two solutions, q1 = 4lc ^rL + prLL — 8crD (1 — k) J and q2 = 4^ ^rL — prL — 8crD (1 — k) J,
with q1 >q2 . However, it is straightforward to show that both banks and borrowers are
better off with the higher level of monitoring. To see this, note that, in equilibrium, bank
profits are given by
∏(q) = q(rL — (1 — k) — ) — krE — cq2 = qrL — (1 — k)rD — krE — cq2,
(11)
which is strictly increasing in q for q ≤ rL. Since q2 < q1 < rL, banks prefer the equilibrium
with the higher level of monitoring. From the firm’s perspective, its equilibrium return is
either equal to rB when borrowers compete for funds or it is just CS(q) = q(R — rL) when
banks compete for borrowers. In the former case, the borrowers are indifferent to the choice
of q, whereas in the latter case, substituting for the equilibrium interest rate rL = R+(12 k)cD
we have
which again is strictly increasing in q . Since depositors are indifferent between the two levels
of monitoring, the higher level of monitoring, q1 , yields a Pareto-superior equilibrium. We
focus on this equilibrium in what follows.
CS(q) = q R—
R +(1 — k) rD
2
= 2(qR —(1 — k)rD ),
2
(12)
Having solved the last stage, stages 2 and 3 follow along the lines of the previous sections.
The rate on the loan, rL , is given either by the maximum rate that is consistent with
borrowers’ participation constraints when there is an excess supply of projects, or by the
rate that maximizes the return to borrowers, R+(1~k)cD, when there is an excess supply of
funds. Solving the first stage, where banks or the regulator choose the level of capital, we
obtain the following result.
Proposition 7 When there is an excess supply of funds (N>M) and no deposit insurance,
there exists a value rD (R, rE, c) > 0 such that kreg < kCS for rD < rD.
Proof: See the appendix. □
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