subject to
rL - (1 - k)rD
q = mint------2c------, 1t;
rL =argmaxΠ(r);
r
CS = q(R - rL) ≥ rB;
0 ≤ k≤1.
The optimization problem is similar to before, with the important difference that the regula-
tor chooses only the level of capital, and that it does so in order to maximize social welfare.
The loan rate is still set as part of the market solution, as given in Proposition 1.
Proposition 2 When there is an excess demand for credit, capital regulation that maximizes
social welfare requires that banks hold capital equal to k = 1 — rc (rE — rD), which is positive
as long as rD > max ∣R — 2c, pc(c + 2rE) — c}.
Proof: See the appendix. □
Proposition 2 implies that welfare-maximizing capital regulation requires a positive level
of capital due to its positive incentive effect on bank monitoring. This occurs when the
required return for depositors rD is sufficiently high that banks would not monitor fully
when they have no capital (i.e., when rD >R— 2c), and also high enough that the positive
incentive effect on social welfare of raising capital outweighs the cost rE (i.e., when rD >
pc(c + 2ге ) — c).
Comparing Propositions 1 and 2 leads to the following immediate result.
Proposition 3 When there is an excess demand for credit, capital regulation requires banks
to hold a higher amount of capital than the market ifrD > max
2c, Pc(c + 2ге) — c∣.
This result establishes that a regulator will often require a higher amount of capital than
the amount that maximizes banks’ profits, and never a lower amount. Regulation can thus
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