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 - kcS)rD) - kcSrE - c = c - kcSrE,

which, after setting equal to zero, yields kcS = ɪ as long as c < rE. In this case, we have

rL =(1


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

Otherwise, for c>rE, kcS =1, which implies that rL =2c. Moreover, substituting this
value of
rL into q = min ∣rL-(1-k——, 1} and observing that kcS = 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:

1) For R > 2c2rE-D
rD


monitoring is q = min {R, 1}, and capital equals kreg =


min{        , 1},


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

2) For R < 2c2-e---d, monitoring is q = R-(1-k—rD 1 and capital equals kreg =

RrD +rD2 -8c(rE -rD)
min(-----D-rD-------,1;


which is less than 1 for R < 8c(rE-rD) 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 - 2cq) - rE + rD.

∂k ∂k

28



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