In this exercise, we examine the adverse selection issue discussed in the chapter. Call as the share of safe projects and (1- a_s) the share of risky projects. Assume that a safe project yields a return of R, with 100% probability. Assume that a risky project yields a return of R, with probability p, and a return of 0 with probability (1 - p_r). Assume that the lender has perfect information about which projects are safe and which are risky. What is the minimum interest rate necessary to recover a loan of 1 with the safe project? What is the minimum interest rate necessary to recover a loan of 1 with the risky project? Assume that the lender cannot recognize which loans are safe and which are risky. What, then, is the minimum interest rate the bank must charge in order to recover a loan of 1? Above what interest rate would the safe projects stop demanding a loan?