Question 4

A credit market has two types of borrowers: s (safe) and r (risky); each has proportion 1/2. Any borrower borrows 1 unit of capital to invest in a project. A project can result in either one of the two outcomes: good or bad. Under bad outcome, the return is 0. Under good outcome, the return is xs = 108 for type s and xr = 111 for type r. The probability of good outcome is ps = 2/9 for type s and pr = 1/6 for type r.

A credit contract is given by interest i (which includes both principal and interest). Under this contract, a borrower pays back i to lender if the outcome is good and pays back nothing if the outcome is bad. The opportunity cost of a borrower is B0 = 12. The opportunity cost of a lender is L0 = 7. Assume the credit market is competitive, so a lender makes zero net profit. Showing all steps of your work, answer the following questions.

(a) [3 points] Find the maximum acceptable rate of interest for each type. (b) [5 points] Consider the full information case where a lender knows types of individual borrowers. Determine interest rates offered, which type gets loan and the aggregate income. (c) [9 points] Consider the asymmetric information case where a lender does not know types of individual borrowers and only knows there is proportion 1/2 of each type. Determine interest rate offered, which type gets loan and the aggregate income. Then determine if there is a problem of underinvestment or overinvestment.