A borrowing sovereign has its output fluctuating following a uniform distribution [16,24] U [ 16 , 24 ] .

Suppose that the government borrows =6 L = 6 before the output is known; this loan carries an interest rate r L . The loan is due after output is realized. Suppose that if the government defaults on the loan, then it faces a cost equivalent to =0.5 c = 0.5 of its output. The loan is supplied by competitive foreign creditors who has access to funds from world capital markets, at a risk-free interest rate of 12.5%. **

Part a. (5 marks) Find the equilibrium r L . **

Part b. (5 marks) What is the probability that the government will repay its loan? **

Part c. (5 marks) Would the borrowing country default if = r L = r ? Prove it.