Economics Macroeconomic Theory. Spring Final Exam, Tuesday 6 May 2003

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1 Economics Macroeconomic Theory Spring Final Exam, Tuesday 6 May 2003 Please answer: ALL QUESTIONS IF YOU DO PART 1 3 OUT OF 4 QUESTIONS IF YOU DO PART 2 Each question in each part carries equal marks PART 1 (ANSWER ALL QUESTIONS) 75 minutes 1. Suppose that an economy s production function is a Cobb-Douglas with constant returns to scale, and that the labor s share of GDP is 70%. The economy is in steady state equilibrium. The ratio of capital to output is 2.5. The ratio of labor to output is 2. The depreciation rate is 4% per year, and the growth rate of output is 3% per year. a. What must the saving rate be in the initial steady state? b. What is the marginal product of capital MPK in the initial steady state? What is the marginal product of labor MPL? c. Suppose that public policy changes the saving rate so that the economy reaches the Golden Rule level of capital. What will the MPK be at the Golden Rule steady state? Compare the MPK at the Golden Rule steady state to the MPK in the initial steady state. Comment the intuition behind this result. d. What will the capital-output ratio be at the Golden Rule steady state? e. What must the saving rate be to reach the Golden Rule steady state? f. Under the policy change in (c), describe what happens over time to output, consumption and investment as the saving rate changes. 2. This question analyses the small-open economy model with perfectly flexible prices. a. What determines the trade balance and the real exchange rate in this model? b. Suppose the world interest rate rises. What happens to the trade balance and to the real exchange rate (1) if the purchasing power parity (PPP) does not hold perfectly; (2) if the PPP holds perfectly? c. Does the PPP hold in the real world? d. Assume the PPP holds. What determines the nominal exchange rates? 3. The government should subsidize research and development because, in the end, research generates knowledge and knowledge is the only engine of growth. Explain the meaning of this claim and discuss its implications for the rate of growth of output. 1

2 PART 2 (ANSWER 3 OUT OF 4 QUESTIONS, ALL QUESTIONS CARRY EQUAL MARKS) 75 minutes 1. A topic of debate among economists is whether economic policy should be conducted by rule or by discretion. a. Why might policy be improved by commitment to a policy rule? Discuss offering examples. b. Various rules have been suggested for central banks, in particular money supply rule, nominal GDP targeting rule, inflation targeting, and interest rate (Taylor) rule. Discuss each of them. Are these rules active or passive? c. In the real world, does the Federal Reserve (or other central banks) act under commitment or under discretion? Is there any evidence that independent central banks are more successful in fighting inflation? 2. Consider the following economy. The consumption function is given by: C = ( Y T ) The investment function is I = r Government purchases G and taxes T are both 100. The money demand function is (M/P) d = Y 100 r The money supply is 1000 and the price level is P=2 a. Find the equilibrium interest rate and the level of income. b. Suppose that the exogenous component of investment is raised from 200 to 250. Calculate the new equilibrium interest and the level of income. c. Derive and graph an equation for the aggregate demand curve. What happens to the aggregate demand curve as exogenous investment increases? d. Comparing the result you get in part (b) versus part (a), does the average propensity to consume raise, falls or stay constant as income changes? Is this prediction of the model supported by the data? Are there other theories of consumption that can support this prediction? 2

3 3. Suppose the world interest rate r* rises. What effect does this have on the IS* and LM* curves and what happens to output, the exchange rate and the current account under: a. fixed exchange rates b. flexible exchange rates c. flexible exchange rates, but the country is a great importer of foreign goods Suppose now money demand depends on disposable income, so that the equation for the money market becomes M/P = L (r, Y-T) d. Analyze now the impact of a tax cut under flexible and fixed exchange rates. 4. Suppose the price level is fixed. Assume consumption depends on current disposable income and investment depends on the interest rate. Money demand depends on income and interest rates. For each of the following changes, what are the short-run effects on the real interest rate and output? a. An increase in government purchases, financed by borrowing b. An increase in government purchases, financed by an equal increase in taxes (assume taxes are lump-sum) c. An increase in government purchases, financed by an equal increase in money supply d. Comparing case (a) and case (b), in which case is the increase in income greater? e. How would the answers above change if consumers were Ricardian? Why? f. How would the answers above change if the price level is flexible? 3

4 PART 1. SKETCH ANSWERS QUESTION 1 This is 8.2 This is basically question 2 from Chapter 8, page 66 in the Answer workbook. The last part requires students to draw Figure 7.10, page 199 in the textbook. The extra bit (added to check that some of them think too) is that L/Y=2. This implies that MPL=.70*Y/L=.7/2=.35 QUESTION 2 In equilibrium, we need S - I(r) = NX(e) The trade balance depends on G, G*, I The real exchange rate adjusts to clear the market. A rise in r* leads to a rise in S-I, hence NX must rise, hence the currency must depreciate. Under PPP, the required depreciation is very small, since the real exchange rate is always 1. If RER holds, the nominal exchange rates are determined by the respective money supplies in each country. QUESTION 3 Students should elaborate some convincing stories having to do with endogenous growth theories. The best ones might want to describe and use the two-sector model we went through in class, page 224 in Mankiw (give credit) and Problem 8.5 (solution in the workbook page 69: give extra credit if they go in detail following the structure of that problem) 4

5 PART 2. SKETCH ANSWERS QUESTION 1 Rules are better because of time inconsistency problem... examples: terrorist negotiations, taxation of fixed factors, etc... Monetary policy rules are discussed on page 394 of Mankiw. Taylor rule is extensively discussed in Mankiw, page 396. Taylor rule is an active rule. Fed seems to follow Taylor rule. Alesina and Summers (JMCB, 1993) show that independent central banks are more successful in fighting inflation. QUESTION 2 This is 11.3 Solution is in the workbook, from page 98 on. As exogenous investment increases, AD shifts right by an amount equal to the Keynesian multiplier (taking into account the increase in the interest rate...). Give credit to those who shift it exactly by the increase in output with fixed prices. Comparing b versus a, we know that APC=Cbar/Y+c. Hence, as income rises, the average propensity to consume falls. This prediction is true in crosssectional data, but not in time series data. The LCH hypothesis and the permanent income hypothesis can both explain the puzzle, since they present models of consumption in which the APC is constant over time but decreasing with income cross-sectionally (see Mankiw, pages ) QUESTION 3 This is 12.2, for the first two points Rise in r*: output falls under fixed rates Rise in r*: output rises under flexible rates (see question 12.2), page 119 of the workbook Rise in r*, foreign goods import: output rises by less: it might fall if the price level rises (which shifts the LM to the left) This is 12.5 Tax cut, flexible rates: IS shift to the right, the LM to the left Tax cut, fixed rates: IS shift to the right, the LM to the right to keep e fixed QUESTION 4 a. is the standard IS-LM case. IS shift is 1/(1-c) b. gets a small multiplier. IS shift is 1 (the balanced budget multiplier) c. gets a huge multiplier. IS shift is 1/(1-c), but LM shifts too d. (a) gives a bigger income increase than in (b). e. If consumers were Ricardian, however, the increase in income should not depend on how G is financed f. If prices are flexible, assuming that G is spending on consumption goods, the level of output cannot be affected. 5