4. Limited Liability and 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 40% of the farmers are SAFE and 60% 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 $250 from his savings account where he earns an interest rate of 30%. He is also a monopolist who offers the same type of limited liability loans that Raj offered (fully repay under good harvest; repay 40% of the total debt obligation if harvest is bad).

1. What type of asymmetric information problem does Isaac face? Write a short explanation justifying your answer.
2. What is the maximum interest rate Isaac can charge so that both types of farmers would want to borrow?
3. Let be Isaac's profit. Derive an expression for (), 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 she has given the loan!).
4. What is the maximum interest rate Isaac can charge so that at least one type of farmer will want a loan?