A risk-neutral firm is looking to hire a worker. The firm's output, denoted y, depends on the worker's effort e and a random factor . More precisely, y = 2e + 1 + , with E() = 0 and Var() = 2. Suppose that the output price is equal to 1. Let the worker's utility be given by U(s, e) = E(s) Var(s) e^2/2 , where s denotes the salary paid by the firm. Assume the worker's utility from the best alternative job is 0. Suppose the firm offers to the worker a salary contract that takes the form s = a + by.

(a) [20 marks] Derive the incentive compatibility and the participation constraints.

(b) [20 marks] Determine the equilibrium effort level and the equilibrium salary.