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Chapter 13. Labor Markets. © 2004 Thomson Learning/South-Western. Marginal Productivity Theory of Input Demand. Input prices are also determined by the forces of supply and demand. The firms are on the demand side while the supply comes from individuals.

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Chapter 13 l.jpg

Chapter 13

Labor Markets

© 2004 Thomson Learning/South-Western


Marginal productivity theory of input demand l.jpg
Marginal Productivity Theory of Input Demand

  • Input prices are also determined by the forces of supply and demand.

  • The firms are on the demand side while the supply comes from individuals.

  • The theory of input demand relies on Ricardo’s theory of marginal productivity.


Profit maximizing behavior and the hiring of inputs l.jpg
Profit-Maximizing Behavior and the Hiring of Inputs

  • A profit-maximizing firm will hire additional units of any input up to the point at which the additional revenue from hiring one more unit is exactly equal to the cost of hiring that unit.

  • Let MEK and MEL denote the marginal expense of hiring capital and labor, respectively.


Profit maximizing behavior and the hiring of inputs4 l.jpg
Profit-Maximizing Behavior and the Hiring of Inputs

  • Let MRK and MRL be the extra revenue that hiring more units of capital and labor allows the firm to bring in.

  • Profit maximizing behavior requires:


Price taking behavior l.jpg
Price-Taking Behavior

  • If the firm is a price taker in the capital and labor market then it can always hire an extra unit of capital at the prevailing rate (v) and an extra unit of labor at the wage rate (w).


Marginal revenue product l.jpg
Marginal Revenue Product

  • Marginal product is how much output the additional input can produce.

  • Marginal revenue (MR) is the extra revenue obtained from selling an additional unit of output.

  • Thus, the profit maximizing rules are:


Marginal revenue product7 l.jpg
Marginal Revenue Product

  • The marginal revenue product of labor and capital are the extra revenue obtained from selling the output produced by hiring an extra worker or machine.

  • These show how much extra revenue is brought in by hiring one more unit of an input.


A special case marginal value product l.jpg
A Special Case--Marginal Value Product

  • If the firm is also a price taking in the goods market, marginal revenue equals the price (P) at which the output sells.

  • The profit maximizing conditions become


Marginal value product l.jpg
Marginal Value Product

  • The marginal value product (MVP) of capital and labor, respectively, are special cases of marginal revenue product in which the firm is a price taker for its output.


Application 13 1 hiring by nonprofit firms l.jpg
APPLICATION 13.1: Hiring by Nonprofit Firms

  • Most hospitals in the U.S. operate on a not-for-profit basis.

  • In some cases hospitals are owned by public corporations and presumably strive for maximum profits.

  • Economists have found important differences in the labor demand for these two types of institutions.


Application 13 1 hiring by nonprofit firms11 l.jpg
APPLICATION 13.1: Hiring by Nonprofit Firms

  • Some of the differences may relate to a “quality bias” for non-profit hospitals.

  • Such hospitals seem to hire more high-wage labor (physicians) and less lower-wage labor (nurses) than do for-profit hospitals.

  • One explanation for this result may be that nonprofit hospitals are run by physicians who gain utility from high-quality (high-cost) surroundings which the managers of for-profit hospitals have a more “bottom line” mentality.


Application 13 1 hiring by nonprofit firms12 l.jpg
APPLICATION 13.1: Hiring by Nonprofit Firms

  • Virtually all colleges and universities are operated as nonprofit institutions.

  • It is not surprising that faculty hiring does not follow the principles of profit maximization.

  • On most campuses, more than 50% of the faculty has the rank of full professor but, on average, full professors are paid nearly twice as much as assistant professors and instructors.


Responses to changes in input prices single variable input case l.jpg
Responses to Changes in Input Prices: Single Variable input Case

  • Assume the firm has fixed capital and can only vary its labor input in the short run.

  • Labor will exhibit diminishing marginal physical productivity so labor’s MVP will decline as more labor is hired.

