Problem
1. Explain the concept of assortative matching under group lending from the microfinance institutions' standpoint. Focus your explanation on the scope for mitigating adverse selection inefficiencies.
2. A bank is considering extending loans to a population of four potential borrowers with identities A, B, C, and D. Borrowers A and B are of type 1, while borrowers C and D are of type 2. The bank can't observe borrowers' types, but it knows that there are two borrowers of type 1 and two of type 2. With a $100 loan, a type 1 borrower can invest in a project and get a gross return of y1 = $200 with certainty, while a type 2 borrower can obtain a gross return of y2 = $360 with probability 0.75. The opportunity cost for a borrower of type 1 is $18, and it is $20 for a borrower of type 2. If denied a loan, type 1 potential borrowers can earn a wage of $18 in the labor market, and type 2 potential borrowers can earn a wage of $20. The gross cost of a $100 loan for the bank is $160. The bank is competitive and aims only to break even. Borrowers are protected by limited liability.
a. If group lending is not possible, will all potential borrowers have access to loans? Derive the interest rate that the bank will charge in this case, and briefly explain your answer.
b. Now suppose that the bank can lend to jointly liable pairs of borrowers, and can observe all borrowers' final returns. Compute the interest rate at which the bank will lend in this case. Briefly explain your answer, comparing it to your answer to part (a).
c. What lessons does this exercise provide with respect to group lending under joint responsibility?