Consider a job market signaling problem. There are two types of workers with ability high (ƟH) and low (ƟL), where ƟH > ƟL.
A worker with education level e knows his productivity Ɵ while his potential employer firm does not know Ɵ (although the potential employer observes the level of education (e).
Firms are behaving competitively. The proportion of the high ability workers in the market is half. The worker chooses the level of education e which the firms can observe. The worker’s payoff is w-(e2 /Ɵ), where w is the wage offered by his employer.
Assume ƟH =3 and ƟL =2.
i. What would be the equilibrium under symmetric information (i. e. theta is common knowledge)?
ii. Under asymmetric information, what is the minimum level of education e the high type worker acquires in separating equilibria? What is the level of education acquired by the low type worker in such equilibria? Discuss how your answer would change if productivity became Ɵ +e.

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