Problem
Consider a bank that conducts a microlending program in four stages-at dates zero, one, two, and three. At date zero, the bank lends to thirty-five poor clients an amount 6,000 taka per person. At date one, each individual borrower pays back at most 7,000 taka. The cost of serving each client, however, is 2,000 taka. At date one, if the bank makes losses, it goes bankrupt. If it doesn't, it can continue expanding by lending to sixty-five poor clients. (Assume that the bank can increase its clientele by systematically either breaking even or making positive profits.) Suppose that all sixty-five clients obtain an identical loan size, and that the bank gets an identical return per client in date two. Because of economies of scale, the cost of serving each individual borrower, however, drops to 1,500 taka per borrower. At date two, and provided the bank continues breaking even or making positive profits, it can expand its scale of operations by extending loans to 100 poor clients. Again, assume that the size of the loan per client remains unchanged and that it is the same for all clients. Assume again that, as a result of economies of scale, the cost of serving each borrower drops even further, to 500 taka per borrower. Now suppose that by the virtue of having access to a loan, the borrowers can reduce the risk to their income from 17 percent to 3 percent. Assume that, if the borrower can not obtain a loan from the bank, she has an income of 500 taka. And when she invests with the proceeds of a loan from the bank, she also gets 500 taka after repaying her debt. Finally, assume that all agents in the economy are risk neutral, and that there is no discounting between periods. Would you favor subsidization of formal banking activities in this case? For example, will you favor write-offs of all potential losses at each stage? Explain your answer.