Credit Market Competition and Capital Regulation

₂(₂rR^r-_rD) < c < RR, and in this range kCS = rc and k^reg = RrD +rD -^-8c^rr rD). The difference

k^reg - k^CS simplifies to

(rE - c)r_D² +(R +8c)rErD - 8cr_E² =0

The relevant solution is

r_r (R+8c) - √32c²+R²+16c(R+2r_r )

2(c- rE)

which implies k^reg > kCS only if rD > r_D. □

Proof of Proposition 7: Assume that there is an excess supply of funds so that, as before,
consumer surplus is maximized by setting

We can substitute this into the equation for q, recalling that c_D = ^rD, and solve for q to
obtain q₁ = 8C ^R + pR² — 16crD (1 — k) ´ and q₂ = -ɪ- (R — pR² - 16crD (1 — k) ´. We
focus again on the Pareto dominant equilibrium with a higher level of monitoring (q1).

We proceed by maximizing CS with respect to the choice of capital, k. However,
we know from above that the combination of rL = R⁺(¹2 ^k)^cD and the highest possible
k will be optimal for borrowers. We therefore introduce the participation constraint for
the bank, that Π = q(r_L — (1 — k)c_D) — kr_E — cq² ≥ 0. Substituting for r_L gives q =
8C (R + RR- — 16cr_d (1 — k) I, and we obtain

П2

— krE = 0

Focusing on parameter values for which there is an interior solution for k, the solution is

<<   32   33   34   35   36   37   38   >>

More intriguing information