Intermediate Macroeconomic Theory II, Winter 2007 Instructor: Dmytro Hryshko Solutions to Problem Set 4 (35 points).

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1 Intermediate Macroeconomic Theory II, Winter 2007 Instructor: Dmytro Hryshko Solutions to Problem Set 4 (35 points). 1. (20 points) Use the IS{LM model to determine the short- and long-run eects 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 eects for normal cases, i.e., do not bother about vertical/horizontal IS/LM curves. (a) (5 points) A reduction in the eective tax rate on capital that increases desired investment. (b) (5 points) A severe water shortage causes sharp declines in agricultural output and sharp increases in food prices. Assume that the long-run level of output falls but the short run fall of output is much larger (i.e., the economy is hit severely in the short run but rebounds in the long run). (Hint: The AD curve will be stable since it relates the changes in output to the changes in the aggregate level of prices, given the money supply in the economy. The AD shifts, in response to changes in the money market, only if there are shocks to the money supply or money demand, not to prices. I.e., if the price changes the LM will shift but the AD will not.) (c) (5 points) A permanent increase in the price of oil (a permanent adverse supply shock). Assume that besides reducing the current productivity of capital and labor, the permanent supply shock lowers both the expected future M P K and households' expected future incomes. (d) (5 points) The expected rate of ination 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 inationary 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 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). 1

2 (b) The water shortage causes the aggregate price level to increase in the short run. Thus, the SRAS curve shifts up. AD is assumed to be stable since we assumed that there were no shocks to the expenditures components. Moreover, the long run level of output falls but by a smaller margin than the fall of output in the short run. Thus, the vertical LRAS will shift to the left (you may think here that the water shortage aected the technology somehow and therefore aected the economy's ability to produce output). All this indicates the following: In the SR, there is a substantial price increase that causes the LM curve to shift to the left. Y #, r ", I #, C #, P ", (M=P ) # (the real money balances fall mechanically since the money stock is assumed to be constant, and the aggregate price level increases). In the LR, the price level falls, and the LM curve shifts to the right, up to the point when it intersects the IS curve and new LRAS curve at the new long-run level of output. Thus, in the LR, compared to the initial equilibrium, Y #, C #, I #, r ", P ", (M=P ) #. It is ne if you compared all of these variables to their values in the short run equilibrium. 2

3 (c) There are too many answers here, as I emphasized in class. All of them depend on your assumptions. Here are some plausible assumptions: 1) The price increase in the short run aected the LM curve by a larger margin than the change in the IS caused by the fall in current and future MP Ks; 2) Since the oil price shock is permanent, the LRAS supply will shift to the left, largely reecting the idea that the costs of producing output increase in the LR (after all, gasoline and oil are major inputs into many technological processes). The subsequent transition (from the short run to the new long run equilibrium) dynamic of the real interest rate, aggregate prices, real money balances, consumption, and investment depends on your assumption about the relative fall of output in the short run (whether the shock was huge enough to cause output to fall by a large magnitude in the short run, and then rebound to a higher value in the long run, which is of course lower than the initial long run level of output; or whether the shock was not that huge in the short run but the long run fall in output is much larger than in the short run). (d) 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 eects on the price level (as the price is stuck in the short run), and no eects on the real money balances (as both the money supply and the level of prices are xed 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 ination), 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-fullling here, i.e., the expected ination leads to the actual ination. 3

4 2. (5 points) Suppose that investment expenditures change very little with a change in the real interest rate. Show what this implies for the slope of the IS curve, and for the relative eectiveness of monetary and scal 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 aect 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 scal policy would bring the economy back to its long run, full employment level of output. 4

5 3. (10 points) Mankiw, Chapter 11, Problem 7. (Hint: If the central bank adjusts the money supply holding the interest rate constant, the LM curve will be horizontal.) 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. If the central bank changes money supply so as to keep the real interest rate constant, the LM curve will be horizontal. (a) The better 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 (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 aecting 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 unaected. 4. (5 points) Output, total hours worked, and average labor productivity are all pro-cyclical (i.e., increase or fall together over the business cycle). Which variable, output or total hours worked, increases by a larger percentage in expansions and falls by a larger percentage in recessions? (Hint: Average labor productivity=(output/total Hours Worked).) Denote output by Y ; total hours worked by L; and dene the average labor productivity by AP L = Y. L % AP L = Y L. From the statement of the problem we know that % AP L, and Y L L Y are both positive when > 0. Hence, output should grow at a faster rate than L Y total hours worked in expansions, to make % AP L positive. Similarly, in recessions, when output and hours worked are falling, the average labor productivity will be falling only if output is falling by a larger percentage than the total hours worked. Thus, hours worked are less volatile than total output over the business cycle. 6