  • In Figure 13.1, the profit maximizing firm will hire L1 labor hours when the wage rate is w1.


Figure 13 1 change in labor input when wage falls single variable case l.jpg
FIGURE 13.1: Change in Labor Input When Wage Falls: Single Variable Case

MVP

Wage

w1

w2

MVPL

0

L1

L2

Labor hours


Responses to changes in input prices single variable input case15 l.jpg
Responses to Changes in Input Prices: Single Variable input Case

  • If the wage rate falls to w2 the firm hires increased labor out to L2.

    • If the firm continued to hire L1 it would not be maximizing profit since labor would be capable of producing more in additional revenue than hiring additional labor would cost.

  • With one variable input, diminishing marginal productivity results in a downward sloping demand curve.


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A Numerical Example Case

  • Table 13.1 shows the productivity for Hamburger Heaven when it uses four grills

  • The marginal product declines as more workers are assigned to the grills

  • Marginal Revenue Product is simply price, $1.00 times the marginal product.

  • At a wage of $5.00, the firm should hire four workers.



The substitution effect l.jpg
The Substitution Effect Decision

  • The substitution effect, in the theory of production, is the substitution of one input for another while holding output constant in response to a change in the input’s price.

  • In Figure 13.2(a), a fall in w will cause the firm to change from input combination A to B to equate RTS to the new w/v.

  • Diminishing RTS leads to more labor hired.


Figure 13 2 substitution and output effects of a decrease in price of labor l.jpg
FIGURE 13.2: Substitution and Output Effects of A Decrease in Price of Labor

Capital

per week

Price

MC

K1

A

P

K2

q1

0

L1

L2

Labor hours

per week

0

q1

Output

per week

(a) Input Choice

(b) Output Decision


Figure 13 2 substitution and output effects of a decrease in price of labor20 l.jpg
FIGURE 13.2: Substitution and Output Effects of A Decrease in Price of Labor

Price

Capital

per week

MC

K1

A

P

K2

B

q1

0

L1

L2

Labor hours

per week

0

q1

Output

per week

(a) Input Choice

(b) Output Decision


The output effect l.jpg
The Output Effect in Price of Labor

  • The output effect is the effect of an input price change on the amount of the input that the firm hires that results from a change in the firm;s output level.

  • In Figure 13.2(b), the lower w causes the marginal cost curve to shift to MC’.

  • The profit maximizing output raises to q2 resulting in more labor hired.


Figure 13 2 substitution and output effects of a decrease in price of labor22 l.jpg
FIGURE 13.2: Substitution and Output Effects of A Decrease in Price of Labor

Price

Capital

per week

MC

MC’

K1

A

P

K2

B

q1

0

L1

L2

Labor hours

per week

0

q1

q2

Output

per week

(a) Input Choice

(b) Output Decision


Figure 13 2 substitution and output effects of a decrease in price of labor23 l.jpg
FIGURE 13.2: Substitution and Output Effects of A Decrease in Price of Labor

Price

Capital

per week

MC

MC’

K1

A

C

P

K2

q2

B

q1

0

L1

L2

Labor hours

per week

0

q1

q2

Output

per week

(a) Input Choice

(b) Output Decision


Summary of firm s demand for labor l.jpg
Summary of Firm’s Demand for Labor in Price of Labor

  • A fall in the wage rate will cause the firm to hire more labor for two reasons:

    • The firm will substitute the now cheaper labor for other inputs that are now relatively more expensive, the substitution effect.

    • The decline in wages will lower marginal costs so the profit maximizing firm will produce more output which requires hiring more labor, the output effect.


Responsiveness of input demand to price changes l.jpg
Responsiveness of Input Demand to Price Changes in Price of Labor

  • Ease of Substitution

    • The size of the substitution effect will depend upon how easy it is to substitute other factors of production for labor.

    • The size of the substitution effect will also depend upon the length of time as it becomes easier to find substitutes in a longer period of time.


