Exercise 2: Adverse selection, competing principals and signalling. Consider a setting where several agents are facing c

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Exercise 2 Adverse Selection Competing Principals And Signalling Consider A Setting Where Several Agents Are Facing C 1 (66.85 KiB) Viewed 66 times

Exercise 2: Adverse selection, competing principals and signalling. Consider a setting where several agents are facing competing employers. Agents have distinct abilities. Let a € (2,4) denote an agent's ability. The variable a is known to the agent only and is not verifiable. Principals know that, a priori, a = 2 with a probability of . Agents have the possibility to select an education level s € (0,1). Note that the level of education is a continuous variable. The level of education chosen by any agent is verifiable. Employers can therefore offer different wages based on the level of education chosen by the agent. Let w(s) denote the wage paid to a agent with education level s. Let q(s) be the probability that an employer assigns to facing a high ability agent, that is such that a = 4, when the level of education chosen by the agent is s: q(5) - Pr(a = 4/8). All parties are risk neutral. The payoff to a principal is given by T = a -w. The utility of an agent depends on his ability. The high ability agent has a lower cost of education: 8 un (w.s) = w-- a Utility of a high ability agent who has a productivity a = 4 ug (w,s) = w - 2s. Utility of a low ability agent who has a productivity a = 2 uz (w.s) = w - 4s.