5. Limited Liability and Asymmetric Information. Diego has decided to retire. Yaxi is a ender from a neighboring village who decides to offer loans in Nyabiheke. However, since she is from a different village, she does not know the farmers in Nyabiheke. She only knows that half of the farmers are SAFE and half are RISKY. As a result, she has to charge a single interest rate to everybody who wants a loan. Like Diego. Yaxi's opportunity cost is also 20%. (a) What type of asymmetric information problem does Yaxi face? (b) What is the maximum interest rate Yaxi can charge so that both types of farmers would want to borrow? (c) Let ? be Yaxi's profit. Derive an expression for E (T), the expected value of Yaxi'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 Yaxi cannot tell to which type of farmer she has given the loan!). (d) Explain what will happen if Yaxi increases the interest rate above the interest rate you (e) What is the maximum interest rate Yaxi can charge so that at least one type of farmer will (f) Derive an expression for Yaxi's expected profit, E (T), as a function of the interest rate for (g) What will happen if Yaxi increases the interest rate above the interest rate you identified in (h) Use the expressions from parts (c) and (f) to graph Yaxi's expected profit as a function of the identified in (b)? want a loan? values between the interest rates you identified in part (b) and part (e) interest rate for interest rates between 0 and 3. Label this "Figure 4: Lender Expected Profit under Asymmetric Information (i) What is the equilibrium interest rate charged by Yaxi? G) What is Yaxi's expected profit? (k) Which type of types of farmers take the loan? 5. Limited Liability and Asymmetric Information. Diego has decided to retire. Yaxi is a ender from a neighboring village who decides to offer loans in Nyabiheke. However, since she is from a different village, she does not know the farmers in Nyabiheke. She only knows that half of the farmers are SAFE and half are RISKY. As a result, she has to charge a single interest rate to everybody who wants a loan. Like Diego. Yaxi's opportunity cost is also 20%. (a) What type of asymmetric information problem does Yaxi face? (b) What is the maximum interest rate Yaxi can charge so that both types of farmers would want to borrow? (c) Let ? be Yaxi's profit. Derive an expression for E (T), the expected value of Yaxi'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 Yaxi cannot tell to which type of farmer she has given the loan!). (d) Explain what will happen if Yaxi increases the interest rate above the interest rate you (e) What is the maximum interest rate Yaxi can charge so that at least one type of farmer will (f) Derive an expression for Yaxi's expected profit, E (T), as a function of the interest rate for (g) What will happen if Yaxi increases the interest rate above the interest rate you identified in (h) Use the expressions from parts (c) and (f) to graph Yaxi's expected profit as a function of the identified in (b)? want a loan? values between the interest rates you identified in part (b) and part (e) interest rate for interest rates between 0 and 3. Label this "Figure 4: Lender Expected Profit under Asymmetric Information (i) What is the equilibrium interest rate charged by Yaxi? G) What is Yaxi's expected profit? (k) Which type of types of farmers take the loan