its market value rises. The higher market value of capital attracts investment, and so the capital stock begins to rise. As it does so, the industrys output rises, and thus the relative price of its product declines; thus profits and the value of capital fall. The process continues until the value of the capital returns to normal; at this point there are no incentives for further investment.

Now consider an increase in output that is known to be temporary. Specifically, the industry begins in long-run equilibrium. There is then an unexpected upward shift of the profit function; when this happens, it is known that the function will return to its initial position at some later time, T.

The key insight needed to find the effects of this change is that there cannot be an anticipated jump in q. If, for example, there is an anticipated downward jump in q, the owners of shares in firms will suffer capital losses at an infinite rate with certainty at that moment. But that means that no one will hold shares at that moment.

Thus at time T, and q must be on the saddle path leading back to the initial long-run equilibrium: if they were not, q would have to jump for the industry to get back to its long-run equilibrium. Between the time of the upward shift of the profit function and , the dynamics of and q are determined by the temporarily high profit function. Finally, the initial value of is given, but (since the upward shift of the profit function is unexpected) q can change discretely at the time of the initial shock.

Together, these facts tell us how the industry responds. At the time of the change, q Jumps to the point such that, with the dynamics of and q given by the new profit function, they reach the old saddle path at exactly time T. This is shown in Figure 8.6. q jumps from Point E to Point A at the time of the shock, q and then move gradually to Point B, arriving there at time T. Finally, they then move up the old saddle path to E.

This analysis has several implications. First, the temporary increase in output raises investment: since output is higher for a period, firms increase their capital stocks to take advantage of this. Second, comparing Figure 8.6 with Figure 8.5 shows that q rises less than it does if the increase in output is permanent; thus, since q determines investment, investment responds less. Intuitively, since it is costly to reverse increases in capital, firms respond less to a rise in profits when they know they wiU reverse the increases. And third. Figure 8.6 shows that the path of and q crosses the = 0 line before it reaches the old saddle path-that is, before time T. Thus the capital stock begins to decline before output returns to normal. To understand this intuitively, consider the time just before time T. The profit function is just about to return to its initial level; thus firms are about to want to ha\e smaller capital stocks. And since it is costly to adjust the capital stock and since there is only a brief period of high profits left, there is a benefit and almost no cost to beginning the reduction immediately.

These results imply that it is not just current output but its entire path over time that affects investment. The comparison of permanent and temporary output movements shows that investment is higher when output

FIGURE 8.6 The effects of a temporary increase in output

is expected to be higher in the future than when it is not. Thus expectations of high output in the future raise current demand. In addition, as the example of a permanent increase in output shows, investment is higher when output has recently risen than when il has been high for an extended period. This impact of the change in output on the level of investment demand is known as the accelerator.

The Effects of Interest-Rate Movements

Recall that the equation of motion for q is q = rq - iriK) (equation [8.24]). Thus interest-rate movements, like shifts of the profit function, affect investment through their impact on the equation for q. Their effects are therefore similar to the effects of output movements. A permanent decline in the interest rate, for example, shifts the = 0 locus up. In addition, since r multiplies q in the equation for q, the decline also makes the locus steeper. This is shown in Figure 8.7.

The figure can be used to analyze the effects of permanent and temporary changes in the mterest rate along the lines of our analysis of the effects of permanent and temporary output movements. A permanent fall in the interest rate, for example, causes q to jump to the pohit on the new saddle path (Point A in the diagram). and q then move down to the new long-run equilibrium (Point E). Thus the permanent decline in the interest

FIGURE 8.7 The effects of a permanent decrease In the interest rate

rate produces a temporary boom in investment as the industry moves to a permanently higher capital stock.

Thus, just as with output, both past and expected future interest rates affect investment. The interest rate in our model, r, is the instantaneous rate of return; thus it corresponds to the short-term interest rate. One implication of this analysis is that the short-term rate does not reflect all the information about interest rates that is relevant for investment. As we will see in more detail in Section 9.3, long-term interest rates are likely to reflect expectations of future short-term rates. If long-term rates are less than short-term rates, for example, it is likely that investors are expecting short-term rates to fall; if not, they are better off buying a series of short-term bonds than buying a long-term bond, and so no one is willing to hold long-term bonds. Thus, since our model implies that increases in expected future short-term rates reduce investment, it implies that, for a given level of current short-term rates, investment is lower when long-term rates are higher. Thus the model supports the standard view that long-term interest rates are important to investment.

The Effects of Taxes: An Example

A temporary investment tax credit is often proposed as a way to stimulate aggregate demand during recessions. The argument is that an investment tax credit that is known to be temporary gives Arms a strong incentive to