Credit Market Competition and Capital Regulation

a higher interest rate on the loan, and so borrowers should just require the lowest possible
interest rate consistent with q =1, which is satisfied by rL =(1- k)rD +2c.Ifweagain
substitute this value of rL into the expression for bank profits we obtain

Π = (rL - (1 - k^cS)rD) - k^cSrE - c = c - k^cSrE,

which, after setting equal to zero, yields k^cS = ɪ as long as c < r_E. In this case, we have

rE )rD + 2c = ( ^rE^-c )rD + 2c.

Otherwise, for c>rE, k^cS =1, which implies that rL =2c. Moreover, substituting this
value of rL into q = min ∣rL^-(1^-k——, 1} and observing that k^cS = 1, we obtain that Π > 0
and q = min 4R-,_c, 1} = 1 for R ≥ 4c, and is less than 1 otherwise. All together, this implies
that q ≥ 1 for R ≥ 4c, and q < 1 for R < 4c. □

Proposition 5B When there is an excess supply of funds, capital regulation that maximizes

social welfare requires:

which is less than 1 for R>4c and equal to 1 otherwise.

2) For R < 2c^2-e_-^--d, monitoring is q = R-(^1-k—^rD < 1 and capital equals k^reg =

which is less than 1 for R < 8c^(rE-r^D) and equal to 1 otherwise.

Proof: Start by maximizing social welfare with respect to k, assuming that the loan rate is
set to maximize CS, i.e., that rL = R⁺(1₂ k^)-D. Social welfare is given by

maxSW =Π+CS- (1-q)(1- k)rD =qR- (1- k)rD - krE - cq².
k

We can now take the first order condition to get

∂SW ∂q

ɪ" = ɪ ^{(R - 2}cq) ^- rE ^{+ r}D.

∂k ∂k

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