Queen s University Faculty of Arts and Science Department of Economics ECON 222 Macroeconomic Theory I Fall Term 2012 Sections 001 and 002 Instructors: Margaux MacDonald (001), Robert McKeown (002) Final Examination 5 December 2012 Instructions: Put your student number on the front and all pages of all answer booklets. This examination is THREE HOURS in length. You may use a non-programmable hand calculator (with a gold or blue sticker or a Casio 991). No other aids are allowed in this examination. The exam consists of two parts, A and B. Part A consists of short questions. Do FOUR of the six questions. Each question in Part A is worth 10 marks for a total of 40 marks. Part B consists of long questions. Do THREE of the five questions. Each question in Part B is worth 20 marks for a total of 60 marks. The total number of marks is 100. Read the questions carefully. For questions that involve a numerical part be sure to show your calculations and intermediate steps. Please answer all questions in the answer booklets provided. GOOD LUCK! Please note: Proctors are unable to respond to queries about the interpretation of exam questions. Do your best to answer exam questions as written. This material is copyrighted and is for the sole use of students registered in ECON 222 and writing this exam. This material shall not be distributed or disseminated. Failure to abide by these conditions is a breach of copyright and may also constitute a breach of academic integrity under the University Senate s Academic Integrity Policy Statement.
PART A: Short Questions. Answer any FOUR of the following six questions. Each question is worth 10 marks for a total of 40 marks. Question A.1: IS-LM-FE (10 Marks) During the Industrial Revolution in Britain, new machinery and innovation allowed each worker to produce more output than they were previously able. In other words, the marginal productivity of workers increased. Assuming the economy was in general equilibrium before the revolution began, what happens to the real interest rate and output in the very short run, before the price level has adjusted to restore general equilibrium? Explain carefully, using graphs, the changes happening in this situation. Question A.2: Consumption-Savings Decision and Government Policy (10 Marks) (i) Consider the two period model used in class. Explain the consumption-savings decision of a borrower when the interest rate increases. Clearly differentiate between the income (wealth) and substitution effects in your explanation. Does future consumption increase, decrease or is the result ambiguous? (ii) Suppose the government is concerned citizens are not saving enough income for retirement. What policies could the government implement to encourage private savings? Question A.3: Foreign Exchange Markets (10 Marks) As a Canadian holder of wealth you are trying to make portfolio allocation decisions. You have decided to put 20, 000 of your savings into government bonds, but are still trying to determine whether or not you should purchase Canadian bonds or Chinese bonds. A one year Canadian bond pays i = 10%, and one year Chinese bond pays i = 7%. The current nominal exchange rate is e nom = 6.25 /$. You expect the Chinese yuan to appreciate over the next year to e f nom = 5.5 /$. (a) Based on the information given, which bond is the better investment? How much is the expected gross nominal rate of return on each investment? (b) Suppose that the Chinese government imposes a tax on net investment income of t CNY = 50%. Does this change your answer from part (a)? 2
Question A.4: International Macroeconomics (10 Marks) (i) Identify the three features of the open-economy trilemma and note the benefit to each. Which features has Canada chosen? (ii) Suppose a small open economy has a fixed exchange rate that is considered overvalued by international traders. Is the current fixed exchange rate viable in the long run? Describe the mechanics of a speculative run using a properly labelled graph. What must the central bank have to stop the speculative run from succeeding? Question A.5: Business Cycles (10 Marks) Draw a diagram showing the phases and turning points of a business cycle. Be sure to label all important points of the graph. If you knew the economy was falling into a recession, what would you expect to happen to production during the next few quarters? to investment? to average labour productivity? to the unemployment rate? Explain the difference between the Classical and Keynesian beliefs about how long it will take the economy to recover from this recession. In particular, comment on their beliefs of the usefulness of anti-recessionary policies. Question A.6: Asset Market (10 Marks) James Bond invests $350,000 of his income into government bonds. He places the remainder of his income, an amount of $150,000, into a chequeing account with a zero nominal interest rate. Mr. Bond informs his broker that his policy is to invest $10,000 into government bonds for every percentage point the nominal return on bonds is above the nominal return on his chequeing account. The current nominal interest rate on government bonds is 5%. (i) Suppose Mr. Bond has a nominal money demand of the form: M d /P = L(Y, i) L(Y, i) = l y Y + l i (i) P = 1 where Y is Mr. Bond s income, i is the nominal interest rate on government bonds and l y, l i are coefficients. Use the above information to solve for the coefficients on Mr. Bond s money demand function. (ii) Suppose the money demand function of Mr. Bond now represents money demand for the entire economy. A productivity shock changes output (Y) to 400,000. What is the short-term real rate of interest that clears the asset market? Assume i = r + π e, expected inflation (π e ) is zero. 3
