4. A producer of chemical fertilizers has developed a new product that has performed well on all measures except soil leeching. Because of the potential for soil leeching, management is concerned that the government may impose restrictions on the sale and use of their new product. Management estimates that there is a 50-50 chance that restrictions will be imposed. With no restrictions, profit from the new product is estimated to be $125 million; with restrictions, the amount of profit will only be $25 million. Management must decide now, before knowing whether there will be restrictions, on whether to reformulate the product to solve this problem. The cost of the reformulation will be $25 million. There is a 0.6 chance that the reformulation will be successful, in which case, no restrictions will be imposed. There is 0.4 chance that it will fail. a. Assume the producer is risk neutral. What is the producer's best course of action? [Hint: it will be easiest to solve this problem by setting up a decision tree. Start with the producer's decision, which has two options. This leads to a point of risk.] b. Now, assume that the producer is risk averse. This requires the use of expected utility, rather than expected value. i. Start by assigning the correct utility to the $0 outcome. What is the utility of $0? ii. Then, assign the correct utility to the $125 outcome. What is the utility of $125? iii. Now, use the following to find the utility of the $25 and $100 outcomes. Figure 1: Firm is indifferent between this gamble and $25 Firm Gamble Risk No gamble .25 1-25 $25 U($125) U(SO) Figure 2: Firm is indifferent between this gamble and $100 Firm Gamble Risk No gamble .85 1-85 $100 U($125) U(SO) iv. Compute the expected utility of both of the firm's options. What course of action should it take using this framework