4. (35 points) Erik works in a factory and his employer is redesigning his compensation contract. Erik generates revenues for his employer by putting in effort, denoted by 9: TR 2 6002+ p. ,u is a random shock to production with an expected value of (l and a standard deviation 0' > 0. However, effort is costly to Erik, whose marginal cost of effort is equal to 3e. Furthermore, Erik can reject the employer's new compensation contract, quit his job and nd another job which gives him a net utility denoted by W. The employer cannot observe Erik's effort level, so compensation can depend on revenue, but not on effort. Moreover, only contracts that are linear in revenue can be used: 1 (TR) 2 42+ ,6 TR. The employer designs the compensation contract, i.e., or and , to maximize profits, H : TR I (TR) . Finally, Erik is risk averse while the employer, who has her resources well diversied, is risk neutral. a) Derive the rst-best productively efcient level of effort (call it e\"). b) Erik chooses his effort level to maximize the difference between expected wage and the cost of effort. Derive the effort level that Erik will optimally choose as a function of the incentive coefcient in the compensation contract, (call it 91,6); c) If the firm's objective were to implement efficiency in production, what level of ,6 should it choose? Explain your answer. d) If the firm's objective were to implement efficiency in risk-sharing, what level of ,3 should it choose? Explain your answer. e) Given your answer in parts c) and d), in what range will the profit-maximizing choice of ,6 lie? Discuss factors that would make the employer choose a more high-powered incentive contract (i.e., a high level of ,6). You do not have to make any calculations. f) Emma works next to Erik performing the same task. Would the employer want to base Erik's compensation in part on how much output and revenue Emma produces? Explain your