PART B: Long Questions. Answer any THREE of the following five questions. Each question is worth 20 marks for a total of 60 marks. Question B.1: IS-LM-AD for a Closed Economy (20 Marks) The following describes some key relationships for a closed economy: C d = 1140 + 0.5(Y T ) I d = 900 200r M d = P (0.5Y 200(r + π e )) Y is real output, P is the price level, r is the real interest rate, G is government spending, T is a lump sum tax, M is the nominal money supply. Expected inflation is zero, π e = 0. (a) Derive the IS and LM equations (curves) for this economy, with the real rate of interest on the lefthand side. Be sure to describe briefly your steps. Use the IS and LM relationships to derive the aggregate demand curve (AD), rearrange this equation so you have Y on the left-hand side of your equation. Explain the relationship between output and the price level that you find. In your results, show G and T separately in each of the relationships. (b) You are given the following information: G = T = 450, M = 2250 and P = 1. Based on this, use the model you derived in part (a) to solve for Y and r. Find the values of C d and I d associated with these levels of output and interest rate. (c) Suppose that instead of balancing it s budget, the government decides to run a budget deficit equal to 50 by keeping it s spending constant, G = 450 and lowering taxes. Find the new value of output Y in this case (assume Ricardian Equivalence does not hold and all other variables are held constant). Explain, with the help of a graph, the mechanism that generates your results. (d) Assume that the government reverts to a balanced budget, G = T = 450. The central bank increases the money supply to 2280. Assume all other variables are unchanged. Calculate the new level of output Y. Explain, with the help of a graph, the mechanism that generates your results. (e) Compare the effects of the fiscal expansion (part (c)) and monetary expansion (part (d)). What would be the long-term effects if the government continued to run a fiscal deficit? What would be the long-term effects if the government continued to increase the money supply? 4
Question B.2: Open Economy IS-LM (20 Marks) Consider the following large open economy: Y = 25, 000 C = 1000 + 0.5(Y T ) 8000r T = 5000 G = 6000 I = 9500 12000r and M/P = 0.5(Y ) 20, 000i π = 0 i = r + π e M = 832, 500 NX = 3000 0.1(Y ) 1000(e) + 0.075(Y for ) e = 1.5 Y for = 12, 000 P for = 1 where Y is output, Y for is foreign output, T is a lump sum tax, G is government spending, i is the nominal interest rate, NX is net exports, e is the real exchange rate, π e is expected inflation, P for is the foreign price level and M is the nominal money supply. You may assume there is a single world-wide real rate of interest. Furthermore, assume that the three markets discussed in class are always in equilibrium. (a) What is the value of net exports? If the economy were closed instead of open and holding all else equal, would the level of investment be higher, lower or the same? Use your intuition to explain why. Solution (b) What is the open economy long-run real rate of interest and level of savings? If the economy were closed instead of open and holding all else equal, would the real rate of interest be higher, lower or the same? Use your intuition to explain why. (c) What is the price level in equilibrium? If the economy were closed instead of open and holding all else equal, would the price level be higher, lower or the same? Explain. (d) Calculate the nominal exchange rate. In general, explain the factors that affect the supply and demand for money in the international foreign exchange market. Draw a diagram of the international foreign exchange market with the supply and demand of domestic currency. Label the axes properly. (e) Suppose the government is concerned about its level of debt. As a result the government decides to increase taxes from 5000 to 6200. Assume output and the real exchange rate are unchanged and Ricardian equivalence does not hold. What is the new long run real rate of interest, price level and nominal exchange rate? You may round your answers to four decimal places if required. Has national savings increased or decreased? Explain. 5
