ICS Industries can have a high value = $18 or a low value = $11 next year. (These values already account for the managers base salary, but they do not account for a possible bonus.) The likelihood of a high value depends on the effort expended by the manager. If the effort is high, then the (risk-neutral) probability of a high value is 2/3, otherwise it is 1/3. The managers base salary is $2 and the high effort level costs the manager the equivalent of $1 in psychic pain, so without an incentive the manager will choose a low effort. For simplicity, assume that the risk-free rate is 0. a) (2 marks) How much of a bonus in the high-value state would a risk-neutral manager require to be induced to put forth a high effort? b) (2 marks) Should the firm adopt the compensation incentive plan in part a? (Does it add value to the firm? How much?) c) (2 marks) Suppose the manager is risk averse, so that now the expected value of the logarithm of her pay less cost of effort has to be at least as high with high effort as with low. How much of a bonus in the high state would this risk-averse manager require? d) (1 mark) Should the firm adopt the compensation incentive plan in part c? (Does it add value to the firm? How much?)