Raj has decided to retire. His grandson, Isaac, will be the new lender in the village....

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Raj has decided to retire. His grandson, Isaac, will be the new lender in the village. Isaac has lived his whole life in the big city and does not know the farmers in the village of Yolo-land. Isaac only knows that 70% of the farmers are SAFE and 30% are RISKY. As a result, he has to charge a single interest rate to everybody who wants a loan. Like Raj, in order to offer a loan, Isaac must withdraw $100 from his savings account, where he earns an interest rate of 15%. He is also a monopolist who offers the same type of limited liability loans that Raj offered (fully repay under good harvest; repay 0% of the total debt obligation if harvest is bad). a. What type of asymmetric information problem does Isaac face? Write a short explanation justifying your answer. b. What is the maximum interest rate Isaac can charge so that both types of farmers would want to borrow? c. Let be Isaac's profit. Derive an expression for E(), the expected value of Isaacs's 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, Isaac cannot tell to which type of farmer he has given the loan!). d. Explain what will happen if Isaac increases the interest rate above the interest rate you identified in b? e. What is the maximum interest rate Isaac can charge so that at least one type of farmer will want a loan? f. Derive an expression for Isaac's expected profit, E(), 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 Isaac increases the interest rate above the interest rate you identified in part e? h. Use the expressions from parts c and f to graph Isaac's expected profit as a function of the interest rate for interest rates between 0 and 3. Label this graph "Figure 4. Lender's Expected Profit under Asymmetric Information" and insert it in the box below. i. What is the equilibrium interest rate charged by Isaac? j. What is Isaac's expected profit? 13 k. Which type or types of farmers take the loan? 1. For the type(s) of farmer(s) identified in (k), find the expected income. m. Under symmetric information, a monopolist lender will drive the expected income of the borrower(s) to zero. Based on your answer to part 1, is that still the case for a monopolist under asymmetric information? Raj has decided to retire. His grandson, Isaac, will be the new lender in the village. Isaac has lived his whole life in the big city and does not know the farmers in the village of Yolo-land. Isaac only knows that 70% of the farmers are SAFE and 30% are RISKY. As a result, he has to charge a single interest rate to everybody who wants a loan. Like Raj, in order to offer a loan, Isaac must withdraw $100 from his savings account, where he earns an interest rate of 15%. He is also a monopolist who offers the same type of limited liability loans that Raj offered (fully repay under good harvest; repay 0% of the total debt obligation if harvest is bad). a. What type of asymmetric information problem does Isaac face? Write a short explanation justifying your answer. b. What is the maximum interest rate Isaac can charge so that both types of farmers would want to borrow? c. Let be Isaac's profit. Derive an expression for E(), the expected value of Isaacs's 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, Isaac cannot tell to which type of farmer he has given the loan!). d. Explain what will happen if Isaac increases the interest rate above the interest rate you identified in b? e. What is the maximum interest rate Isaac can charge so that at least one type of farmer will want a loan? f. Derive an expression for Isaac's expected profit, E(), 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 Isaac increases the interest rate above the interest rate you identified in part e? h. Use the expressions from parts c and f to graph Isaac's expected profit as a function of the interest rate for interest rates between 0 and 3. Label this graph "Figure 4. Lender's Expected Profit under Asymmetric Information" and insert it in the box below. i. What is the equilibrium interest rate charged by Isaac? j. What is Isaac's expected profit? 13 k. Which type or types of farmers take the loan? 1. For the type(s) of farmer(s) identified in (k), find the expected income. m. Under symmetric information, a monopolist lender will drive the expected income of the borrower(s) to zero. Based on your answer to part 1, is that still the case for a monopolist under asymmetric information?