it could be that the no monitoring is ever optimal. We assume therefore that ∂R, while
negative, is of sufficiently small magnitude that at least some monitoring is always optimal.
We can now use the FOC to find -k by use of the implicit function theorem (IFT). Define
∂G
G ≡ R — (1 — k)cD — 2cq + q--R, which is identically equal to 0. By the IFT, -k = -⅛.
q ∂q
However, since the problem is concave in q, we have that —G < 0, which means that the
sign of ∂-k is the same as the sign of -G = cD > 0. Therefore, -k > 0, implying that capital
provides incentives to monitor. Therefore, we conclude that our results continue to hold
even in the case where limited liability for banks creates a risk-shifting problem.
7 Concluding remarks
A standard view of capital regulation is that it offsets the risk-taking incentives provided by
deposit insurance. A common approach in the study of bank regulation has been to assume
that any capital requirements will be binding, since equity capital is generally believed to
more costly than other forms of finance. However, in many cases such as the U.S. in the 1990’s
they appear not to be binding. In this paper we have developed an alternative view of capital
that is consistent with the observation that capital constraints may or may not be binding.
In particular, when there is an excess supply of funds relative to the number of attractive
projects available so that banks compete for projects, the level of capital determined by the
market can be higher than the level required by a regulator that maximizes social welfare.
Our main results continue to hold even in the absence of deposit insurance. First, we
show that the market equilibrium can still involve a positive level of capital, whether there
is an excess supply or a shortage of bank funds. In addition, the optimal amount of capital
from a social welfare point of view can be above or below the equilibrium level in the market.
Our model has a number of implications which are in line with recent empirical observa-
tions. First, it suggests that capital requirements may not bind when, as in the last decade
(see, e.g., Boot and Thakor, 2000), the competitiveness of credit markets increases. Second,
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