QUEEN S UNIVERSITY FACULTY OF ARTS AND SCIENCE DEPARTMENT OF ECONOMICS

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1 QUEEN S UNIVERSITY FACULTY OF ARTS AND SCIENCE DEPARTMENT OF ECONOMICS Economics 222: Macroeconomic Theory I Midterm Examination, Answer Key May 26, 2009 Instructor: Monica Jain Duration: 1.5 hours (90 minutes) INSTRUCTIONS: Use the EXAMINATION BOOKLETS to answer. Show ALL RELE- VANT STEPS. Calculators: non-programmable, Casio 991, blue sticker, gold sticker. Part A (Short Questions, True/False/Uncertain): Do FOUR of the SIX questions. State whether you think the statement is true/false/uncertain, and explain why, using the appropriate diagrams if applicable. No marks will be given for answers lacking an explanation. Each question is worth 10 MARKS for a total of 40 MARKS. Part B (Long Questions): Do TWO of the THREE questions. Each question is worth 30 MARKS for a total of 60 MARKS. TOTAL: 100 MARKS. 1

2 Part A Short Questions (True/False/Uncertain) Do four (4) of the six (6) questions. Each question is worth 10 marks, for a total of 40 marks. State whether you think the statement is true/false/uncertain, and explain why, using the appropriate diagrams if applicable. No marks will be given for answers lacking an explanation. Question A1: In a closed economy, it is not possible for the GDP de ator and the CPI to move in opposite directions (for example, the GDP de ator increases while the CPI falls). FALSE. It is possible for the GDP de ator and the CPI to move into opposite directions (for example, the GDP de ator increases while the CPI falls). The GDP de ator measures how fast the prices of goods and services produced domestically change over time; while the CPI measures how fast the prices of goods and services bought by consumers change over time. So, if the prices of goods purchased by consumers fall while the prices of domestically produced goods that are purchased by rms and/or government increase (enough), then the GDP de ator can increase while the CPI falls. In constructing the GDP de ator, it compares the prices of goods and services that are currently produced with the prices of goods and services that are produced in the base year. In computing the CPI, it compares the price of a xed basket of goods and services with the price of the basket in the base year. Therefore, If the quantities of goods and services used in constructing the GDP de ator are more than the quantities of goods and services used in computing the CPI, then it is possible for the GDP de ator to increase and the CPI to fall. By construction di erent goods can be included in the calculation of CPI and GDP de ator (as CPI includes only includes goods and services households buy while the GDP de ator includes all domestic production including those not bought at all by households) thus there is no guarantee both measures will be the same or move to the same direction. The CPI and GDP de ator also each employ di erent weights as (1) the CPI is base weighted while the GDP de ator is current weighted; and (2) the weight attached to the same goods can di er in the calculation of CPI and GDP de ator (as consumers may only buy a portion of the domestic output and rms/government buy the remainder), thus both measures of the average/aggregate price level di er. Question A2: In a closed economy, the impact of a balanced budget change made by the government (i.e. the government increases taxes and government purchases by equal amounts) on national savings depends on the marginal propensity to consume (MPC). 2

3 TRUE. Consider the national income accounts identity for national saving: National Saving = PrivateSaving + PublicSaving = [Y T C(Y T )] + [T G] We know that Y is xed by factors of production. We also know that the change in consumption equals the MPC times the change in disposable income. This means that: National Saving = [ T M P C( T )] + [T G] = [ T + MP C(T )] + 0 = (MP C 1)T: Which tells us that impact on saving of an equal increase in T and G does depend in the size of the MPC. For example, if the MPC = 1, then the fall in consumption equals the rise in government purchases, so national saving is unchanged. The close MPC is to 0, the greater is the impact on saving. Since we assume that the MPC is less than 1, we expect that national saving falls in response to an equal increase in taxes and government spending. Question A3: In a closed economy, an increase in government spending will crowd out investment unless the economy is caught in a liquidity trap. Support your answer with a diagram(s). TRUE. This question goes back to our discussion of Paul Krugman s article "Liquidity preference, loanable funds, and Niall Ferguson". In this article, he compares the usual result in which an increase in government spending causes a rise in the real interest rate and therefore a fall in private investment, to the current situation, in which there is an excess supply of savings even at a zero interest rate. This situation can be depicted as follows: 3

4 So government borrowing would gives some of these excess savings a place to go, and in the process expands overall demand, and hence GDP. It would not crowd out private spending, at least not until the excess supply of savings has been eliminated, which is the same thing as saying not until the economy has escaped from the liquidity trap. Question A4: In an open economy, expansionary scal policy always leads to twin de cits. FALSE/UNCERTAIN. The answer depends on whether Ricardian Equivalence is assumed to hold. An increase in the government budget de cit will raise the CA de cit only if this increase reduces S d. Then, less saving would be sent abroad and the current account would fall. Expansionary scal policy means either G is increased or T falls. The de cit caused by increased government purchases reduces desired national saving causing the CA balance to decline, leading to a twin de cit. The de cit caused by cuts in current taxes will cause S d to fall only if it causes desired consumption to rise. Cuts in current taxes do not raise desired consumption when the Ricardian equivalence holds since people simply save their tax cut to pay of their future debt associated with the tax cut. Empirically, the evidence on the Ricardian equivalence is mixed, so twin de cit logic might still hold. Question A5: A small open economy will always run a current account de cit if it increases government purchases during a war. (note: you may assume CA=NX for this question). Support your answer with a diagram(s). 4

