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By Gerhard Clemenz

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If its return is a concave function of the loan size L, it is easy to show that their demand for a loan is a decreasing function of R: (24) (25) g x(L) - RL ag aL where x'CO) x'CL) - R 00 o and x'Coo) o are assumed to hold. then 32 (26) < x"(L) (27) - 1 dL aR < 0 0 Hence (28) dL 1 dR x' , (L) < 0 The projects are assumed to be identical. In addition to the loan, clients also demand some other banking service, the price of which is denoted as b. The demand of the i-th client for the banking service is given by the following function (29) DI = Di (b, Li), aDi /aLi > 0 It is assumed that the n clients of a bank can be indexed in such a way that i > j =) aDI/at > aDJ/aL, Y L ~ O.

It would not pay a bank to increase R since this would reduce p and result in losses for her. : A bank could attract both borrowers and depositors by reducing R and increasing i and still make a profit. u. with respect to R. If P has, say, two local maxima then an equilibrium 46 may exist with two loan rates and rationing at the lower of the two. To see this consider Figure 3. ~. ~. E ~. _. Suppose HW is a Walrasian, market clearing equilibrium. It is not, according to Stiglitz and Weiss, the only possible equilibrium.

K) which specifies the loan rate and the number of loans for each of the k possible realizations of i. If n < 1. e. if the number of loans granted is smaller than the number of applicants then rationing is assumed to occur at random. Hence. from a borrower's point of view n(i) is the probability that he gets a loan in state i. (39) is the above mentioned constraint on the utility borrowers derive from the contract. (40) states that the number of loans cannot exceed the number of clients (recall m=l) and (41) is the usual nonnegativity constraint on the number of loans.

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