Consider the signaling model of the value of schooling discussed in class. There are two types of workers, high-skilled and low-skilled. Assume that high-skilled workers have ability aH = 10 and low-skilled have ability aL = 6. The share of workers with high ability is H = 0.6, the share of workers with low ability is L = 1 H = 0.4. Worker's ability is known to the worker. Suppose that a firm is willing to pay $10 per unit of ability.

1.Suppose that the firm can observe workers' ability. What wage will it offer to a high-skilled worker? What wage will it offer to a low-skilled worker? Denote these wages wH and wL, respectively. If all high-skilled workers are paid wH and all low-skilled workers are paid wL, what is the average wage in the economy, w?

2.Suppose now that a firm cannot observe worker's ability but can ask a worker about it. If a worker say she has high ability, the firm offers her the wage wH. If a worker says she is low ability, the firm offers her the wage wL. Will workers tell the truth about their ability?

4.In a pooling equilibrium of the model, the firm does not ask about workers' ability and pays only one wage to everybody, the average wage w. Do workers like this equilibrium or would they rather in a world where they are paid wH and wL depending on their ability?

4.Suppose now that firm says that every worker who obtains a college degree will be paid wH, and workers without a college degree will be paid wL. Getting the college degree is costly: it costs cH for high ability workers and cL for low ability workers. For each values of cL, cH given below evaluate whether a separating equilibrium, in which high types go to college and the low types do not go to college, exits. HINT: For such an equilibrium to exist, it has to be the case that low ability workers prefer not to go to college, and high ability workers prefer to go college.

a) cL = 0, cH = 0

b) cL = 30, cH = 30

c) cL = 50, cH = 50

d) cL = 30, cH = 50

e) cL = 50, cH = 30

5.Provide economic explanation why separating equilibrium exists in some cases of 1.4 and not in the others.