Problem

Consider a similar economy as the one described in the previous exercise. In this case, however, assume 3 types of potential borrowers, all protected by limited liability. If she succeeds, borrower 1 gets a gross return y1 = $300 with probability 0.9; she gets a return of zero if she fails. Borrower 2 gets a gross return y2 = $333.33 with probability 0.75 and zero if she fails. Borrower 3 gets a gross return y3 = $500 with probability 0.5 and zero if she fails. Each type counts for one third of the population in this economy. The opportunity cost (i.e., the labor market wage) for each potential borrower is $40. All three potential borrowers need $150 to carry out their projects, and the lender's cost of capital is $54 for each $150 loan.

a. If group lending is not available as an option, can all potential borrowers gain access to credit to carry out their investment projects? Explain your answer.

b. Now suppose that group lending with joint liability contracts is feasible, that matching is assortative, and that the bank can observe the final returns of all borrowers. The bank will take the entire revenue of the lucky borrower if her partner defaults. Compute the interest R** and briefly explain your result.

c. How relevant is this exercise to the case of solidarity groups in practice?