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12.4 Review and Practice

Summary

In this chapter we have extended our understanding of the operation of perfectly competitive markets by looking at the market for labor. We found that the common sense embodied in the marginal decision rule is alive and well. A firm should hire additional labor up to the point at which the marginal benefit of doing so equals the marginal cost.

The demand curve for labor is given by the downward-sloping portion of the marginal revenue product (MRP) curve of labor. A profit-maximizing firm will hire labor up to the point at which its marginal revenue product equals its marginal factor cost. The demand for labor shifts whenever there is a change in (1) related factors of production, including investment in human capital; (2) technology; (3) product demand; and (4) the number of firms.

The quantity of labor supplied is closely linked to the demand for leisure. As more hours are worked, income goes up, but the marginal cost of work, measured in terms of forgone leisure, also increases. We saw that the substitution effect of a wage increase always increases the quantity of labor supplied. But the income effect of a wage increase reduces the quantity of labor supplied. It is possible that, above some wage, the income effect more than offsets the substitution effect. At or above that wage, an individual’s supply curve for labor is backward bending. Supply curves for labor in individual markets, however, are likely to be upward sloping.

Because competitive labor markets generate wages equal to marginal revenue product, workers who add little to the value of a firm’s output will receive low wages. The public sector can institute a minimum wage, seek to improve these workers’ human capital, or subsidize their wages.

Conceptual Problems

  1. Explain the difference between the marginal product of a factor and the marginal revenue product of a factor. What factors would change a factor’s marginal product? Its marginal revenue product?
  2. In perfectly competitive input markets, the factor price and the marginal factor cost are the same. True or false? Explain.
  3. Many high school vocational education programs are beginning to shift from an emphasis on training students to perform specific tasks to training students to learn new tasks. Students are taught, for example, how to read computer manuals so that they can more easily learn new systems. Why has this change occurred? Do you think the change is desirable?
  4. How would an increase in the prices of crops of fresh produce that must be brought immediately to market—so-called truck crops—affect the wages of workers who harvest those crops? How do you think it would affect the quantity of labor supplied?
  5. If individual labor supply curves of all individuals are backward bending, does this mean that a market supply curve for labor in a particular industry will also be backward bending? Why or why not?
  6. There was an unprecedented wave of immigration to the United States during the latter third of the nineteenth century. Wages, however, rose at a rapid rate throughout the period. Why was the increase in wages surprising in light of rising immigration, and what probably caused it?
  7. Suppose you were the economic adviser to the president of a small underdeveloped country. What advice would you give him or her with respect to how the country could raise the productivity of its labor force? (Hint: What factors increase labor productivity?)
  8. The text argues that the effect of a minimum wage on the incomes of workers depends on whether the demand for their services is elastic or inelastic. Explain why.
  9. How would a successful effort to increase the human capital of unskilled workers affect their wage? Why?
  10. Does the Case in Point on computer technology and labor demand suggest that bank tellers and automatic tellers are substitutes or complements? Explain.
  11. What does the airline pilot’s supply curve in the Case in Point on how she has dealt with wage cutbacks look like? Does the substitution effect or the income effect dominate? How do you know?
  12. Given the evidence cited in the Case in Point on the increasing wage gap between workers with college degrees and those who have only completed high school, how has the greater use by firms of high-tech capital affected the marginal products of workers with college degrees? How has it affected their marginal revenue product?
  13. Explain how each of the following events would affect wages in a particular labor market:

    1. an increase in labor productivity in the market.
    2. an increase in the supply of labor in the market.
    3. an increase in wages in another labor market that can be easily entered by workers in the first labor market.
    4. a reduction in wages in another market whose workers can easily enter the first market.
    5. an increase in the price of the good labor in the market produces.
  14. How can a supply curve for labor be backward bending? Suppose the equilibrium wage occurs in the downward-sloping portion of the curve. How would an increase in the demand for labor in the market affect the wage? How would this affect the quantity of labor supplied?
  15. How do you think a wage increase would affect the quantity of labor supplied by each of the following speakers?

    1. “I want to earn as much money as possible.”
    2. “I am happy with my current level of income and want to maintain it.”
    3. “I love my work; the wage I’m paid has nothing to do with the amount of work I want to do.”
    4. “I would work the same number of hours regardless of the wage I am paid.”

Numerical Problems

  1. Felicia Álvarez, a bakery manager, faces the total product curve shown, which gives the relationship between the number of bakers she hires each day and the number of loaves of bread she produces, assuming all other factors of production are given.

