Problem
A microfinance institution aims to break even. Its manager cannot distinguish between entrepreneurs of different types, but she knows that the population of potential borrowers contains entrepreneurs who are safe with probability 0.5 and risky with probability 0.5. Safe entrepreneurs contract $100 loans and obtain $200 from investing with probability 1. Risky entrepreneurs contract $100 loans and obtain $222 from investing with probability 0.9, and zero with probability 0.1. If the cost of raising capital for the institution is $40 per loan, then the institution will charge an interest rate of 40 percent and break even without subsidies. In plain and clear language, explain why this is the case.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.