconomic outcome is: Yt = ]0 AS0 +AD ]1 −AS1 AD ]0 = 1.35; AD ]1 − AS1 = 0.11; AS0 = −0.03; AD1 = 0.0033 Plugging Using the available information, AD these parameters in the expression of Yt yields: Yt = 12.37 πt = 0.011 If you take all decimals, Yt = 12.4529148, and πt = 0.011509716 c) Graphically analyze in the AS-AD diagram the effects of a fiscal contraction in the form of an increase of (domestic) income taxes, T, under the assumption that the initial medium-run macroeconomic outcome for output is the one given in part (b) In addition to a graphical analysis, provide a detailed economic rationale as to how the medium-run output and inflation effects arise • Answer: An increase in domestic income taxes reduces disposable income for households, therefore reducing aggregate demand, enforced by the Keynesian multiplier The decrease in output triggers an increase in the risk premium, thus leading to a crowding-out of consumption, investment, government expenditure and trade balance In the short-run, we end up in point B Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 4.4 THE AD-AS MODEL DURING DEEP CRISIS 67 Figure 4.7: Increase of domestic income taxes during deep crisis time • In the medium-run, the lower output translates into lower wage mark-ups, thus leading to lower inflation The lower inflation increases YtZLB |πt , thus increasing the risk premium, leading to a further crowding-out of demand (B to C) Due to adaptive inflation expectations, these are revised downwards, such that the real interest increases, leading to a further crowing-out The AD-curve shifts to the left, the AS-curve downwards We end up with lower output and inflation 4.4.2 The Non-conditioned π ZLB We have derived the formula for YtZLB |πt as: YtZLB |πt = Y¯ φy φy − r¯tM P − πte − φπ · (πt − π T ) It is natural to ask, what is the level of inflation when the RM P hits the zero lower bound? Similarly, we can set RM P = 0, and solve for the πtZLB |Yt , which satisfies the RM P = condition at different values of Yt Figure 4.8: πtZLB |Yt when RM P = r¯tM P + πte + φy · r¯tM P + πte + φy Y¯ Yt −Y¯ Y¯ + φπ · (πtZLB |Yt − π T ) · Yt − φy + φπ · πtZLB |Yt − φπ · π T = φπ · πtZLB |Yt = φy − r¯tM P − πte − πtZLB |Yt = π T + φπ φy Y¯ · Yt + φ π · π T φy − r¯tM P − πte − φy Y¯ ·φπ · Yt At the kinked point, πt = πtZLB |Yt , and Yt = YtZLB |πt , the extended TR curve sets: Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com) lOMoARcPSD|2935381 68 CHAPTER THE MACROECONOMY IN THE MEDIUM RUN rt = r¯M P + rtRP = −π e + r¯RP because the term Yt − YtZLB |πt in rt = −πte + r¯RP − ry · Yt − YtZLB |πt drops out Using this result in the IS curve yields: Yt = IS0 − IS1 · −π e + r¯RP Therefore, πtZLB |Yt = π T + φy φy − r¯tM P − πte − ¯ · IS0 − IS1 · −π e + r¯RP = π ZLB φπ Y · φπ (4.20) Equation (3.20) shows that πtZLB |Yt does not depend on the value of Yt , it is known at the non-conditioned π ZLB Downloaded by EBOOKBKMT VMTC (nguyenphihung1009@gmail.com)