Costs and the output effect l.jpg
Costs and the Output Effect in Price of Labor

  • The size of the output effect will depend upon

    • How large the increase in marginal costs brought about by the wage rate increase is, and

    • How much quantity demanded will be reduced by a rising price.

    • The first depend upon how important labor is in production while the latter depends upon the price elasticity of demand for the final product.


Application 13 2 controversy over the minimum wage l.jpg
APPLICATION 13.2: Controversy over the Minimum Wage in Price of Labor

  • The Fair Labor Standards Act of 1938 established a national minimum wage of $.25 per hour.

  • Each increase raises debate about whether such increases are counterproductive

  • In Figure 1(a) the equilibrium wage is w1 with l1 units of labor hired.


Figure 1 effects of a minimum wage in a perfectly competitive labor market l.jpg
FIGURE 1: Effects of a Minimum Wage in a Perfectly Competitive Labor Market

Wage

Capital

per week

S

w2

Wage = w1

w1

q1

D

q2

0

L2

Labor

per week

0

l1

Labor

per week

(a) The Market

(b) Typical Firm


Application 13 2 controversy over the minimum wage29 l.jpg
APPLICATION 13.2: Controversy over the Minimum Wage Competitive Labor Market

  • A minimum wage of w2 will cause firms to hire less, l2, units of labor while more labor L3 will be supplied

  • The imposition of a minimum wage will result in an excess supply of labor over the demand for labor of L3 - L2.


Figure 1 effects of a minimum wage in a perfectly competitive labor market30 l.jpg
FIGURE 1: Effects of a Minimum Wage in a Perfectly Competitive Labor Market

Wage

Capital

per week

Wage= w2

S

w2

Wage = w1

w1

q1

D

q2

0

L1

L2

L3

Labor

per week

0

l2

l1

Labor

per week

(a) The Market

(b) Typical Firm


Minimum wages and teenage unemployment l.jpg
Minimum Wages and Teenage Unemployment Competitive Labor Market

  • Teenagers are most likely to be affected by minimum wage laws because their skills are usually at the lower end of the spectrum.

    • While many factors are at play, a major study in the 1970s found that a 1-percent increase resulted in a 0.3 percent reduction in teenage employment.

    • Minority group members have rates that exceed 30 percent.


Recent disputes over the evidence l.jpg
Recent Disputes over the Evidence Competitive Labor Market

  • A 1994 study by Card and Krueger challenged the belief that minimum wages reduced employment opportunities.

    • Their study of fast-food restaurants in New Jersey and Pennsylvania found no negative effects on employment.

    • However, an analysis of different data from these states found negative employment effects


Input supply l.jpg
Input Supply Competitive Labor Market

  • Resources come from three major sources:

    • Labor is provided by individuals.

    • Capital equipment is produced which other firms can buy outright or rent.

    • Natural resources are extracted from land and can be used outright or sold to other firms.

  • As shown in earlier chapters, capital and natural resources have upward sloping supply curves.


Labor supply and wages l.jpg
Labor Supply and Wages Competitive Labor Market

  • Wages represent the opportunity cost of not working at a paying job for individuals.

  • For purposes of this analysis, wages should be interpreted to include all forms of compensation.

  • Individuals will balance the monetary rewards from working against the psychic benefits of other, nonpaid activities.


Labor supply and wages35 l.jpg
Labor Supply and Wages Competitive Labor Market

  • Labor supply curves will differ based upon individual preferences.

    • Noneconomic factors such as pleasant working conditions will affect the location of the supply curve.

  • It is likely that an increase in the wage will result in more labor supplied to the market.

    • Graphically, the market labor supply curve is likely to be positively sloped.


Equilibrium input price determination l.jpg
Equilibrium Input Price Determination Competitive Labor Market

  • In Figure 13.3, the market demand for labor is labeled D, and the market supply of labor is labeled S.

  • The equilibrium wage and quantity is where quantity demanded equals quantity supplied, [w*, L*].

