3. (12 marks) The Republic of Delinquia has a non-disaster output level of $100 each year. With 10% probability each year, output falls to a disaster level of $80, and the country will feel so much pain that it will default and pay neither principal nor interest on its debts. The country decides to borrow $20 at the start of the year, and keep the money

under the mattress. It will default and keep the money in the event that output is low, but this will entail sacrificing $4 in punishment costs. Otherwise, it pays back principal and interest due. Lenders are competitive and understand these risks fully.

a.What is the probability of default in Delinquia?

b.The interest rate on safe loans is 8% per annum, so a safe loan has to pay off 1.08 times $20. What is the lending rate charged by competitive lenders on the risky loan to Delinquia?

c.What does Delinquia consume in disaster years? In non-disaster years?

d.d. Repeat part (c) for the case in which Delinquia cannot borrow. Is Delinquia better off with or without borrowing?