Problem

Consider a bank that conducts businesses in three stages. At stage 0, the bank lends to thirty poor clients, lending $1,000 per person. In stage 1, each individual borrower repays $1,200. The cost of serving each client, however, is $400. In stage 1, if the bank makes losses, it goes bankrupt. If it doesn't, the bank can continue to expand by lending to fi fty poor clients. (Assume that the bank can increase its clientele with donor's resources if the bank either breaks even or makes positive profits.) Suppose that all fi fty clients access an identical loan size, and that the bank gets an identical return per client in stage 2. Because of economies of scale, the cost of serving each individual borrower now drops to $300 per borrower. Provided that the bank continues to at least cover its costs in stage 2, it can expand its scale of operations by serving an additional one hundred poor clients. Again, the size of the loan per client remains unchanged and is the same for all clients. Now, as a result of economies of scale, the cost of serving each borrower has dropped further, to $100 per borrower. Suppose that each time a poor borrower is served by a formal microfinance institution, the net benefit to society is $5 and the benefit for the borrower is also $5. Finally, assume that all agents in the economy are risk-neutral, and that the economy-wide discount rate is zero. Assess arguments for subsidization of microlenders in this particular case. Would you favor write-offs of all potential losses at each stage?