Problem
Consider a two-period economy. Suppose that at date 0 a risk neutral borrower obtains a loan I and invests it in a project which yields a gross return I · y at date 1 with probability p and 0 with probability 1 - p, where p is exogenous. If the borrower repays her debt obligation R, the bank will offer her a new loan, λ times larger than the previous one, at date 1. If the borrower invests at date 1, her gross return at date 2 is I · y · λ with probability p and 0 with probability 1 - p. Assume that the borrower's production technology exhibits constant returns to scale, and that her discount factor is δ < 1. the borrower's only source of income is the return realization on her project, and she is protected by limited>
a. Compute the maximum gross loan repayment R* that the bank can set without undermining the borrower's incentives to repay at date 1.
b. Consider the case in which I = $100, λ = 1.5, y = 3.5, δ = 0.8, p = 0.9, and the gross cost of lending $1 for the bank is $1.2. Assume that the bank just wants to break even. Would you expect both parties to agree on a loan contract? Explain your answer.
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.