Intermediate Macroeconomic Theory II, Winter 2009 Solutions to Problem Set 2.

Transcription

1 Intermediate Macroeconomic Theory II, Winter 2009 Solutions to Problem Set (14 points, 2 points each) Indicate for each of the statements below whether it is true or false, or elaborate on a statement if it does not require a true/false judgment. Briefly explain, supporting your argument with graphs, formulas, or simple reasoning. (a) In accordance with the classical dichotomy, an increase in the aggregate price level in the economy should lead to an increase in the real production over the long run. (b) Suppose the economy is on a balanced growth path; the growth in the efficiency of labor is equal to 5%; and the growth of population is equal to 5%. If the growth of the money stock is equal to 5%, and the income velocity of money is constant, the inflation rate in the economy will be equal to 5% in the long run, and the aggregate prices will be increasing in the long run. (c) Suppose the government sets taxes on the nominal capital gains. If the ex ante nominal interest rate is equal to 2%, the expected and realized inflation rate are equal to 0%, and the tax rate on nominal gains is equal to 40%, then the investor s real purchasing power will increase by 1.2%. (d) Suppose the government sets taxes on the real capital gains. If the ex ante nominal interest rate is equal to 2%, the expected inflation rate is equal to 0%, realized inflation rate is equal to 2%, and the tax rate on real gains is equal to 40%, then the investor s real purchasing power will increase by 0%. (e) If the realized inflation turns out to be higher than expected inflation, we may expect that debtors lose and creditors gain in real terms. (f) (OE LR) Assume two countries with different but constant income velocities of money. Assume that country I(-ndustrialized) has money growth equal to 2%, while country D(-eveloping) has money growth equal to 10%. Assume that the population growth in both economies as well as the growth of the efficiency of labor are zero. Assume that the absolute purchasing power parity for both economies holds. We may conclude that, in the long run, currency of country I will depreciate in nominal terms relative to the currency in country D by 8%. (g) (RBC) Suppose the economy s output fluctuates due to real technological shocks, and the economy s prices are fully flexible. If the central bank aims to stabilize the price level, what would it do to the money supply? As a result of this policy, does output change in the same direction as money supply? Would you make an inference that money causes output (as monetarists claim), or the real shocks cause unidirectional fluctuations in money and output (as RBC theorists would)? (a) False. The classical dichotomy states that nominal variables should not affect real variables in the long run. Real output is a real variable, and the aggregate price level is a nominal variable; thus, they should not be related in the long run in accordance with the classical view of the economy. 1

2 (b) False. n = g = From the quantity equation of money M V = P Y, M M + V V = P P + Y V Y. If the income velocity constant, V = 0, and from the Solow model with technological and population growth we know that Y Y = n + g. Thus, P P = π = = Price are falling in the long run for this economy, and we will observe deflation. (c) True. The real purchasing power is determined by the ex post real interest rate. r = i(1 t) π = (1 0.4) = = 1.2%. (d) True. r = (1 t)(i π) = (1 0.4) ( ) = 0%. (e) False. Ex ante, the real purchasing power of creditors should increase by i π e percent. Ex post, the realized real gain to creditors is equal to i π. Creditors gain and debtors lose if (i π) (i π e ) > 0, i.e., if π e > π. In our case, π > π e and so creditors lose and debtors gain. (f) False. It follows that π I = ( M M )I = 0.02; π D = ( M M )D = 0.1. If we further assume that the relative purchasing power parity holds in the long run, q q = 0 = e e +(πi π D ), then e e = πd π I = (We assumed that country I is domestic country, and D is foreign country.) Thus, in the long run, we should expect that the currency of country I should appreciate relative to the currency of country D by 8%. (g) Equilibrium in the money market demands the equation M/P = L(r, Y ) to hold. If output increases and prices are fully flexible, P should fall, to accommodate increases in the money demand the RHS of the equation. If the central bank smoothes the prices in the economy, it will expand the money supply. If all of this is the case, then the beneficial real shocks cause both output and money supply to increase, definitely a story that the RBC theorists would be comfortable with. 2. (10 points) Use the IS LM model to determine the short- and long-run effects of each of the following on the equilibrium values of the output, the real interest rate, consumption, investment, the price level, and the real money balances. Draw the relevant diagrams to show how you arrived at your answer. Assume that consumption is not responsive to changes in the real interest rate; and that the economy is initially at the natural level of output. Track the effects for normal cases, i.e., do not bother about vertical/horizontal IS/LM curves. (a) (5 points) A reduction in the effective tax rate on capital that increases desired investment at any real interest rate. (b) (5 points) The expected rate of inflation rises. (a) The IS will shift to the right, causing output and the real interest rate to increase. In the SR, compared to the initial equilibrium: C since the real disposable income increases, I (since the autonomous investment rises by a larger margin than the fall in investment caused by an increase in the real interest rate); r ; M/P since neither money stock nor prices change in the short run; Y. In the LR, prices will adjust upwards following an inflationary change in the aggregate demand. LM curve will shift to the left up to the point when it intersects the new IS curve at the long-run level of output, Y. Thus, compared to the initial equilibrium, in the long run, Y, r, C, I (investment should be lower than what it 2

