Y = E{Y, i - 77 G, T) + NX{Y, i - 7 G, T, eP* IP),

(5.22)

where £(«) is domestic residents planned expenditure. £(«) is assumed to satisfy 0 < £f < 1, EPe < 0, £ > 0, and £ < 0. We can then use (5.21) to substitute for net exports, and thereby eliminate the exchange rate from the model:

Y = £(y, i - 77 G, ) - Cf (/ - / *).

(5.23)

Since Cf(i - /*) is increasing in i, the set of points satisfying (5.23) is downward-sloping in {Y,i) space. This locus is shown in Figure 5.9 as the /5** curve. Note that the exchange rate is implicitly changing as we move along the curve. Since the interest rate affects in (5.23) both through its direct effect on domestic demand and through its effect on the exchange rate and net exports, the /5** is flatter than a conventional IS curve. In the extreme case of perfect capital mobility, the IS** curve is flat at z *. The LM curve is the same as before.

IS"

FIGURE 5.9 The case of imperfect capital mobility and a floating exchange rate

affected by the exchange rate, the model can be analyzed graphically. With this assumption, we can write planned expenditure as the sum of domestic residents planned expenditure (on both domestic and foreign goods) and net exports:

FIGURE 5.10 The effects of an increase in government purchases with imperfect capital mobility and a floating exchange rate

The resuhs for this case typicaUy fall between those for a closed economy and those for perfect capital mobility. Consider again the effects of an increase in government purchases. Since this increase raises expenditure for a given mterest rate, the IS** curve shifts to the right, as shown in Figure 5.10. Thus, in contrast to what happens with perfect capital mobihty, and Y rise for a given price leveL Since the 75** curve is flatter than the closed-economy 75 curve, however, the effects are weaker than they are in a closed economy. The effects of other shocks can be analyzed in similar ways.

5.4 Alternative Assumptions about Wage and Price Rigidity

We now turn to the aggregate supply side of the model. This section describes various ways that a nonvertical AS curve might arise. In all of them, incomplete nominal adjustment is assumed rather than derived. Thus this sections purpose is not to discuss possible microeconomic foundations of nominal stickiness; that is the job of Chapter 6. Instead, the goal is to explore some combinations of nominal wage and price rigidity and characteristics of the labor and goods markets that give rise to a nonvertical AS

Case 1: Keyness Model

The aggregate supply portion of the model in Keyness General Theory (1936) begins with the assumption that the nominal wage is rigid (at least over some range):

W = W. (5.24)

Output is produced by competitive firms. Labor, L, is the only factor of production that is variable in the short run, and it is subject to decreasing returns:

Y = F{L), £(•)> 0, fCXO. (5.25)

Since firms are competitive, they hire labor up to the point where the marginal product of labor equals the real wage:

F(L) = -f. (5.26)

Equations (5.24)-(5.26) imply an upward-sloping AS curve. Since the wage is fixed, a higher price level implies a lower real wage. Firms respond by raising employment, which increases output. Thus there is a positive relationship between P and .

The reason that incomplete nominal adjustment causes shifts in aggregate demand to change output in this case is straightforward. With rigid nominal wages, increases in the price level reduce the real wage and therefore increase the amount that firms want to sell. As a result, increases in aggregate demand lead not just to increases in prices, but to increases in both prices and output.

Figure 5.11 shows the situation in the labor market for a given price level. Employment and the real wage are determined by labor demand at the real wage that is implied by the fixed nominal wage and the price level (Point E in the diagram). Thus there is involuntary unemployment: some workers would like to work at the prevailing wage but cannot. The amount of unemployment is the difference between supply and demand at the prevailing real wage (distance EA in the diagram).

Fluctuations in aggregate demand lead to movements of employment and the real wage along the downward-sloping labor demand curve. A decline in demand, for example, leads to a fall in the price level, a rise in the

curve. The different sets of assumptions have different implications for unemployment, for the behavior of the real wage and the markup in response to aggregate demand fluctuations, and for firms pricing behavior.

We consider four sets of assumptions. Each is of interest in its own right. Together, they illustrate the wide range of possibilities.