Question 1:
Assume that workers know their abilities, but employers do not. Also assume:
• all workers are college educated, but half of them are high-ability and half are low-ability.
• the respective productivities of high- and low-ability workers are all = $150 and aL = $80;
• because of the extra effort involved, graduating with "honors" costs high-ability workers $50 and low-ability workers $80 relative to a standard degree.
• the extra requirements for the "honors" designation have no effect on productivity, but employers can easily verify whether a worker graduated with honors.
a) Show that under these conditions, a "signaling" equilibrium exists, in which high-ability and low-ability workers make different educational investments and receive different wages. Describe employer beliefs, workers' educational investments (whether or not they invest in earning honors), and wages under the signaling equilibrium-record the equilibrium set of beliefs and actions using the table below (next page). Show/briefly explain why this set of beliefs and actions is an equilibrium.
b) Suppose that the honors program were watered down so that the costs of graduating with honors were only $20 for high-ability types and $60 for low-ability types. How, if at all, would this change the equilibrium outcomes? Explain briefly.
c) Suppose instead that that the honors program is made more difficult so that the costs of graduating with honors are $80 for high-ability types and $100 for low-ability types. Now what would happen to the equilibrium outcomes? Explain briefly.
Question 2:
A clothing chain (call it the Gup) wishes to hire sales workers who are genuinely enthusiastic about their brand because they are more productive sales people. Suppose there are two types of job seekers. Type H (for high enthusiasm) loves Gup clothes and purchases at least $100 worth of their clothes each month. Type L (for low enthusiasm) does not especially like Gup clothes and would never buy them. When working for the Gup, average productivity of Type H workers is $500/month while average productivity of Type L workers is only $400 per month. Both types of workers are equally productive when working elsewhere and can earn the market wage of $450 per month.
Gup managers could tell the two types of workers apart by performing extensive interviews, but the chain receives many applications and interviewing each applicant is very costly. Also, the Gup does not wish to pay workers on commission because they have found that this discourages team work and creates an unpleasant environment that makes customers uncomfortable.
Gup's HR manager conies up with a new strategy: the Gup places job advertisements explaining that their compensation package is $400 per month plus $80 worth of Gup clothes each month. Briefly explain how compensation package helps the Gup with its hiring goals.
Question 3:
A particular diploma costs a high ability person $16K and costs a low ability person $25K. Firms wish to use education as a screening device where they intend to pay $75K to workers with a diploma and $Y to those without a diploma. In what range must Y be to make this an effective screening device?