Quantitative Problems

1.
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What are the principal features of the Roy model?
2.
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Consider a simple economy with two occupations: law (L) and medicine (M), and a large number of workers. Each worker's ability is described by , where λ is his talent as a lawyer and μ his talent as a doctor. Suppose that the pairs are uniformly distributed, with . (This means that each pair is equally represented in population: if there are 10 workers with the ability level (3, 3), then there are also 10 with the ability level (2, 2).)

The market rewards legal skills, at the rate $, and medical skills at the rate $m, where .

For added concreteness, suppose the facts are as follows: . (Notice that, these numbers do satisfy the condition )

(a) What are the average legal and medical abilities in the population at large? What are average earnings if everybody picks his occupations randomly?

(b) In the case of indifference, assume workers elect to become lawyers. Given this, depict the individuals who choose law and those who choose to become doctors. Depict the average earnings of lawyers. How do they compare with the answer in (a)?

(c) Depict the effects of a small increase in the value of m upon the occupational disposition.
3.
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An employer has a vacancy it is seeking to fill. It can immediately fill this position with a low-ability worker (in which case, its revenues are $100). Alternatively, it can reject the worker and search for another. (The average ability in the population is $250 and the average wage is $100.) What is the most it would be willing to pay the low-ability worker?
4.
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Assume that workers know their abilities, but employers do not. The facts are as follows: the respective productivities of high- and low-ability workers are and ; education has no effect on productivity; and because of the extra work involved, an engineering degree costs high-ability workers $50 and low-ability workers $80 relative to a degree in advanced flower pressing. Can high-ability workers use an engineering degree to signal their abilities to employers? What would happen if it cost low-ability workers only $60 to take engineering?
5.
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What is meant by countersignaling?
6.
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Bedard (2001) uncovered evidence suggesting that there are a greater number of high school dropouts in cities in which a university is very close by. Why might a signaling explanation account for this?

Hint. A proximate university reduces college costs, encouraging greater attendance among high school graduates who might otherwise not have enrolled in college.
7.
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What is the major difference between signaling and screening as it pertains to the labor market? In the United States, employers can be subject to huge fines if they discriminate against women and other minority groups. Given this, suppose that an employer offers everybody equal wages and fringe benefits. However, imagine that it requires workers to be available over some weekends and begin work at 6:30 a.m. Furthermore, it offers no child-care facilities and provides an excellent company gym that has almost no cardio equipment at all. What is the firm attempting to do?
8.
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What factors might account for the fact that some employers hire risky workers, whereas others go for safer ones whose productivities are known?
9.
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Assume that there are two types of workers: those with high abilities and those with low abilities . The productivity, y, of each worker type depends upon education, e, and his ability, a, according to . The worker's utility, U, depends upon his education and his ability according to .

(a) Assume that ability is publicly observable, what wage offers arise in competitive equilibrium? Depict the optimal educational choices of high- and low ability workers.

(b) Now suppose that workers know their abilities, but employers do not. Depict the signaling equilibrium that arises in this environment, assuming high ability workers choose the lowest level of education (denoted e*) that is just sufficient to separate them from their low-ability peers.

(c) Using your answer in (b) as a guide, calculate the optimal educational choices of each worker type. (Hint. For a worker with ability a, the marginal cost of education (denoted MC) is MC = e/a, and the marginal benefit (denoted MB) is MB = a.)

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