There is an equal proportion of smart and dumb people in the economy. If employers knew the "type" of each job applicant, then each and every firm in the economy would pay a smart individual 80 monetary units (in lifetime earnings) and a dumb individual 50 units.

Whenever the firms cannot tell their job applicants apart, they pay each individual his or her expected value. Due to the nature of the industry, keeping an employee for an extended period of time does not give the firms any additional information about their intrinsic abilities a. Given the proportion of smart and dumb types in the population, what are the expected lifetime earnings of a person picked at random? Next, suppose there is a credential (a degree, perhaps) that a smart person can obtain at a cost of 5 monetary units and a dumb person can obtain at twice that cost, 10 units.

For the purposes of this problem, assume that all individuals of a certain type make the same decision, and that anyone with a degree in hand is automatically assumed to be smart and anyone without a degree assumed to be dumb.

b. Present the game in the normal form. Set the payoff (utility) of each person equal to the amount of their lifetime earnings minus the cost of obtaining the degree. c. State the dominant strategy of each type player, if such strategies exist. d. State the Nash equilibrium of the game. e. Would you say that under these parameters the market allocation of labor resources is efficient? Explain why or why not. f. Can the efficiency in this market be improved? Propose what needs to be done in order for that to happen.

g. Demonstrate the validity of your proposal using a numerical example. For the purposes of this exercise, let's assume that a dumb person's cost of obtaining the credential is always twice as large as that for a smart person.