Question 1:
Consider the possibility that employers take the degree to be a reliable signal that a worker is a high-ability worker. Given this belief, employers pay workers $wh if they have the degree and $wl if they do not. Let high-ability workers be twice as productive as low-ability workers, with wh=40,000 and wl=20,000.
Let c=15,000. Let σh=3,000 and σl=10,000.
Given all these assumptions, who will choose to get the degree? Will it be an equilibrium for firms to pay wh to workers with the degree and wl to workers without the degree? Explain.
Remember: “equilibrium” means no tendency for change. To show that something is an equilibrium in this model, you must show that no one would want to change their behavior. Will low-ability workers want to change their decision about whether or not to get the degree? Will high-ability workers want to change their decision? Will employers want to change their decision about paying $wh to workers with the degree and $wl to workers without the degree?
Let “c” be exogenous. In other words, do not worry about whether “the school” would want to change the level of tuition that it charges.
Question 2:
Return to the situation in Q1: Employers consider education to be a reliable signal about whether or not a worker is of high-ability, and “the school” is exogenous (i.e. “the school” is not part of society).
Answer the following questions under the assumptions in Q1:
From a high-ability worker’s point of view, does it make sense to earn the degree?
From society’s point of view, does it make sense for high-ability workers to earn the degree?
From society’s point of view, would efficiency be enhanced by a government prohibition on paying higher wages to people who earned the degree? Would such a prohibition be a Pareto improvement? Explain.