Consider Spence’s job-market signaling model with the following specifications. There are two types of workers, 1 and 2. The productivities of the two types, as functions of the level of education E, are
The costs of education for the two types, as functions of the level of education, are
Each worker’s utility equals his or her income minus the cost of education. Companies that seek to hire these workers are perfectly competitive in the labor market.
(a) If types are public information (observable and verifiable), find expressions for the levels of education, incomes, and utilities of the two types of workers.
Now suppose each worker’s type is his or her private information.
(b) Verify that if the contracts of part (a) are attempted in this situation of information asymmetry, then type 2 does not want to take up the contract intended for type 1, but type 1 does want to take up the contract intended for type 2, so “natural” separation cannot prevail.
(c) If we leave the contract for type 1 as in part (a), what is the range of contracts (education-wage pairs) for type 2 that can achieve separation?
(d) Of the possible separating contracts, which one do you expect to prevail? Give a verbal but not a formal explanation for your answer.
(e) Who gains or loses from the information asymmetry? How much?