and are positive. Policymakers want to stabilize output, but they cannot observe or the shocks, Eis and elm- Assume for simplicity that p is fixed.

(fl) Suppose the policymaker fixes / at some level /. What is the variance of y?

(b) Suppose the policymaker fixes m at some level Tn. What is the variance of y?

(c) If there are only LM shocks (so aj = 0), does money targeting or interest-rate targeting lead to a lower variance of y?

id) If there are only /5 shocks (so af = 0), does money or interest-rate targeting lead to a lower variance of y?

(e) Explain your results in parts (c) and (d) intuitively.

(f) When there are only IS shocks, is there a policy that produces a variance of that is lower than either money or interest-rate targeting? If so, what policy minimizes the variance of y? If not, why not? (Hint: consider the LM curve, m - p= hy-ki.)

9.15. Uncertainty and policy. (Brainard, 1967.) Suppose output is given by = X + (k + Ek)z + u, where z is some policy instrument controlled by the government and is the expected value of the multiplier for that instrument. Ek and are independent, mean-zero disturbances that are unknown when the policymaker chooses z, and that have variances al and a. Finally, x is a disturbance that is known when z is chosen. The policymaker wants to minimize E[{y-y*n

(a) Find £[(y - y*)] as a function of x, k,y*, al, and al.

(b) Find the first-order condition for z, and solve for z.

(c) How, if at all, does a affect how policy should respond to shocks (that is, to the realized value of x)? Thus, how does uncertainty about the state of the economy affect the case for "fine tuning"?

(d) How, if at all, does al affect how policy should respond to shocks (that is, to the realized value of x)? Thus, how does uncertainty about the effects of policy affect the case for "fine tuning"?

9.16. Growth and seignorage, and an alternative explanation of the inflation-growth relationship. (Friedman, 1971.) Suppose that money demand is given by ln(M/P) = a - bi + In y, and that is growing at rate gy- What rate of inflation leads to the highest path of seignorage?

9.17. (Cagan, 1956.) Suppose that instead of adjusting their real money holdings gradually toward the desired level, individuals adjust their expectation of inflation gradually toward actual inflation. Thus equations (9.39) and (9.40) are replaced by m(t) = Ce-f and (f) = fiWd) - -nm, 0 < p < 1/b.

(a) Follow steps analogous to the derivation of (9.45) to find an expression for TTit) as a function of -( ).

(b) Sketch the resulting phase diagram for the case of G > S*. What are the dynamics of -*" and m?

(c) Sketch the phase diagram for the case of G < S*.

Chapter 10 UNEMPLOYMENT

10.1 Introduction: Theories of Unemployment

In almost any economy at almost any time, many individuals appear to be unemployed. That is, there are many people who are not working but who say they want to work in jobs like those held by individuals similar to them, at the wages those individuals are earning.

The possibility of tmemployment is a central subject of macroeconomics. There are two basic issues. The first concerns the determinants of average unemployment over extended periods. The central questions here are whether this unemployment represents a genuine failure of markets to clear, and if so, what its causes and consequences are. There is a wide range of possible views. At one extreme is the position that tmemployment is largely illusory, or the working out of unimportant frictions in the process of matching up workers and jobs. At the other extreme is the view that unemployment is the result of non-Walrasian features of the economy and that it largely represents a waste of resources.

The second issue concerns the cyclical behavior of the labor market. As described in Chapter 5, the real wage does not appear to be highly procyclical. This is consistent with the view that the labor market is Walrasian only if labor supply is highly elastic or if shifts in labor supply play an important role in employment fluctuations. But as we saw in Section 4.10, there is little support for the hypothesis of highly elastic labor supply. And it seems imlikely that shifts in labor supply are central to fluctuations. The remaining possibility is that the labor market is not Walrasian, and that its non-Walrasian features are central to its cyclical behavior. That possibility is the focus of this chapter.

The issue of why shifts in labor demand appear to lead to large movements in employment and only small movements in the real wage is important to aU theories of fluctuations. For example, we saw in Chapter 6 that if the real wage is highly procyclical in response to demand shocks, it is essentially impossible for the small barriers to nominal adjustment to generate substantial nominal rigidity. In the face of a decline in aggregate

demand, for example, if prices remain fixed the real wage must fall sharply; as a result, each firm has a huge incentive to cut its price and hire labor to produce additional output. If, however, there is some non-Walrasian feature of the labor market that causes the cost of labor to respond little to the overall level of economic activity, then there is some hope for theories of small frictions in nommal adjustment.

This chapter considers various ways m which the labor market may depart from a competitive, textbook market. We investigate both whether these departures can lead to substantial unemployment and whether they can have important effects on the cyclical behavior of employment and the real wage.

If there is unemployment m a Walrasian labor market, unemployed workers immediately bid the wage down until supply and demand are in balance. Theories of imemployment can therefore be classified according to their view of why this mechanism may fail to operate. Concretely, consider an unemployed worker who offers to work for a firm for slightly less than the firm is currently paying, and who is otherwise identical to the firms current workers. There are at least four possible responses the firm can make to this offer.

First, the firm can say that it does not want to reduce wages. Theories in which there is a cost as well as a benefit to the firm of paying lower wages are known as efficiency-wage theories. (The name comes from the idea that higher wages may raise the productivity, or efficiency, of labor.) These theories are the subject of Sections 10.2 through 10.4. Section 10.2 first discusses the possible ways that paying lower wages can harm a firm; it then analyzes a simple model where wages affect productivity but where the reason for that link is not explicitly specified. Section 10.3 considers an important generalization of that model. Finally, Section 10.4 presents a model formalizing one particular view of why paying higher wages can be beneficial. The central idea is that if firms cannot monitor their workers effort perfectly, they may pay more than market-clearing wages to induce workers not to shirk.

The second possible response the firm can make is that it wishes to cut wages, but that an explicit or impUcit agreement with its workers prevents it from doing so. Theories in which bargaining and contracts affect the macroeconomics of the labor market are known as contracting models.

Contracting models are the subject of Sections 10.5 through 10.7. Section 10.5 presents some basic models of contracting. Sections 10.6 and 10.7 then investigate what happens when some workers are represented in the bargaining process and others are not. Section 10.6 explores the implications of this distinction between insiders and outsiders for the cyclical behavior of labor costs and for average unemployment. Section 10.7 investigates its effects on the behavior of unemployment over time.

The firm can also be prevented from cutting wages by minimum-wage laws. In most settings, this is relevant only to low-skill workers; thus it does not appear to be central to the macroeconomics of unemployment.