  • Other things equal, this equilibrium will tend to persist from period to period.


Figure 13 3 equilibrium in an input market l.jpg
FIGURE 13.3: Equilibrium in an Input Market Competitive Labor Market

Wage

S

w*

D

0

Labor hours per week

L*


Shifts in demand and supply l.jpg
Shifts in Demand and Supply Competitive Labor Market

  • Any factor that shifts the firms’ underlying production function will shift its input demand curve.

  • Since the demand for an input is derived from the demand for the output, changes in the prices of the output will shift input demand curves


Shifts in demand and supply39 l.jpg
Shifts in Demand and Supply Competitive Labor Market

  • In Figure 13.3, the demand curve shifts to D’ which reduces equilibrium wages from w* to w’ and equilibrium employment from L* to L’.

  • The various factors that shift input demand and supply curves are summarized in Table 13.2.


Figure 13 3 equilibrium in an input market40 l.jpg
FIGURE 13.3: Equilibrium in an Input Market Competitive Labor Market

Wage

S

w*

w’

D

D’

0

Labor hours per week

L’

L*



Application 13 3 why is wage inequality increasing l.jpg
APPLICATION 13.3: Why is Wage Inequality Increasing? Curves

  • Wage inequality has a long history, but seems to have increased recently.

  • Measuring Wage Inequality

    • To control for differences in hours, researchers look at “full-time, year-round” workers.

    • Usually, they concentrate on one gender and try to include total wages including fringe benefits.

    • A common approach is to compare workers in the 90th to workers in the 10th percentile.


Application 13 3 why is wage inequality increasing43 l.jpg
APPLICATION 13.3: Why is Wage Inequality Increasing? Curves

  • U.S. studies for the 1965-1995 period find

    • The 90/10 ratio in 1965 stood at about 4.3 for male, full-time, year round workers.

    • By 1995, this 90/10 ratio had increased to 5.4.

  • European countries have also experienced an increase in inequality although only the United Kingdom has had increases similar to the U.S.


Application 13 3 why is wage inequality increasing44 l.jpg
APPLICATION 13.3: Why is Wage Inequality Increasing? Curves

  • Factors that increase the supply of low-wage workers or increase the demand for high-wage workers would help to explain these trends.

  • Two Important Trends

    • A sharp increase in the relative demand for technically skilled workers which partially explains the rising wages of college graduates.


Application 13 3 why is wage inequality increasing45 l.jpg
APPLICATION 13.3: Why is Wage Inequality Increasing? Curves

  • The second factor, which explains less of the trend, is that there has also been a decline in the demand for low-wage workers.

  • Two reasons for the decline

    • A decline in the importance of manufacturing industries in the overall economy, and

    • Sustained increases in imports of goods that are produced primarily with unskilled labor


  • Application 13 3 why is wage inequality increasing46 l.jpg
    APPLICATION 13.3: Why is Wage Inequality Increasing? Curves

    • Trends in labor supply have exacerbated the demand effects.

      • Large (legal and illegal) immigrations in the 1990s may have increased the supply of low-wage workers.

      • The increase in labor supply of women has probably had its greatest impact on low-wage men.


    Monopsony l.jpg
    Monopsony Curves

    • If the firm is not a price taker in the input market, it may have to offer a higher wage to attract more employees.

    • A monopsony is the condition in which one firm is the only hirer in a particular input market.

    • If the firm is a monopsony, it faces the entire market supply curve for the input.


    Marginal expense l.jpg
    Marginal Expense Curves

    • The marginal expense of an input is the cost of hiring one more unit of an input.

      • The firm has to offer a higher wage to the hired worker and to the workers already employed.

      • The marginal expense of labor (MEL) will exceed the price of the input if the firm faces an upward-sloping supply curve for the input.


    A numerical illustration l.jpg
    A Numerical Illustration Curves

    • Suppose the Yellowstone Park Company is the only hirer of bear wardens.

