ANALYTICAL PROBLEMS

1. Suppose firms invest in a new artificial intelligence program that develops high caliber robots that can handle large amounts of data and deliver instructions to workers.

a.

b. Suppose the workers' productivities and expected incomes are unaffected. How will this affect the AS curve with and without this assumption? value of output, Y, be 50, and graph the level of out­put over time as it is hit by the “positive" and “nega­tive" shocks (coin flips). For example, if your first four flips are three heads and a tail, output takes the values 51, 52, 53, 52. After fifty flips, have your small shocks produced any large cycles in output?

7. In a particular economy the labor force (the sum of employed and unemployed workers) is fixed at 100 million. In this economy, each month 1% of the work­ers who were employed at the beginning of the month lose their jobs, and 19% of the workers who were unem­ployed at the beginning of the month find new jobs.

a. The January unemployment rate is 5%. For the rates of job loss and job finding given, what will the unemployment rate be in February? In March?

b. In April an adverse productivity shock raises the job loss rate to 3% of those employed. The job loss rate returns to 1% in May, while the job finding rate remains unchanged at 19% throughout. Find the unemployment rate for April, May, June, and July.

8. (Appendix 10.B) Consider the following economy:

IS curve r = 2.47 - 0.0004Y.

Real money demand L = 0.5Y — 500(r + π^e).

Short-run aggregate supply

Here, r is the real interest rate, Y is output, and P is the price level. Assume that expected inflation, π^e, is 0, nominal money supply, M, is 88,950, and full­employment output, Y, is 6000.

a. Use the notation of Appendixes 9.B and 10.B. What are the values of the parameters α_ls, β _is, a_LM, β_lm, I_r, and b? (Hint: Solve for asset market equilibrium to obtain the coefficients of the LM equation.)

b. What is the equation of the aggregate demand curve?

c. Suppose that the expected price level, P^e, is 29.15. What are the short-run equilibrium values of the price level, P, and output, Y?

d. What are the long-run equilibrium values of the price level, P, and output, Y?

c. For simplicity, we keep the assumption in part (b). Use your answers in (a) and (b) to discuss the real interest rate, employment, real wages, nominal wages, consumption, investment, and the price level.

d. Based on the misperceptions theory, modify the above AS-AD graph to show the short-run equilibrium.

2. Use the classical IS-LM model to analyze the effects of a permanent increase in government purchases of 100 per year (in real terms). The increase in purchases is financed by a permanent increase in lump-sum taxes of 100 per year.

a. Begin by finding the effects of the fiscal change on the labor market. How does the effect of the permanent increase in government purchases of 100 compare with the effect of a temporary increase in purchases of 100?

b. Because the tax increase is permanent, assume that at any constant levels of output and the real interest rate, consumers respond by reducing their consumption each period by the full amount of the tax increase. Under this assumption, how does the permanent increase in government purchases affect desired national saving and the IS curve?

c. Use the classical IS-LM model to find the effects of the permanent increase in government purchases and taxes on output, the real interest rate, and the price level in the current period. What happens if consumers reduce their current consumption by less than 100 at every level of output and the real interest rate?

3.

a. Employment

b. The real wage

c. Average labor productivity

d. Investment

e. The price level

4. Starting from a situation with no government spend­ing and no taxes, the government introduces a foreign aid program (in which domestically produced goods are shipped abroad) and pays for it with a temporary 10% tax on current wages. Future wages are untaxed.

What effects will the temporary wage tax have on labor supply? Use the classical IS-LM model to find the effects of the fiscal change on output, employ­ment, the (before-tax) real wage, the real interest rate, and the price level.

5. This problem asks you to work out in more detail the example of reverse causation described in the text. Suppose that firms that expect to increase production in the future have to increase their current transac­tions (for example, they may need to purchase more raw materials). For this reason, current real money demand rises when expected future output rises.

a. Under the assumption that real money demand depends on expected future output, use the classi­cal IS-LM model to find the effects of an increase in expected future output on the current price level. For simplicity, assume that any effects of the increase in expected future output on the labor market or on desired saving and investment are small and can be ignored.

b. Suppose that the Fed wants to stabilize the current price level. How will the Fed respond to the increase in expected future output? Explain why the Fed's response is an example of reverse causation.

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