Class #2 Highlights

In this class, we studied the information problem in a competitive equilibrium setting. Here, we took a standard labor market setting and tweaked it by adding private information about worker productivity and outside options. Under complete information, the market equilibrium was, of course, efficient as per the first welfare theorem.

Adding private information complicates the computation of equilibrium by adding beliefs on the part of firms as to the average productivity of the labor pool attracted by a given wage offer. In our setting, demand is infinite if beliefs > wage. Demand is zero if beliefs < wage. Demand is anything if beliefs = wage. Therefore, in any competitive equilibrium, beliefs = wage.

Beliefs are correct if, ex post, the average worker productivity is equal to beliefs. A wage offer of w will attract workers of types [theta_0, r-1(w)]. Thus, beliefs must be E[theta | theta <= r-1(w)] when wage w is offered. Combining this with the zero profit condition yields a competitive equilibrium. That is, any wage w such that

w = E[theta | theta <= r-1(w)]

is a competitive equilibrium. 

The key properties of competitive equilibrium are:

1. Allocations can be inefficient. 

2. Under some conditions, the market can completely unravel. 

3. There can be multiple equilibria, which are Pareto rankable. The "best" equilibrium is the one with the highest wage. 

Finally, we examined whether a policy maker could do better absent knowledge of thetas and absent the ability to compel workers to accept employment. Under these conditions, a policy maker can do no better than to choose the highest equilibrium wage provided that it must satisfy budget balance.

Key things should be able to do after this class:

1. Compute a competitive equilibrium in a market with private information.
2. Determine whether there is an efficiency loss in such an equilibrium and compare the outcome to a first-best benchmark.