1. Consider the Competitive banking model of Freixas and Rochet Section 3.1. where Banks' profit function is given by #(D, L) = (rL-r)L+(r(1-a) - rp)D- C(D, L), where r, is the rate of interest charged on loans, rp is the rate of interestpaid on depsoits and r is the interbank interest rate and a.is the reserve requirement. Suppose that r, ,rD rD a and the cost function is given by C(D. L) = 2(D²+L?-DL)+ + ito+4 100 (a) Is the cost function Convex? (b) Derive Banks equilibrium level of Deposits and Loans (c) If the reserve requirment, a, on the level of deposits increases to will the level of loans awarded by the bank go up?
1. Consider the Competitive banking model of Freixas and Rochet Section 3.1. where Banks' profit function is given by #(D, L) = (rL-r)L+(r(1-a) - rp)D- C(D, L), where r, is the rate of interest charged on loans, rp is the rate of interestpaid on depsoits and r is the interbank interest rate and a.is the reserve requirement. Suppose that r, ,rD rD a and the cost function is given by C(D. L) = 2(D²+L?-DL)+ + ito+4 100 (a) Is the cost function Convex? (b) Derive Banks equilibrium level of Deposits and Loans (c) If the reserve requirment, a, on the level of deposits increases to will the level of loans awarded by the bank go up?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1. Consider the Competitive banking model of Freixas and Rochet Section 3.1. where Banks'
profit function is given by (D,L) = (rL-r)L+(r(1-a)-rp)D- C(D, L), where r
is the rate of interest charged on loans, rp is the rate of interestpaid on depsoits and r
is the interbank interest rate and a.is the reserve requirement. Suppose that ri =rD
rD Ha= and the cost function is given by C(D, L)= 2(D+L? -DL)+ + 6o+A
100
100
(a) Is the cost function Convex?
(b) Derive Banks equilibrium level of Deposits and Loans
(c) If the reserve requirment, a, on the level of deposits increases to will the level of
loans awarded by the bank go up?
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