A risk-averse employer is looking to hire a risk-neutral worker. The employer'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: Q, with probability F(E) and Qâ‚‚ with probability 1 - F(E), where Q2 0 and F"<0. The employer offers a salary W, and it has a utility over net profits given by U(Q-W), with U> 0 and U" <0. Assume the worker's utility from the best alternative job is Um >0.
(a) [5 marks] Write down the expected utility of the employer and the worker assuming the employer pays W, if output is high, and W 2 if output is low.
(b) [12 marks] Derive the first-order conditions for the optimal contract (W1W 2 E) of the employer under symmetric information, (that is, assuming the worker's effort
(c) Assume 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* (WW2)=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.
