4 Excess demand for credit
We begin with the case where there is a shortage of loanable funds relative to the demand
for credit, which implies that banks will be able to obtain their preferred terms. This case
reflects a situation where there are fewer banks than investment projects (N<M), so that
borrowers compete away the return on their projects in order to attract funding.
Banks set k and rL so as to maximize their expected profits, taking into account their
subsequent monitoring choice and the fact that borrowers accept the loans only if they have
a non-negative surplus. Thus, the profit-maximizing contract solves the following problem:
max Π = q(rL - (1 - k)rD) - krE - cq2 (6)
k,rL
subject to
rL - (1 - k)rD
q
CS
= mint----2c----, T
= q(R - rL) ≥ rB;
0 ≤ k≤1.
The first constraint represents the monitoring effort that banks choose in order to maximize
expected profits after lending to borrowers, which was obtained above. The second constraint
is the participation constraint of borrowers, labelled as consumer surplus (CS), and states
that borrowers will be willing to accept loans only if they can earn an expected return no
less than rB . The last constraint is simply a physical constraint on the level of capital, in
that banks can choose between raising only deposits, a mixture of deposits and capital, or
being entirely equity financed.
The solution to this maximization problem yields the following result.
Proposition 1 When there is an excess demand for credit, banks maximize profits by holding
no capital (k = 0) and offering a loan rate equal to the maximum possible return on the
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