Problem
This exercise is similar to the previous one, but timing of events is crucial. Consider the following timing: loans are made at date 0, borrowers' types are revealed at date 1, and returns are realized at date 2. Borrowers want to invest in projects that cost $100 at date 0, but they do not have any wealth of their own. Until their types are revealed at date 1, borrowers are identical to the bank; ex ante there is an equal probability (of π = 0.5) that a borrower will turn out to be type 1 and type 2. The rest of the environment is exactly the same as in the previous exercise.
a. If group lending can't be implemented in this economy, can all agents borrow? What interest rate would the bank charge if they can? Briefly explain your answer.
b. Now suppose that the bank can lend to jointly liable pairs of borrowers and can also observe the final returns of each borrower. Compute the interest rate at which the bank will lend in this case, and briefly explain your answer in light of the results obtained in (a).
c. Explain the kind of credit market inefficiencies this exercise highlights, and the way such inefficiencies are mitigated by group lending under joint liability.
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.