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. Credit Market Equilibrium under Multiple Borrower Types Now we turn to a different problem, namely, what happens when lenders face borrowers of different types. In question 3, the lender is a monopolist who offers limited liability loans under symmetric information. In question 4, the lender is a monopolist who offers limited liability loans under asymmetric information. Question 3: Limited Liability and Symmetric Information Joanna is a moneylender who lives in the village of Yolo-land. 80% of the farmers in Yolo- land are SAFE farmers and 20% are RISKY farmers. Both types of farmers need a loan of $1,200 in order to farm. Farmers will take a loan as long as they can earn at least zero expected income. SAFE farmers have a good harvest in which they earn revenues of $2,100 with 100% probability. They never have a bad harvest. RISKY farmers have a good harvest in which they earn revenues of $3,900 with 55% probability. They have a bad harvest in which they earn revenues of $0 with 45% probability. Joanna has lived in Yolo-land her entire life and thus has perfect information about the farmers, ie., she knows who is a SAFE farmer and who is RISKY. As a result, she can offer different contract terms to SAFE and RISKY types. If Joanna offers a loan, she must withdraw $1,200 from her savings account, where she earns an interest rate of 10%. Joanna offers limited liability credit contracts in which the farmer must repay the full loan plus interest if the harvest is good, and they don't have to repay anything if the harvest is bad. (Note: The lender's opportunity cost and the amount of limited liability are different compared questions 1 and 2.) a. Let ys and ya denote the incomes of SAFE and RISKY farmers, respectively. Derive expressions for E(ys) and E(yR), the expected incomes of SAFE and RISKY farmers, respectively. For each expression, report both the "Setup" equation (as discussed in section) and your final equation. Report your final equations in intercept-slope format as in the questions above. b. Let aS and AR denote Joanna's profits from a loan to SAFE and RISKY farmers, respectively. Derive expressions for E(ms) and E(AR), the expected values of Joanna's profits from loans to SAFE and RISKY farmers, respectively, as functions of the interest rate, i. For each expression, report both the "Setup" equation (as discussed in section) and your final equation. Report your final equations in intercept-slope format as in the questions above