Assignment questions, image attached for better quality.

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 rm. The interest rate is variable and may be set by the bank. After the bank sets the interest rate the manager can select actions that affect the outcome of the project. In particular, assume that the manager of the rm can choose the degree of risk in the business. If the manager of the rm is cautious and takes safe actions, then the revenue to the rm 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 rm follows a risky strategy, then the revenue to the rm is R = 1.07 with probability 0.25 and R = l with a probability of 0.75. The bank can set the interest rate 1" and the rm will be scheduled to repay 1 + r. The prot to the rm is the revenue less interest expenses and the payoff to the bank is the amount of 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 rm. So if R = 1.03 and 1 + 7' = 1.04, then the bank payoff will be the full revenue of the rm (1.03) and the rm will receive a payoff of zero. (a) Consider the behaviour of the manager of the rm. Calculate the expected prot to the rm as a function of the interest rate if the manager of the rm selects the safe project. (I mark) (1)) Calculate the expected prot to the rm 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 prot of the rm. Describe under what conditions the rm manager will select the risky project and under what conditions the rm manager will select the safe project. (1 marks) ((1) 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 prot, what interest rate should it charge the rm? Provide some intuition to explain this result. (2 marks)