2. Consider the GhatakGuinnane framework from the lecture: risk-neutral borrower and |ender.The borrower wants to borrow 1 to invest in a project that pays Y with probability p, 0 otherwise. The opportunity cost of capital is p. the opportunity cost of borrower's time is is. The lender can only collect in the high state, and may offer either an individual liability contract (repay T when own project is successful) or a joint liability contract (repay 7" when own project is successful, plus an additional c if partner's contract is unsuccessful). a. Under what (formal) condition is the project socially profitable? b. Henceforth we assume the project is socially profitable. Suppose that the probability of success is determined by costly effort, with the cost of attaining 39 equal to %ryp2. Suppose initially that the borrower were using his/her own money for investment. What would be the optimal choice of effort, p? c. Now instead the borrower must borrow from the lender if s/he is to invest. If the lender cannot observe or directly influence 3:), what is the borrower's choice ofp now? How does it compare to under (b)? What do we call this problem? d. Now suppose the borrower is under a joint liability contract. If his/her partner chooses effort level 10', what is the borrowers optimal choice of p? How does it vary with p'? e. If borrowers do not act cooperatively, what is the symmetric Nash level of effort? 1". If the borrowers can cooperate, what is the level of effort? How does it compare to individual liability, and what does that tell us about JLL in theory? N.B. You can assume 7 > 20