Credit Market Competition and Capital Regulation

choice of capital from a social welfare perspective when we assume that there is an excess
supply of funds, and rates are set as part of a market solution to maximize the return to
borrowers. In other words, a regulator would solve the following problem.

max SW = Π + CS - (1 - q)(1 - k)rD
k

= qR - (1 - k)r_D - kr_E - cq²                    (9)

subject to

rL - (1 - k)rD
^q = mini------2------, ¹∫;

r_L =argmaxCS = q(R - r)
r

0 ≤ k≤1.

Again, we focus here on the case of an interior solution, and leave the other cases, which are
qualitatively similar, to the appendix.

Proposition 5 Assume that R < 2c2^rE_r-^rD . When there is an excess supply of funds, cap-
ital regulation that maximizes social welfare requires banks to hold capital equal to k^reg =

min n RrD^+rD r8^{c(rE r}D), 1O, which is less than 1 for R < 8c(rE-D)
Equilibrium monitoring is q = R-(^1-C g)^rD < 1.

Proof: See the appendix, which contains a full characterization of the equilibrium. □

While the interest rate on the loan is determined in a competitive market setting and not
subject to regulatory interference, a regulator may want to impose a capital requirement for
banks in order to ensure they have sufficient incentives to monitor. In contrast to Proposition
2, now the regulator is more likely to require that banks hold a positive amount of capital, and
this amount is greater than in the case where bank funds are in short supply. The reason
is that the market sets a lower loan rate when borrowers obtain the surplus than when

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