    • The number of people willing to take this job (L) is given by

    • This relationship is shown in Table 13.3



    A numerical illustration51 l.jpg
    A Numerical Illustration Yellowstone Park

    • Total labor costs (w·L) is shown in the third column and the marginal expense of hiring each warden is shown in the fourth column.

    • Since the new warden and the existing wardens receive the wage increase, the marginal expense exceeds the wage rate.


    A numerical illustration52 l.jpg
    A Numerical Illustration Yellowstone Park

    • Figure 13.4 shows the supply curve (S) for wardens.

      • If Yellowstone wishes to hire three wardens it must pay $6 per hour with total outlays of $18 (point A on the graph).

      • The wage must be increased to $8 to get a fourth warden (point B) which results in total outlays of $32.


    Figure 13 4 marginal expense of hiring bear wardens l.jpg
    FIGURE 13.4: Marginal Expense of Hiring Bear Wardens Yellowstone Park

    Hourly

    wage

    S

    B

    $8

    A

    6

    0

    3

    4

    Bear wardens per hour


    A numerical illustration54 l.jpg
    A Numerical Illustration Yellowstone Park

    • The marginal expense of the fourth warden, $14 is reflected in the graph.

      • The hourly wage ($8) is shown in gray.

      • The extra outlay to the three previous workers ($8 per hour versus $6 per hour previously) is shown in color.

      • Total outlays exceed the amount for three wardens by the sum of these two areas.


    Figure 13 4 marginal expense of hiring bear wardens55 l.jpg
    FIGURE 13.4: Marginal Expense of Hiring Bear Wardens Yellowstone Park

    Hourly

    wage

    S

    B

    $8

    A

    6

    0

    3

    4

    Bear wardens per hour


    Monopsonist s input choice l.jpg
    Monopsonist’s Input Choice Yellowstone Park

    • The profit-maximizing monopsonist will hire up to the point where the additional revenue equals the additional cost of hiring one more unit of input.

    • For labor this requires:

    • Only if the firm is a price taker will MEL = w.


    A graphical demonstration l.jpg
    A Graphical Demonstration Yellowstone Park

    • The demand curve in Figure 13.5 is D.

    • Since marginal expense (MEL) exceeds the wage, the marginal expense curve is above the supply curve (S).

    • L1 is the profit maximizing choice while the marginal value product is MVP1 and the wage is w1.


    Figure 13 5 pricing in a monopsonistic labor market l.jpg
    FIGURE 13.5: Pricing in a Monopsonistic Labor Market Yellowstone Park

    ME

    Wage

    S

    D

    0

    Labor hours

    per week


    Figure 13 5 pricing in a monopsonistic labor market59 l.jpg
    FIGURE 13.5: Pricing in a Monopsonistic Labor Market Yellowstone Park

    ME

    Wage

    S

    MVP1

    D

    0

    Labor hours

    per week

    L1


    Figure 13 5 pricing in a monopsonistic labor market60 l.jpg
    FIGURE 13.5: Pricing in a Monopsonistic Labor Market Yellowstone Park

    ME

    Wage

    S

    MVP1

    w1

    D

    0

    Labor hours

    per week

    L1


    A graphical demonstration61 l.jpg
    A Graphical Demonstration Yellowstone Park

    • L1 is less than L*, the amount hired with perfect competition.

    • As with a monopoly, the “demand curve” for a monopolist actually consists of the single point given by L1, w1.


    Figure 13 5 pricing in a monopsonistic labor market62 l.jpg
    FIGURE 13.5: Pricing in a Monopsonistic Labor Market Yellowstone Park

    ME

    Wage

    S

    MVP1

    w*

    w1

    D

    0

    Labor hours

    per week

    L1

    L*


    Monopsonists and resource allocation l.jpg
    Monopsonists and Resource Allocation Yellowstone Park

    • Since the monopsonist restrict its input use, it pays an input less than its marginal value product (w1 < MVP1).

