Question 2 A risk-averse employer is looking to hire a risk-neutral worker. The em- ployer's output, denoted Q, depends on the worker's effort E, which has a dis-utility c(E) = k E, k > 0. Output can take two possible values: Q1 with probability F(E) and Q2 with probability 1 - F(E), where Q2 0 and F" 0 and U" 0. (a) [5 marks] Write down the expected utility of the employer and the worker assum- ing the employer pays W if output is high, and W if output is low. (b) [12 marks] Derive the first-order conditions for the optimal contract (W, W2, E) of the employer under symmetric information, (that is, assuming the worker's effort E is observable and verifiable). (c) [10 marks] Assume effort E is observed only by the worker, and show that her optimal effort level E* satisfies F'(E*) (W - W) = k. (d) [8 marks] Compare the first-best and the second-best contracts emerging from (b) and (c). Justify briefly any differences and/or similarities between the two. Question 2 A risk-averse employer is looking to hire a risk-neutral worker. The em- ployer's output, denoted Q, depends on the worker's effort E, which has a dis-utility c(E) = k E, k > 0. Output can take two possible values: Q1 with probability F(E) and Q2 with probability 1 - F(E), where Q2 0 and F" 0 and U" 0. (a) [5 marks] Write down the expected utility of the employer and the worker assum- ing the employer pays W if output is high, and W if output is low. (b) [12 marks] Derive the first-order conditions for the optimal contract (W, W2, E) of the employer under symmetric information, (that is, assuming the worker's effort E is observable and verifiable). (c) [10 marks] Assume effort E is observed only by the worker, and show that her optimal effort level E* satisfies F'(E*) (W - W) = k. (d) [8 marks] Compare the first-best and the second-best contracts emerging from (b) and (c). Justify briefly any differences and/or similarities between the two