5 FALSE. The answer to this question does depends on the initial current account balance of the small open economy. If the world interest rate is such that the small open economy has a balanced current account (i.e. CA=0), then increasing government purchases would cause the saving curve to shift left and (since a small open economy cannot a ect the world real interest rate) leading to a current account de cit. Similarly, if the small open economy starts o with a current account de cit, increasing goverment purchases leads to an even greater current account de cit. On the other hand, if the small open economy start o with a current account surplus, the increase in government purchases may not be large enough to lead to a current account de cit, but simply reduces the small open economy s surplus. Question A6: In a world with only two large open economies, the equilibrium world real interest rate must equate one country s desired national saving to the other country s desired national investment. Support your answer with a diagram(s). FALSE. With only two large open economies, the equilibrium world real interest rate will be such that the lending country s CA surplus will be equal the borrowing country s CA de cit. That is, the world desired saving will be equal to the world desired investment. This can be shown graphically: 5

6 Part B Long Questions Do two (2) of the three (3) questions. Each question is worth 30 marks, for a total of 60 marks. Question B1: Production with Human Capital Consider a Cobb-Douglas production function with three inputs: K is capital (the number of machines), N is labour (the number of workers), and H is human capital (the number of workers which have university degrees). The production function is given by: Y = K N H ; where ; and are all between 0 and 1 and + + = 1: a) Derive an expression for the marginal product of labour and the marginal product of human capital. How does an increase in human capital a ect each of these marginal products? [10 marks] The marginal product of labour (MPN) is found by di erentiating the production function with respect to labour: MP N = dy dl = K N 1 H ; which is increasing in human capital because more human capital makes all the existing labour more productive. The marginal product of human capital (MPH) is found by di erentiating the production function with respect to human capital: MP H = dy dh = K N H 1 ; which is decreasing in human capital because there are diminishing returns. b) Calculate the income share paid to labour and the income share paid to human capital. In the national accounts of this economy, what share of total income would you expect workers to receive? [5 marks] 6

7 The labour share of output is the proportion of output that goes to labour. The total amount of output that goes to labour is the real wage which equals the MPN times the quantity of labour. Therefore the labour share can be calculated as follows: Labour Share = (K N 1 H )N K N H = : The human capital share can be found in similar way: Human Capital Share = (K N H 1 )H K N H = : Since workers own their own human capital, we would expect workers to receive a + share of output. c) Suppose an unskilled worker earns the marginal product of labour, whereas a skilled worker earns the marginal product of labour plus the marginal product of human capital. Using your results in part a), nd the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital a ect this ratio? Explain. [10 marks] The ratio of the skilled wage to the unskilled wage is: W skilled W unskilled = MP N + MP H MP N = K N 1 H + K N H 1 K N 1 H = 1 + N H This ratio is always greater than one because skilled workers get paid more than unskilled workers. Also when H increases, the ratio falls because the dimishing returns to human capital lower its return, while at the same time increasing the marginal product of unskilled workers. d) Some people suggest that government funding of university scholarships helps create less wage inequality. Based on your answers above, what would 7

8 have to be true about university scholarships for this claim to be true. [5 marks] If more university scholarships increase H, then it does lead to less wage inequality. The policy would lower the return to education, decreasing the gap between the wages of more and less educated workers. The policy would even raise the absolute wage of the unskilled workers because their marginal product rises when the number of skilled workers rises. Question B2: Labour Market Equilibrium First, consider an economy with a homogeneous labour force. That is, all workers are of the same type. In this economy, the marginal product of labour (MPN) is MP N = 27 0:5N, where N is the amount of labour used. Labour supply is given by NS = 30w, where w is the real wage. (Note: for this question, your diagrams need not be drawn to scale, but you must correctly label all important points for full marks) a) What are the equilibrium values of employment and the real wage? Plot this point on a labour market diagram along with the NS ND curves. [10 marks] First we need to nd the labour demand. MP N = w. 27 0:5N = w 27 w = 0:5N N = 54 2w To nd the equilibrium wage we need to equate the labour demand with the labour supply. ND = NS 54 2w = 30w 54 = 32w w = 1:6875 Now we can plug w in the supply or in the demand of labour to nd the equilibrium value of employment, we get that N = 50:625. Now suppose there is heterogeneity in the labour force such that there are two groups of workers, group A and group B. Both groups have di erent experience, education and 8