Question B.3: Two Period Model of Consumption Behaviour (20 Marks) Consider the following information about an average consumer who lives for two periods. In the first period she earns an income y 1 and in the second period she earns y 2. She consumes c 1 and c 2 in periods one and two, respectively. She is subject to an income tax rate of t 1 and t 2 in each period, such that her after tax income in period one will be y 1 (1 t 1 ), and in period two y 2 (1 t 2 ). The interest rate in this (closed) economy is r. Assume she has zero assets at the beginning of time. (a) Write the consumer s lifetime budget constraint (also called the inter-temporal budget constraint), this should be an equation in terms of (c 1, c 2, y 1, y 2, t 1 and t 2 ). (b) Assume income in period one is y 1 = 1000 and in period two is y 2 = 5000, taxes are set at t 1 = t 2 = 0.15, and the interest rate is r = 0.10 = 10%. What is this consumer s present value of lifetime resources? What is the highest feasible consumption in the future period? What is the highest feasible consumption in the current period? (c) Our consumer wishes to smooth his consumption over time, so that c 1 = c 2 = c. Find the optimal consumption in each period, c, and the amount of saving/borrowing in the first period. Is this individual a borrower or a lender? Draw the lifetime budget constraint graphically, include an indifference curve representing preferences that clearly identifies c as the optimal consumption point. (d) Suppose in the first period the government gives everyone a lump sum tax rebate. Individuals then decide to invest this rebate into a government bond, b. Write the new inter-temporal budget constraint, keeping tax rates written as t 1 and t 2. What must t 2 be for Ricardian Equivalence to hold? Briefly explain the concept of Ricardian Equivalence, noting in particular the effect on c 1 and c 2. (e) Calculate the new level of c 1 if the government pays a tax rebate of $100 to individuals, but they are myopic and assumes that taxes next period will stay constant at t 2 = t 1 = 0.15. Explain the difference in your answers in part (d) and (e). In reality, which outcome do you think is more likely after a government tax rebate? 6
Question B.4: IS-LM-AD for an Open Economy (20 Marks) The following describes some key relationships for a small open economy: C d = 70 + 0.2(Y T ) 60r I d = 30 140r M d P = (1.2Y 830(r + πe )) NX = 20 0.3Y 10e (a) Assume the nominal exchange rate e nom is flexible and that government spending and tax revenue are G = T = 20. Derive algebraic expressions for the IS and LM curves, in each case with the real interest rate (r) on the left hand side of the equations. (b) Given a world interest rate of r = 2.00%, real money supply of M/P = 100, and inflation expectations of π e = 2%, calculate the equilibrium level of real output (Y ), the real exchange rate (e), and the level of net exports (NX) for this economy. Is the country a net exporter or importer? (Hint: The equation for the LM curve you found in part (a) is a useful place to start) (c) Suppose the domestic price level is P = 1, the foreign price level is P F or = 2, and the real exchange rate is as you found in part (b). What is the nominal exchange rate? Briefly state what this value represents. (d) Assume the levels of Y, e, and e nom you found in the previous section are the long-run levels for this economy. Now suppose that there is a decrease in government spending such that G = 15. The real money supply, real exchange rate, and taxes have not changed during this time period. Calculate the new short-run levels of Y and r under these assumptions. Next, find the long-run equilibrium. Calculate the new values of investment, net exports, and the nominal exchange rate. Describe the mechanisms that are shifting this economy to it s new long-run levels, pay particular attention to what is happening with the real exchange rate. 7
Question B.5: Neo-Classical Growth (Solow-Swan) Model (20 Marks) Consider a closed economy with no government spending, an infinite number of time periods and full employment. The population and work force grow at rate n per period and the capital equipment depreciates at rate d. The aggregate production function is: Y = AN 1 α (K) α ln(l) (1) Workers save a fraction (s) of output per time period where (0 < s < 1) so that aggregate savings is: sy = san 1 α (K) α ln(l). (2) where Y is aggregate output, K is aggregate capital, N is aggregate labour, A is total factor productivity and L is hectares of arable land. (a) What is the per worker production function (y) and savings per worker (s) as a function of capital per worker (k)? (b) Write an expression for consumption per worker (c). What is the Golden Rule level of capital per worker (k G )? (c) First, define the condition for a steady state equilibrium. Then suppose that: A = 10 L = 403.43 n = 0.02 d = 0.23 α = 2 3 s = 0.4 Calculate the value of the steady state level of capital (k ss) and the Golden Rule level of capital (k G ), given these numbers. (d) Create a diagram showing the steady state and Golden Rule level of capital you found in part c. Which has a higher level of capital? Explain why the two are different. (e) Suppose global warming has reduced the quantity of arable land by one-half. Furthermore, the population growth rate increases to 3%. Carefully illustrate the effect on per worker output (y), consumption (c) and capital (k) using a (properly labelled) graph. 8