Consider similar economy as in the previous exercise. But in this case there are three types of potential borrowers: Borrower 1 succeeds with probability 90 percent and gets a gross return y1 = \($300.\) If she fails, she does not get anything. Borrower 2 succeeds with 75 percent probability and gets a gross return y2 = \($333.33.\) And with 25 percent probability, she does not obtain anything. Borrower 3 succeeds with 50 percent probability and gets a gross return y3 = \($500.\) This latter type fails with 50 percent probability, in which case she gets zero. Each type counts for one third of the population. The opportunity cost for each potential borrower is \($40.\) Investment in this economy requires \($150,\) and the lender’s cost of capital is \($54\) for the total investment.

Borrowers are protected by limited liability.

a. If group-lending mechanism can not be applied, can all potential borrowers obtain a loan?

b. Now consider group lending. Suppose that the bank can lend to a group of two borrowers on the condition that the borrower will have to pay for her partner if her partner defaults. Suppose that like will match with like and that the bank can observe the final returns of each type: In each group, the bank will take the entire revenue of the lucky borrower if her partner defaults. Compute the interest R**. Briefly explain the result.