There is a borrower in the financial market. The borrower can invest $1000 and get a return 60% of the time of $1,500, 30% of the time of $1000, and 10% of the time $300. For ease of computation, assume that lenders do not accept collateral on any loans and the borrower does not have any money of her/his own. Finally, imagine that in the case of default, the borrower ends up with neither a loss nor a gain; in other words, the lender loses the amount lent and the borrower pays no bankruptcy costs. For lenders, they can either lend the money to the borrower, or they can buy a bond which gives 5% return.

a) What is the equilibrium loan rate a lender will charge on the borrower? Assume that the market is competitive such that lenders (who are risk neutral) in equilibrium are indifferent between purchasing the bond and lending the money to the borrower.

b)If the rate of return on the bond falls from 5% to 2%, what is the equilibrium loan rate you will charge on the borrower in this case?

c) Under the assumption that the rate of return on the bond is 5%, now we consider a case that a new borrower enters the financial market, who can invest $1000 and get a return 30% of the time of $3,000, 60% of the time of $1000, and 10% of the time $0. Assume that lenders cannot tell the types of the two borrowers. Do you expect an increase or a decrease in the equilibrium loan rate charged by a lender? Explain.

No credit will be given if no explanations are provided.

d)If the bond's return is positively correlated with the federal funds rate, what is the impact of an open market purchase on the equilibrium loan rate charged by lenders in the economy? Discuss. We can simply assume that the bond's return is equal to the federal funds rate in equilibrium.

No credit will be given if no explanations are provided.