cost of deposits is high relative to the cost of equity (i.e., when rD is close to rE). One way of
interpreting this finding is that capital can be valuable even when the payment to depositors
accurately reflects the risk they bear, so that banks internalize the cost of their risk-taking.
In other words, there is scope for bank capital to improve welfare even when there is a clear
channel for discipline from the liability side of the bank’s balance sheet. Finally, we note
that since borrowers compete away their surplus, the regulator’s maximization problem is
equivalent to the market’s problem, so there is no additional role for regulation.
6.2 Banks and Asset Substitution
In the analysis above, we have assumed throughout that bank monitoring is strictly value-
increasing, in that greater monitoring increases the expected return of the projects at the
same time that it reduces the probability of failure. Here, we briefly analyze the case where
banks may suffer from an asset substitution problem due to limited liability: since they are
highly leveraged, they may have an incentive to take on risky projects, shifting some of the
risk onto creditors. Specifically, we assume that the maximum return on the projects, R,is
a decreasing function of q , R0 < 0, so that for low monitoring, the return on the projects is
high but risky. By contrast, when a bank monitors a lot and q is high, the return on the
project is lower, but the project is safer. For simplicity, we focus only on the case where
there is a shortage of funds.
Given cD , expected profits for the bank can be expressed as
max Π = q(R--B — (1 — k)cD) — krE — cq2. (13)
The FOC for an interior solution is
R—(1—
k)cD — 2cq + qdR = 0,
∂q
(14)
which defines the equilibrium value of monitoring, q*. Note that, if ∂R is sufficiently negative,
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