Question 4: Limited Liability and Asymmeftric Information Joanna has decided to retire. Her daughter, Emily. will be the new lender in the village. Emily has lived her whole life in the big city and does not know the farmers in the village of Yolo-land. Emily only knows that 80% of the farmers are SAFE and 20% are RISKY. As a result, she has to charge a single interest rate to everybody who wants a loan. Like Joanna. in order to offer a loan, Emily must withdraw $1.200 from her savings account, where she earns an interest rate of 10%. She is also a monopolist who offers the same type of limited liability loans that Joanna offered (fully repay under good harvest: repay 0% of the total debt obligation if harvest is bad). b. What 1s the maximum mterest rate Enuly can charge so that both types of farmers would want to borrow? c. Let w be Enuly's profit. Derive an expression for E(m). the expected value of Emily's profit from a loan, as a function of the interest rate when the interest rate 1s less than or equal to the value you identified 1 part b. Report both the "Setup" equation (as discussed in section) and your final equation. (Remember: Over this range of the interest rate, Emily cannot tell to which type of farmer she has given the loan!). d. Explam what will happen if Enuly increases the interest rate above the interest rate you identified 1n b? e. What 1s the maximmum interest rate Emily can charge so that at least one type of farmer will want a loan? f Derive an expression for Enuly's expected profit, E(x). as a function of the interest rate for values between the interest rates you identified in part b and part e. Report both the "Setup\" equation (as discussed in section) and your final equation