There are two borrowers (denoted by S and R respectively) each of whom need 1 unit of credit for an investment. There is one lender (denoted by L) with one unit of credit and can only lend to one borrower. both the lender and borrowers are risk-neutral (that is, they only care about the expected prots and expected returns respectively). Further, the borrowers and lender have a reservation return of zero (that is, they will undertake to borrow or lend as long as the expected return or prot is strictly greater than zero). Finally, each borrower will repay if she is able to and nothing is repaid if the investment fails (i.e. there is limited liability).

(a) Suppose that there are two states of the world (g, b) each occurring with equal probability. In state g the return to S is 1.4 and Rs return is 1 + d for some d > 0. In state b, Ss return is 1.4 and Rs return is 0. Suppose that the bank can charges a separate interest rate for S and R respectively, denoted by rS and rR respectively. What interest rates rS and rR will the bank choose?

(b) What is Ls expected prot if it lends to S at the rate rS you found above?

(c) What is Ls expected prot if it lends to R at the rate rR you found above?

(d) What is the smallest value of d at which the bank prefer to lend to R over S?

(e) Suppose d = 2, that is to say the Rs project yields a 200% return in the good state of the world. Will the bank want to lend to R?

(f) Now suppose that d = 2 and that the bank can no longer distinguish between S and R. In other words, it can only oer one interest rate r and decides to lend to one of S and R purely as a result of a coin ip. Will the bank lend to either borrower? Justify your answer.

(g) Comment on the merit of this example in understanding the functioning of credit markets.