ANALYTICAL PROBLEMS
1. For each of the following changes, what happens to the real interest rate and output in the very short run, before the price level has adjusted to restore general equilibrium?
a.
Wealth declines.b. The money supply declines.
c. The future marginal productivity of capital declines.
d. Expected inflation rises.
e. Future income rises.
2. Use the IS-LM model to analyze the general equilibrium effects of a permanent increase in the price of oil (a permanent adverse supply shock) on current output, employment, the real wage, national saving, consumption, investment, the real interest rate, and the price level. Assume that, besides reducing the current productivity of capital and labor, the permanent supply shock lowers both the expected future MPK and households' expected future incomes. (Assume that the rightward shift in labor supply is smaller than the leftward shift in labor demand.) Show that, if the real interest rate rises at all, it will rise less than in the case of a temporary supply shock that has an equal effect on current output.
3. Suppose that the price level is fixed in the short run so that the economy doesn't reach general equilibrium immediately after a change in the economy. For each of the following changes, what are the short-run effects on the real interest rate and output? Assume that, when the economy is in disequilibrium, only the labor market is out of equilibrium; assume also that for a short period firms are willing to produce enough output to meet the aggregate demand for output.
a. A decrease in the expected rate of inflation.
b. An increase in consumer optimism that increases desired consumption at each level of income and the real interest rate.
c. A temporary increase in government purchases.
d. An increase in lump-sum taxes, with no change in government purchases (consider both the case in which Ricardian equivalence holds and the case in which it doesn't).
e. A scientific breakthrough that increases the expected future MPK.
4. (Appendix 9.B) In some macroeconomic models, desired investment depends on both the current level of output and the real interest rate. One possible reason that desired investment may depend on output is that, when current production and sales are high, firms may expect continued strong demand for their products in the future, which leads them to want to expand capacity.
Algebraically, we can allow for a link between desired investment and current output by replacing Eq. (9.B.10) with
where iγ is a positive number. Use this alternative equation for desired investment to derive the algebraic expressions for the general equilibrium values of employment, the real wage, output, the real interest rate, and the price level.
5. (Appendix 9.B) Recall from Chapter 7 that an increase in im, the nominal interest rate on money, increases the demand for money. To capture that effect, let's replace Eq. (9.B.17) with
How does this modification change the solutions for the general equilibrium values of the variables discussed in Appendix 9.B, including employment, the real wage, output, the real interest rate, and the price level?