There are two types of workers (L and H) that look ex ante identical. The output of an L-type is 2 and the output of a H-type is 4. Each has a reservation utility of 4. The utility function of the L-type is
uL = 2wL - 6eL
where wL is the wage they receive and eL is the level of education they receive.
Similarly, the utility of the H-type is
uH = 2wH - 2eH
a. If the total population is equally split between Ls and Hs, what is the pooling wage?
Now consider the case when education can be possibly used as a signal of productivity. The game is as follows. The workers decide on the level of e they wish to get. The firms observe e and can offer wages on the basis of e. The workers accept or reject the contracts offered and trade takes place.
What is the minimum level of eH for which a separating equilibrium can exist.
b. What if instead the utility function for the H-type is: uH = 2wH - 6eH. Outline the separating equilibrium in this case. Provide intuition for your result.