Consider a market for college professors (or administrators, if you prefer) in which there are 100 sellers (candidates) and 100 buyers (college search committees). Suppose the supply side of the labor market is made up of two "types" of candidates: {lemons, peaches}. Lemons are poorly-trained slackers and have a low productivity value, whereas peaches are well-trained, have intrinsic motivation, and are highly productive. Assume it is common knowledge that there are 50 lemons and 50 peaches in this market. Buyers (search committees on the demand side) cannot observe a candidate's type. Candidates know their own type.

• A lemon candidate is willing to accept a job for a minimum salary of $60000 and a peach candidatefor $160000 minimum.
• The buyers arewilling to pay a maximum of $200000 for a peach and a maximum of $100000 for a lemon.

Note that if it is easy to verify the quality of the candidates there will be no problems in this market.

The lemons will be usually be hired at some price between $60000 and $100000and the plums will sell at some price between $160000 and $200000.

a) First, suppose there is no asymmetric info. Draw a figure modeling this market with perfect info. How many of each type are hired?

b) Now, assume search committees have to guess about how much each candidate is really worth any "buyer" would be willing to pay a maximum of the expected value of the candidate. Using the numbers described, find the maximum salary any buyer would be willing to offer any candidate. Draw a figure describing the market failure. At this maximum offer, how many lemons and how many peaches will be hired in equilibrium?

c) Give me one simple, potential solution to this market failure resulting from asymmetric information.

d) Finally, consider the case in which the distribution of lemons to peaches credibly shifts: now there are 30% lemons and 70% peaches. Model this market. What is different from the results in parts a-c?

e) Describe the difference between a pooling equilibrium and a separating equilibrium.