    • Total output could be increased by drawing more labor into the market.

    • The more inelastic the labor supply, the more the monopsonists can benefit from this profit opportunity.


    Causes of monopsony l.jpg
    Causes of Monopsony Yellowstone Park

    • If competition for inputs is lacking, monopsony may exit.

      • The input may have high opportunity costs of moving to another input market.

      • The input may be so specialized that there is only one firm that hires that input.

      • Firms may join together to form a cartel in the input market.


    Application 13 4 monopsony in the market for sports stars l.jpg
    APPLICATION 13.4: Monopsony in the Market for Sports Stars Yellowstone Park

    • Because players marginal revenue products are more easily measured and correlated with spectator attendance, sports provides a good market for study.

    • The “reserve clause” in professional baseball found layers to teams that first signed them giving teams monopsony power.


    Monopsony in major league baseball l.jpg
    Monopsony in Major League Baseball Yellowstone Park

    • In a famous 1974 study, G.W. Scully examined the correlation between a team’s winning percentage and its attendance.

    • Next, he analyzed what aspects of an individual’s performance most closely related to a team’s overall performance.

    • He used this information to estimate the MRPs of the players.


    Monopsony in major league baseball67 l.jpg
    Monopsony in Major League Baseball Yellowstone Park

    • He found the MRPs greatly exceeded players salaries.

    • A players strike in 1972 and other legal actions led to the adoption of the free-agent provisions that partially replaced the reserve-clause.

    • This has severely limited the monopsony power of major league teams.


    Basketball and michael jordan l.jpg
    Basketball and Michael Jordan Yellowstone Park

    • While it did not have a reserve clause, the National Basketball Association (NBA) has exercised some monopsony power.

    • Early stars probably were most affected, but Michael Jorden’s multimillion dollar salary was millions of dollars less than what he was worth to the NBA in terms of higher television ratings when he played.


    Bilateral monopoly l.jpg
    Bilateral Monopoly Yellowstone Park

    • A bilateral monopoly is a market in which both suppliers and demanders have monopoly power.

      • Pricing is indeterminate in such markets.

    • In Figure 13.6, “supply” and “demand” intersect at P*, Q*, but this is not equilibrium since neither player is a price taker.


    Figure 13 6 bilateral monopoly l.jpg
    FIGURE 13.6: Bilateral Monopoly Yellowstone Park

    Input

    price

    ME

    S

    D

    MR

    0

    Quantity per

    period


    Bilateral monopoly71 l.jpg
    Bilateral Monopoly Yellowstone Park

    • The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P1, Q1.


    Figure 13 6 bilateral monopoly72 l.jpg
    FIGURE 13.6: Bilateral Monopoly Yellowstone Park

    Input

    price

    ME

    S

    P1

    D

    MR

    0

    Quantity per

    period

    Q1


    Bilateral monopoly73 l.jpg
    Bilateral Monopoly Yellowstone Park

    • The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P1, Q1.

    • The monopsonistic will operate on its marginal expense curve (ME) and prefer combination P2, Q2.


    Figure 13 6 bilateral monopoly74 l.jpg
    FIGURE 13.6: Bilateral Monopoly Yellowstone Park

    Input

    price

    ME

    S

    P*

    P2

    D

    MR

    0

    Quantity per

    period

    Q2


    Bilateral monopoly75 l.jpg
    Bilateral Monopoly Yellowstone Park

    • The monopoly supplier will operate on its marginal revenue curve (MR) and prefer price-quantity combination P1, Q1.

    • The monopsonistic will operate on its marginal expense curve (ME) and prefer combination P2, Q2.

    • The final outcome, after bargaining, will lie between these two combinations.


    Figure 13 6 bilateral monopoly76 l.jpg
    FIGURE 13.6: Bilateral Monopoly Yellowstone Park

    Input

    price

    ME

    S

    P1

    P*

    P2

    D

    MR

    0

    Quantity per

    period

    Q2

    Q1

    Q*