    Number of bakers per day Loaves of bread per day
    0 0
    1 400
    2 700
    3 900
    4 1,025
    5 1,100
    6 1,150

    Assume that bakers in the area receive a wage of $100 per day and that the price of bread is $1.00 per loaf.

    1. Plot the bakery’s marginal revenue product curve (remember that marginal values are plotted at the mid-points of the respective intervals).
    2. Plot the bakery’s marginal factor cost curve on the same graph.
    3. How many bakers will Ms. Álvarez employ per day?
    4. Suppose that the price of bread falls to $.80 per loaf. How will this affect the marginal revenue product curve for bakers at the firm? Plot the new curve.
    5. How will the change in (d) above affect the number of bakers Ms. Álvarez hires?
    6. Suppose the price of bread rises to $1.20 per loaf. How will this affect the marginal revenue product curve for bakers? Plot the new curve.
    7. How will the development in (f) above affect the number of bakers that Ms. Álvarez employs?
  2. Suppose that wooden boxes are produced under conditions of perfect competition and that the price of a box is $10. The demand and supply curves for the workers who make these boxes are given in the table.

    Wage per day Workers demanded Workers supplied
    $100 6,000 12,000
    80 7,000 10,000
    60 8,000 8,000
    40 9,000 6,000
    20 10,000 4,000

    Plot the demand and supply curves for labor, and determine the equilibrium wage for box makers.

  3. Assume that the market for nurses is perfectly competitive, and that the initial equilibrium wage for registered nurses is $30 per hour. Illustrate graphically how each of the following events will affect the demand or supply for nurses. State the impact on wages and on the number of nurses employed (in terms of the direction of the changes that will occur).

    1. New hospital instruments reduce the amount of time physicians must spend with patients in intensive care and increase the care that nurses can provide.
    2. The number of doctors increases.
    3. Changes in the labor market lead to greater demand for the services of women in a wide range of occupations. The demand for nurses, however, does not change.
    4. New legislation establishes primary-care facilities in which nurses care for patients with minor medical problems. No supervision by physicians is required in the facilities.
    5. The wage for nurses rises.
  4. Plot the supply curves for labor implied by each of the following statements. In this problem, actual numbers are not important; rather you should think about the shape of the curve.

    1. “I’m sorry, kids, but now that I’m earning more, I just can’t afford to come home early in the afternoon, so I won’t be there when you get home from school.”
    2. “They can pay me a lot or they can pay me a little. I’ll still put in my 8 hours a day.”
    3. “Wow! With the raise the boss just gave me, I can afford to knock off early each day.”
  5. At an hourly wage of $10 per hour, Marcia Fanning is willing to work 36 hours per week. Between $30 and $40 per hour, she is willing to work 40 hours per week. At $50 per hour, she is willing to work 35 hours per week.

    1. Assuming her labor supply curve is linear between the data points mentioned, draw Ms. Fanning’s labor supply curve.
    2. Given her labor supply curve, how much could she earn per week at the wage of $10 per hour? $30 per hour? $40 per hour? $50 per hour?
    3. Does the substitution or income effect dominate wages between $10 and $30 per hour? Between $30 and $40 per hour? Between $40 and $50 per hour?
    4. How much would she earn at each hypothetical wage rate?
  6. Jake Goldstone is working 30 hours per week. His marginal utility of income is 2, his marginal utility of leisure is 60, and his hourly wage is $20. Assume throughout this problem that the income effect is zero.

    1. Is Mr. Goldstone maximizing his utility?
    2. Would working more or less increase his utility?
    3. If his wage rose to $30 per hour, would he be maximizing his utility by working 30 hours per week? If not, should he work more or fewer hours?
    4. At a wage of $40 per hour, would he be maximizing his utility? If not, would working more or less than 30 hours per week increase his utility?
  7. The table below describes the perfectly competitive market for dishwashers.

    Wage per day

    Quantity demanded per day

    (in thousands)

    Quantity supplied per day

    (in thousands)

    $50 4.0 1.0
    100 3.5 2.0
    150 3.0 3.0
    200 2.5 4.0
    250 2.0 5.0
    1. Draw the demand and supply curves for dishwashers.
    2. What is the equilibrium daily wage rate and quantity of dishwashers?
    3. What is the total (i.e., cumulative) daily income of dishwashers at the equilibrium daily wage?
    4. At a minimum daily wage of $200 per day, how many dishwashers will be employed? How many will be unemployed? What will be the total daily income of dishwashers?
    5. At a minimum wage of $250 per day, how many dishwashers will be employed? How many will be unemployed? What will be the total daily income of dishwashers?