9 ability, but within each group workers are similar (e.g. any two members of group A have the same characteristics). The MPN for each group is given by: MP N A = 30 N A MP N B = 25 N B: The labour supply for each group is given by: N A = 10w A N B = 20w B: b) Calculate the equilibrium real wage and full employment level for each group of workers, and plot these points in a labour market diagram for each group. [10 marks] We have to follow the same procedure as in part a), but this time we have to do it for each group of workers. Lets start with group A workers. Their labour demand is given by: The equilibrium wage is: 30 N A = w A N A = 30 w A ND = NS 30 w A = 10w A 30 = 11w A wa = 2:73 The equilibrium employment level is NA = 30 2:73 = 27:27. For the group B workers: labour demand: Equilibrium wage: 25 N B = w B N B = 25 w B ND = NS 25 w B = 20w B 25 = 21w B wb = 1:19 9

10 Equilibrium employment level N B = 23:81 Comments: The group B workers have a lower wage than when all workers were alike while the group A workers have a higher wage. c) Suppose the economy undergoes a technological change that favours workers in group A. This change raises the MPN of group a workers to MP N A = 35 N A, but reduces the MPN of workers in group B to MP N B = 20 N B. Find the new equilibrium real wage and employment level for each group and depict the results of this technological change in the same diagram drawn in part b). Explain the shifts (if any) in the NS ND curves and discuss the results. [10 marks] Following the same steps as in part b) we have: Group A workers: Labour demand: The equilibrium wage is: 35 N A = w A N A = 35 w A ND = NS 35 w A = 10w A 35 = 11w A wa = 3:18 The equilibrium employment level is NA = 10 (3:18) = 31:82. Group B workers: labour demand: Equilibrium wage: 20 N B = w B N B = 20 w B ND = NS 20 w B = 20w B 20 = 21w B wb = 0:95 Equilibrium employment level NB = 20 (0:95) = 19:05 10

11 The technological change raises the demand for group A workers but reduces the demand for group B workers. At the new equilibrium point, group B workers real wages and employment have risen, and the wages and employment of group B workers have fallen. In part b) the wage gap between the 2 groups was 1.54, at the new equilibrium point it is 2.23, suggesting greater wage inequality as a result of the technological change. Question B3: Modelling Consumption and Savings Decisions Suppose a consumer s life is divided into two periods: working age (period 1) and retirement (period 2). In period 1, he/she works earning y 1 = 2000, and pays taxes t 1 = 200. In the second period when the consumer retires, he/she earns y 2 = 1500 from his RRSP and pays taxes t 2 = 200. Assume the real interest rate is 10 percent (r = 0.10). (Note: for this question, your diagrams need not be drawn to scale, but you must correctly label all important points for full marks) a) Write down the consumer s budget constraint and calculate his/her present value of lifetime resources (PVLR). [5 marks] The consumer s budget constraint is given by c 2 = (y 1 t 1 c 1 )(1 + r) + (y 2 t 2 ) and the PVLR: P V LR = (y 1 t 1 ) + (y 2 t 2 ) (1 + r) ( ) = ( ) + 1:10 = 2981:82 b) What is the highest feasible consumption level in the consumer s working age? What is the highest feasible consumption level when the consumer retires? Use this information to graph the budget line. [5 marks] The highest feasible consumption in period 2: 11

12 c 2 = ( )(1:10) + ( ) = = 3280 The highest feasible consumption in period 1: c 1 = ( ) + = 2981:82 ( ) 1:10 These are the intercepts of the budget line. Suppose from now on that the consumer prefers a smooth consumption path: c 1 = c 2 = c. c) Find the optimal amount of consumption in each period, c, and the amount of saving/borrowing. Is this consumer a borrower or a lender? Plot the optimal consumption point, along with the no borrowing-no lending point, on the budget line. [10 marks] Making use of the consumption smoothing assumption, the lifetime budget constraint becomes: c + c 1:10 = P V LR = 2981:82 Solving this gives c = 1561:91 and therefore savings is s = :91 = 238:09: Since the consumer s saving is positive, he/she is a lender. d) Suppose the central bank raises the real interest rate to 15 percent (r new = 0.15). Find the new optimal consumption and saving/borrowing plan and graphically show the e ects of this policy change. Compare this result with part c) and determine whether the income e ect or the substitution e ect dominates for this consumer. [10 marks] 12

13 With r=0.15, we have P V LR new = ( ) + The lifetime budget constraint becomes = 2930:43 ( ) 1:15 c new + c new 1:15 = P V LR new = 2930:43 and solving this gives c new = 1567:44; and s new = :44 = 232:56: When the real interest rate rises, the price of current consumption increases relative to future consumption, thus providing incentive to save more (substitution e ect). However, the future interest income on the consumer s current saving also rises, which increases PVLR and thereby increases both current and future consumption. This e ect dampens the incentive to save (income e ect). The two e ects work in opposite directions. In the case here, the consumer s savings decreases s new < s and current consumption increases c new > c ; hence the income e ect dominates. 13