1. This question will investigate the possibility that moral hazard may affect interest rates. Suppose a bank has provided a loan of 1 unit to a firm. The interest rate is variable and may be set by the bank. After the bank sets the interest rate the manager of the firm can select actions that affect the outcome of the project. In particular, the manager the firm can choose the degree of risk in the business. If the manager of the firm is cautious and takes safe actions, then the revenue to the firm will be R = 1.04 with a probability of 0.75 and a R = 1 with a probability of 0.25. On the other hand, if the manager of the firm follows a risky strategy, then the revenue to the firm is R= 1.07 with probability 0.25 and R=1 with a probability of 0.75. The bank can set the interest rate r and the firm will be scheduled to repay 1+r. The profit to the firm is the revenue less expenses associated with repayment of the loan (principal and interest). The payoff to the bank is the interest payment received. However, following Stiglitz and Weiss, assume the bank can not receive interest payments greater than the amount of revenue earned by the firm. So if R = 1.03 and 1+r = 1.04, then the bank payoff will be the full revenue of the firm (1.03) and the firm will receive a payoff of zero. (a) Consider the behaviour of the manager of the firm. Calculate the expected profit to the firm as a function of the interest rate if the manager of the firm selects the safe project. (1 mark) (b) Calculate the expected profit to the firm as a function of the interest rate if the manager selects the risky project (1 mark) (c) Assume that the manager wants to maximise the expected profit of the firm. Describe under what conditions the firm manager will select the risky project and under what conditions the firm manager will select the safe project. (1 marks) (d) Assume the bank sets the interest rate understanding how the project choice of the manager responds to interest rates. Is the payoff to the bank always increasing in the interest rate in this problem? If the bank wants to maximise profit, what interest rate should it charge the firm? Provide some intuition to explain this result. (2 marks)