Ram has decided to retire. Ali is a lender from a neighboring village who decides to offer loans in Bagli. However, since he is from a different village,he does not know the farmers in Bagli. He only knows that 80% of the farmers are SAFE and 20% are RISKY. As a result, he has to charge a single interest rate to everybody who wants a loan. Like Ram, Alis opportunity cost is also 25%.

(f) Derive an expression for Alis expected profit, E(pi), as a function of the interest rate for values between the interest rates you identified in part (b) and part (e).

(g) What will happen if Ali increases the interest rate above the interest rate you identified in (e)?

(h) Use the expressions from parts (c) and (f) to graph Alis expected profit as a function of the interest rate for interest rates between 0 and 3. Label this Figure 2: Lenders Expected Profit under Asymmetric Information

(i) What is the equilibrium interest rate charged by Ali?

((b) What is the maximum interest rate Ali can charge so that both types of farmers would want to borrow?

(c) Let pi be Alis profit. Derive an expression for E(pi)the expected value of Alis profit from a loan, as a function of the interest rate when the interest rate is less than or equal to the value you identified in part (b). (Remember: Over this range of the interest rate Ali cannot tell to which type of farmer she has given the loan!).