Question

Suppose there are two types of works: high ability and low ability. The fraction of high ability workers is given by x. Each worker knows her own type. If high workers are employed by a firm they produce output equal to y h . If low ability workers are employed they produce y l where y h > y l > 0. If a worker does not work they produce 0.

1. Suppose firms observe the ability of workers perfectly. The firms are perfectly competitive and they only use labor in the production process. Therefore the profit each firm makes is equal to the output of the worker it hires minus the wages paid to that worker. What wages are firms willing to offer to each type of worker?

2. Now suppose there is asymmetric information. Firms do not know workers’ quality. Higher ability workers also differ from low ability workers in their tolerance for writing CVs. High ability workers have utility functions over wages w and length of CV s: Uh = w − s Low ability workers have utility functions: UL = w − 2s Assume that s>0. The length of CV does not affect worker’s productivity.

3.For what values of s does there exist a pooling equilibrium in which both types of workers write a CV of length s? For what values of s does there exist a separating equilibrium in which high productivity workers write a CV of length s and low productivity workers do not write a CV (i.e s=0).

Answer 1

Answer 1:

Human capital is viewed as an input in the production process-

# Here the firm is assuming their ability based on their output.

Answer (2): The environment mentioned here is corresponds to a dynamic game of incomplete information, individuals know about their ability, but firms do not. In natural equilibrium concept in this case is the Perfect Bayesian Equilibrium .

There are two types of equilibria in this game.

(a) Separating

(b) Pooling

Based on the following algorithm

High ability workers utility functions over wages w and length of CV s: Uh = w − s

Low ability workers utility functions: UL = w − 2s Assume that s>0