R{D)

FIGURE 8.14 The determination of the entrepreneurs required payment to the investor

ttie investor tfie required net revenues. Tfie contract tfierefore specifies ttiis value of D. For the case when the required payment equals Vi, the equilibrium value of D is given by Di in the figure.

If the required net revenues exceed R-ii they equal V3, for example-there is no value of D that yields the necessary revenues for the investor. Thus in this situation there is credit rationing: investors refuse to lend 1-W to the entrepreneur at any interest rate.

Finally, if the required net revenues are between - and R, there are two possible values of D. For example, the figure shows that a D of either

or D yields R{D) = Vz. The higher of these two Ds (Di in the figure) is not a competitive equilibrium, however: if an investor is making a loan to an entrepreneur with a required payment of D, other investors can profitably lend on more favorable terms. Thus competition drives D down to The equilibrium value of D is thus the smaller solution to R{D) = (1 + r){l - W). Expression (8.30) implies that this solution is

D* = 2y - - (2y - c)2 - 4y(l + r)(l - W) for (1 + r)(l - W) < R.

(8.31)

Equilibrium Investment

The final step of the analysis is to determine when the entrepreneur undertakes the project. Clearly a necessary condition is that he or she can

Note that the condition for the expression under the square root sign, (2y - cf -4y(l 4 r)(l - W\ to be negative is that [(2y - c)l2yYy < (1 -h r)(l - that is, that is less than required net revenues. Thus the case where the expression in (8.31) is not defined corresponds to the case where there is no value of D at which investors are wihing to lend.

2y- 2y "aJ

(2y~cV (1 + r)(l - W) 2y )

(8.32)

Straightforward differentiation shows that A is increasing in and r and decreasing in and W. We can therefore write

A = A(c, r, W, y), Ac > 0, Ar> 0, Aw < 0, Ay < 0. (8.33)

The entrepreneurs expected payments to the investor are (1 + r)(l ~W)+ A(c, r, W, y). Thus the project is undertaken if (1 + r){l - W) < R and

- (1 -b r)(l -W)- A{c, r, W, y) > (1 -b r)W. (8.34)

Although we have derived these results from a particular model of asymmetric information, the basic ideas are general. Suppose, for example, that there is asymmetric information about how much risk the entrepreneur is taking. In such a situation, if the investor bears some of the cost of poor outcomes, the entrepreneur has an incentive to increase the riskiness of his or her activities beyond the point that maximizes the expected return to the project; thus there is moral hazard. As a result, asymmetric information again reduces the total expected returns to the entrepreneur and the investor, just as it does in our model of costly state verification. Under plausible assumptions, these agency costs are decreasing in the amount of financing that the entrepreneur can provide (W), increasing in the amoimt that the investor must be paid for a given amount of financing (r), decreasing in the expected payoff to the project (y), and increasing in the magnitude of the asymmetric information (c when there is costly state verification, and the entrepreneurs ability to take high-risk actions when there is moral hazard).

obtain financing at some interest rate. But this is not sufficient: some entrepreneurs who can obtain financing may be better off investing in the safe asset.

An entrepreneur who invests in the safe asset obtains (1 +r)W. If the entrepreneur instead undertakes the project, fiis or her expected receipts are expected output, y, minus expected payments to the outside investor. If the entrepreneur can obtain financing, the expected payments to the investor are the opportunity cost of the investors funds, (1 + r)(l - W), plus the investors expected spending on verification costs. Thus to determine when a project is undertaken, we need to determine these expected verification costs.

These can be found from equation (8.31). The investor verifies when output is less than D *; this occurs with probability D * / 2 . Thus expected verification costs are

D* A= "C 2y

Implications

This model has many implications. As the preceding discussion suggests, most of the major ones arise from financial-market imperfections in general rather than from our specific model. Here we discuss four of the most important.

First, the agency costs arising from asymmetric information raise the cost of external finance, and therefore discourage investment. Under symmetric information, investment occurs in our model if > 1 - r. But when there is asymmetric information, investment occurs only if > I + r + A(c, r, W, y). Thus the agency costs reduce investment at a given safe interest rate.

Second, because financial-market imperfections create agency costs that affect investment, they alter the impact of output and interest-rate movements on investment. Recall from Section 8.5 that when financial markets are perfect, output movements affect investment through their effect on future profitability. Financial-market imperfections create a second channel: because output movements affect firms current profitability, they affect firms ability to provide internal finance. In the context of our model, we can think of a fall in current output as lowering entrepreneurs wealth, W; since a reduction in wealth increases agency costs, the fall in output reduces investment even if the profitabifity of investment projects (the distribution of the ys) is unchanged.

Similarly, interest-rate movements affect investment not only through the conventional channel, but also through their impact on agency costs: an increase in interest rates raises agency costs, and thus discourages investment. Intuitively, an increase in r raises the total amount the entrepreneur must pay the investor. This means that the probabiUty that the investor is unable to make the required payment is higher, and thus that agency costs are higher. Specifically, since the investors required net revenues are (1 + r)(l - W), an Increase in r of increases these required revenues by (1 - W)Ar; thus it has the same effect on the required net revenues as does a faU in W of [(1 - W)/(l + r)]Ar. As a result, as equation (8.32) shows, these two changes have the same effect on agency costs.

In addition, the model implies that the effects of changes in output and interest rates on investment do not all occur through their impact on entrepreneurs decisions of whether to borrow at the prevaUing interest rate;

Similarly, suppose that entrepreneurs are heterogeneous in terms of how risky their projects are, and that risk is not publicly observable-that is, that there is adverse selection. Then again there are agency costs of outside finance, and again those costs are determined by the same types of considerations as in our model. Thus the qualitative results of this model apply to many other models of asymmetric information in financial markets.