Problem
Consider a village inhabited by 3 risk-neutral individuals: a borrower, an inside lender, and an outside lender. The first two are part of a credit cooperative. The borrower wants to invest in a project that costs K = $100. If she exerts effort, the project will be successful with probability 0.9 and will yield a return of y = $240. Otherwise, the project fails and her return is zero. If she "shirks" (i.e., if she does not put in enough effort), her probability of success is only 0.5. The cost of her effort is e = $30. The inside lender can lend at most b = $60 to be used as investment with a gross interest rate R = 160%. The outside lender will lend the rest of the funds needed to start the project at a gross interest rate of R = 210%. In case of default, the outside lender can seize an amount ? = $50 offered as collateral by the inside lender. As she is interested in the result of the project, the inside lender can choose whether to monitor the behavior of the borrower, which would imply a monitoring cost of P = $20. If she monitors, she knows the behavior of the borrower. In the event that misbehavior is discovered, the borrower will then be punished and incur a penalty equivalent to A = $9. Assume that all agents are rational, and that they understand the following time line: lending takes place first; then monitoring decisions are made; choices about effort are made next; and, finally, returns are realized and the borrower decides whether or not to repay.
a. What strategies will the borrower and the inside lender choose and why?
b. Will these strategies change if the inside lender increases the interest rate to R = 200%? Briefly explain your answer.