3 was in the short run, to satisfy the national accounts identity), P, (M/P ) (since money stock is unchanged while the aggregate level of prices increases). (b) If we consider the IS LM diagram with the nominal interest rate on the vertical axis (as in your textbook s discussion of the Great Depression), the IS curve will shift up and to the right, leading to an increase in the nominal interest rate and a reduction in the real interest rate. In the short run, this leads to an increase in the real output (income), and therefore an increase in consumption, an increase in investment, no effects on the price level (as the price is stuck in the short run), and no effects on the real money balances (as both the money supply and the level of prices are fixed in the short run). Compared to the initial equilibrium, in the SR: Y, I, r, C (since the real income increases), P, M/P. In the long-run, the price level will increase (and so will inflation), LM curve will shift to the left, the nominal interest rate will increase, and the real interest rate will increase, back to its previous level. Investment will fall, output will revert to its previous level, and the real money balances will fall. Compared to the initial equilibrium, in the LR: Y, I (since the real interest rate is at its previous level), r, C (since output is at its previous level, and T is the same), P, M/P. Thus, the expectations of rising prices are self-fulfilling here, i.e., the expected inflation leads to the actual inflation. 3

4 3. (5 points) Suppose that investment expenditures do not change with a change in the real interest rate. Show what this implies for the slope of the IS curve, and for the relative effectiveness of monetary and fiscal policy in stabilizing real output. Explain your results. Draw the relevant diagrams. This will result in a steep IS curve. At the extreme, if investment is not responsive to the real interest rate at all, the IS curve will be vertical. If the economy is at its long-run equilibrium and the economy faces the money demand shocks, then output does not change. If the shocks are to the demand for goods and services, i.e., the IS shocks, then any change in the monetary policy will not affect output, resulting only in a change in the real interest rate. Fiscal policy, however, is very potent in bringing output back to its long-run, full-employment level. E.g., if the IS shifts to the left, say, because consumers savings rate increases, then there will be a recession in the economy and only expansionary fiscal policy would bring the economy back to its long run, full employment level of output. 4

5 4. (10 points) The central bank is considering two alternative monetary policies: ˆ holding the money supply constant and letting the interest rate adjust, or ˆ adjusting the money supply to hold the interest rate constant. In the IS LM model, which policy will better stabilize output under the following conditions? Draw the relevant diagrams, and explain how you arrived at your answer. (a) (5 points) All shocks to the economy arise from exogenous changes in the demand for goods and services. (b) (5 points) All shocks to the economy arise from exogenous changes in the demand for money. If the central bank holds the stock of money constant, the LM curve will be upward sloping. (a) The best stabilization policy is the one that brings the least volatile output. If the economy is at its full-employment level of output, the best policy is the one that creates smallest deviations around the full-employment level of output. If all the shocks are the IS shocks, then the policy of keeping the interest rate constant will bring the largest deviations from the full employment level of output. Thus, in this case, it is inferior to the policy of keeping the nominal money stock constant and letting the interest rate to adjust. 5

