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Consider a moneylender who faces two types of potential customers: call them the safe type and the risky type. Each type of borrower needs a loan of (the same) size B to invest in some project or activity. The borrower can repay only if the investment produces sufficient returns to cover the repayment.
Suppose that the safe type is always able to obtain a secure return of R ( R > B ) from his investment. On the other hand, the risky type is an uncertain prospect; he can obtain a higher return R′(where R′ > R ), but only with probability p . With probability1− p , his investment backfires and he gets a return of 0.
Suppose that the lender has enough funds to lend to just one applicant, and that there are two of them (one risky, one safe).
(a) What is the highest interest rate r1 for which the safe borrower wants the loan? What is the highest interest rate r2 for which the risky borrower wants the loan?
(b) If the lender charges r1 or below, both borrowers will apply for the loan. If the lender cannot tell them apart, he has to give the loan randomly to one of them. On the other hand, if a rate slightly higher than r1 is charged, the first borrower drops out and excess
demand for the loan disappears. The lender may then go all the way up to r2 without fear of losing the second customer. Then, the lender’s choice is really between the two interest rates r1 and r2 . Which should he charge? Show that if
then the lender will charge r1 instead of r2 .
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