Question

Question 8. There are two types of works: some have a high productivity, aH, and some have low productivity, aL. Workers can get a job after leaving high school or they can 2 go to college at a cost of cH for high productivity workers and cL for low productivity workers. Assume that aH > aL > 0 and cL > cH > 0. Education has no impact on productivity. Describe a separating equilibrium in which employers pay workers a wage equal to the expected productivity conditional on the level of education. What conditions must be satisfied by the parameters aH, aL, cH and cL in order for such as separating equilibrium to exist?

Answer 1

Given, two types of works: high productivity, aH, and low productivity, aL. This is also the wage of high productivity and low productivity workers, respectively. College at a cost of cH for high productivity workers and cL for low productivity workers. Also, aH > aL > 0 and cL > cH > 0. Let e be an expected level of productivity on which wages are based. Lets assume average productivity e satisfy following equation:

(aH-aL)/cH> e > (aH-aL)/cL

Separating equilibrium occurs only if cL > cH > 0 and aH > aL . At this equilibrium, high educated workers will be given a wage of e. Low educated workers will not be given anything. To show that this is indeed an equilibrium:

Low productivity workers will only attain high productivity only if, benefits exeeds cost, i.e. (aH-aL)> cL*e, but this is not the case here. So, they do not attain high productivity. On the other hand, highly productive workers wil accept this wage because aH-aL>cH*e.

If cH > cL > 0, then separating equilibrium does not exist