6 5. (15 points) (b) All the shocks to the money demand will lead to changes in the real interest rate if the money supply is held constant, and, therefore, cause changes in output by affecting the investment demand. However, if the central bank s policy is to keep the real interest rate constant, it would adjust the money supply, and this will result in a stable LM curve, and no changes in output. Thus, the best policy in the case of money demand shocks prevailing over the goods demand shocks is to adjust the money supply and keep the real interest rate unaffected. (a) (5 points) (OE SR Real shock) Use the Mundell-Fleming model to predict the effects of a fall in domestic consumers confidence on aggregate income, the exchange rate, and the trade balance in a small open economy with a flexible exchange rate regime. (b) (5 points) (OE SR Real Shock) Use the Mundell-Fleming model to predict the effects of a fall in domestic consumers confidence on aggregate income, the exchange rate, and the trade balance in a small open economy with a fixed exchange rate regime. (c) (5 points) (OE SR Money demand shock) Use the Mundell-Fleming model to predict the effects of the introduction of ATMs that leads to a fall in the domestic demand for money on aggregate income, the exchange rate, and the trade balance in a small open economy with a fixed exchange rate regime. (a) The Mundell-Fleming model is comprised of two equations: IS : Y = C(Y T ) + G + NX(q) + I(r ) LM : M/P = L(r, Y ). Assume that IS has the following form: Y = C + α (Y T ) + β r +G + γ q, }{{}}{{} C(Y T ) I(r ) or Y = α 1 α T α (C + β r + G + γ q). Plug this definition of the IS into the LM to obtain: LM : M/P = L[r, α 1 α T α (C + β r + G + γ q) ]. }{{} Y Note that if we graph the demand for liquidity as a function of q, a smaller q will result into a higher NX (since γ is negative) and Y and therefore into a higher demand for liquidity the money demand function is downward sloping and is constructed for given levels of T, r, C, G, and values of α, β, and γ. If any variable or parameter out of {T, r, C, G, α, β, γ} changes the money demand function will shift. We can think of a fall in consumers confidence as a reduction in C, a fall in the autonomous component of aggregate consumption, or a reduction in α, an increase in the savings rate. To simplify the matters, assume that C fell. For a given money stock, the price level, the interest rate, and the real exchange rate, the demand for 6

7 domestic currency will fall, and this will result into depreciation of the nominal and real exchange rates. Since, under the flexible exchange rate, the central bank does not control the nominal exchange rate, it stays at a new, lower, equilibrium level. This, in turn, results into the expansion of NX, and the same output as before. Note, using our original LM and flexible exchange rates, that output can change only if M changes exogenously. (b) In this case, the central bank cannot let the nominal exchange rate to depreciate. It will cut the supply of domestic money to keep the nominal exchange rate at its previous value. Since the market nominal exchange rate was temporarily lower than the one set by the central bank, domestic currency becomes relatively unattractive. The profiteers will purchase Canadian dollars in the market and sell it to the central bank, endogenously contracting the supply of domestic currency. E.g., it the central bank sets e=yen 100/$1 and the market nominal exchange rate is Yen 50/$1, one can purchase $2 in the market for foreign exchange rate for Yen 100 and sell it to the central bank for Yen 200 a pure profit of Yen 100. Since the central bank endogenously contracts the money supply in response to the shock, output will fall by the magnitude of the fall in C, and NX will stay the same since q is held fixed. (c) The introduction of ATMs will lead to a fall in the money demand, for any given nominal and real exchange rate. This must result into depreciation of domestic currency. If the central bank is committed to keep the nominal exchange rate at its fixed level, it will contract the money supply. The results are the following: NX will stay the same since q is held fixed, Y is the same since none of the real components of aggregate demand changed. 7