Equilibrium Contracts for a Worker with Stochastic Revenue and Effort Choice - Prof. Emil , Assignments of Microeconomics

Download Equilibrium Contracts for a Worker with Stochastic Revenue and Effort Choice - Prof. Emil and more Assignments Microeconomics in PDF only on Docsity! ECN 601: Problem Set 7 27 OCT 2008 Consider a number of …rms who compete for the services of a particular worker. When one of the …rms hires the worker, total revenue of amount Y accrues to the …rm. Y is stochastic and can take on one of S possible values, where Ys 2 [Y ; Y ] for s = 1; 2; :::; S with Y1 < Y2 < ::: < YS . The realized state of the world is observed by both parties and can be veri…ed by an independent arbiter. The worker has no assets but can in‡uence the probability, pse > 0, with which each state occurs by choosing one of two e¤ort levels–high, H, or low, L. Assume that e¤ort is productive so E[Y jH] > E[Y jL]: Assume that the worker and all …rms are expected utility maximizers. The …rms are risk neutral and care only about expected pro…ts, while the worker has a Bernoulli utility function given by Us = u(ws) e; where u(ws) is the utility of money in state s and e 2 (eL; eH) is the disutility of the e¤ort level the agent has decided to exert, where eH > eL. Assume that u(E[Y jeH ]) eH > u(E[Y jeL]) eL so that exerting high e¤ort is the socially optimal outcome. Suppose the …rms compete for the services of the worker by o¤ering him contracts C = (fwsgSs=1; e) which specify the e¤ort that the agent must exert and the compensation in each state of the world (for each realized revenue level). The timing of the interaction is as follows: (1) the …rms o¤er contracts to the agent; (2) the agent decides which …rm to work for and what e¤ort level to exert; (3) the amount of total revenue is realized and the …rm gives to the worker the compensation that was stipulated in the signed contract. I. RISK AVERSION. Assume that u(w) is strictly concave. A. Suppose that once the worker has signed a contract, the …rm can enforce the e¤ort level stipulated in the contract. That is, the …rm can observe the e¤ort level exerted by the agent and give him a payment of 0 if he deviates from the recommended level. Setup the optimization problem that describes the contract signed by the worker in equilibrium. Keep in mind that the …rms are competing for the services of the worker. Describe the properties of the equilibrium contract. What is the economic intuition behind this result? From now on, assume that the …rm CANNOT observe the e¤ort level chosen by the agent. That is, all the …rm can observe is the amount of total revenue realized. 1