• Labor demand is more elastic the greater the elasticity of demand for the output. When the wage rises, the marginal cost of production increases. A wage increase, therefore, raises the industry’s price and reduces consumers’ demand for the product. Because less output is being sold, firms cut employment. The greater the reduction in consumer demand (that is, the more elastic the demand curve for the output), the larger the cut in employment and the more elastic the industry’s labor demand curve.
• Labor demand is more elastic the greater labor’s share in total costs. Suppose labor is a relatively “important” input in the production process, in the sense that labor’s share of total costs is large. This situation might occur, for example, when production is very labor intensive, as with a firm using highly trained craftspeople to produce expensive handmade ornaments. In this case, even a small increase in the wage rate would sub- stantially increase the marginal cost of production. This increase in marginal cost raises the output price and induces consumers to cut back on their purchases of the ornaments.
Firms, in turn, would cut back on employment substantially. In contrast, if labor is
“unimportant,” so that labor makes up only a small share of total costs, a wage increase has only a small impact on marginal cost, on the price of the output, and on consumer demand. There is little need for the firm’s employment to shrink. 12
• The demand for labor is more elastic the greater the supply elasticity of other factors
of production, such as capital. We have assumed that firms can hire as much capital as they want at the constant price r. Suppose there is a wage increase and firms want to substitute from labor to capital. If the supply curve of capital is inelastic, so that the price of capital increases substantially as more and more capital is hired, the economic incentives for moving along an isoquant are greatly reduced. In other words, it is not quite as profitable to get rid of labor and employ capital instead. The demand curve for labor, therefore, is more elastic the easier it is to increase the capital stock (that is, the more elastic the supply curve of capital).
and promises the workers that collective bargaining will increase the wage substantially.
Because the firm’s labor demand curve is downward sloping, the firm may respond to the higher wage by moving up its demand curve and cutting back employment. The union’s organizing drive then has a greater chance of being successful when the demand curve for labor is inelastic. After all, an inelastic demand curve ensures that employment is relatively stable even if the workers get a huge wage increase. In other words, the workers would not have to worry about employment cutbacks if they voted for the union. It is in the union’s best interests, therefore, to take whatever actions are available to lower the firm’s elasticity of demand.
In view of this fact, it is not surprising that unions often resist technological advances that increase the possibilities of substituting between labor and capital. The typesetters’
unions, for example, long objected to the introduction of computerized typesetting equip- ment in the newspaper industry. This type of behavior is an obvious attempt to reduce the value of the elasticity of substitution. A smaller elasticity of substitution reduces the size of the substitution effect and makes the demand curve for labor more inelastic.
Similarly, unions want to limit the availability of goods that compete with the output of unionized firms. For example, the United Auto Workers (UAW) was a strong sup- porter of policies that made it difficult for Japanese cars to crack into the U.S. market. If the UAW obtained a huge wage increase for its workers, the price of American-made cars would rise substantially. This price increase would drive many potential buyers toward foreign imports. If the union could prevent the entry of Toyotas, Nissans, and Hondas into the American marketplace, consumers would have few alternatives to buying a high- priced American-made car. It is in the union’s interests, therefore, to reduce the elasticity of product demand by limiting the variety of goods that are available to consumers.
Marshall’s rules also imply that unions are more likely to be successful when the share of labor costs is small. Unions can then make high wage demands without raising the marginal cost (and hence the price) of the output very much. In fact, there is evidence that unions that organize small groups of workers such as electricians or carpenters tend to be very successful in getting sizable wage increases. 13 Because these specialized occupations make up a small fraction of total labor costs, the demand curve for these workers is rela- tively inelastic.
Finally, unions often attempt to raise the price of other inputs, particularly nonunion labor. For example, the Davis-Bacon Act requires that contractors involved in publicly financed projects pay the “prevailing wage” to construction workers. 14 Not surprisingly, the prevailing wage is typically defined as the union wage, even if the contractor hires nonunion labor. This type of regulation raises the cost of switching from union labor to other inputs. Union support of prevailing wage laws, therefore, can be interpreted as an attempt to make the supply of other factors of production more inelastic and hence reduce the elasticity of demand for union labor.
13 These unions are typically called “craft unions,” in contrast to the “industrial unions” that unionize all workers in a given industry (like the UAW).
14 For a review of the economic impact of “prevailing wage” policies, see Robert Goldfarb and John Morrall, “The Davis-Bacon Act: An Appraisal of Recent Studies,” Industrial and Labor Relations Review 34 (January 1981): 191–206; and A. J. Tieblot, “A New Evaluation of Impacts of Prevailing Wage Law Repeal,” Journal of Labor Research 7 (Spring 1996): 297–322.
3-8 Factor Demand with Many Inputs
Although we have assumed that the production function has only two inputs—labor and capital—we can easily extend the theory to account for more realistic production pro- cesses. There are clearly many different types of workers (such as skilled and unskilled) and many different types of capital (such as old machines and new machines). The produc- tion technology is then described by the production function:
q = f(x1, x2, x3,p, xn) (3-18) where x i denotes the quantity of the i th input that is used in production. As before, the pro- duction function tells us how much output is produced by any combination of the inputs.
We can define the marginal product of the i th input, or MP i, as the change in output result- ing from a one-unit increase in that input, holding constant the quantities of all other inputs.
We can use this production function to derive the short- and long-run demand curves for a particular input. It will still be true that a profit-maximizing firm hires the i th input up to the point where its price (or w i ) equals the value of marginal product of that input:
wi = p * MPi (3-19)
All of the key results derived in the simpler case of a two-factor production function con- tinue to hold. The short-run and long-run demand curves for each input are downward sloping; the long-run demand curve is more elastic than the short-run demand curve; and a wage change generates both a substitution effect and a scale effect.
One common empirical finding is that the labor demand for unskilled workers is more elastic than for skilled workers. 15 In other words, for any given percentage increase in the wage, the cut in employment will be larger for unskilled workers than for skilled workers.
An interesting interpretation of this result is that employment is inherently more unstable for unskilled workers than for skilled workers. As various economic shocks shift the wage of the two types of workers, the number of workers demanded will fluctuate significantly among unskilled workers, but much less so among skilled workers.
The presence of many inputs in the production process raises the possibility that the demand for input i might increase when the price of input j increases, but might fall when the price of input k increases. To measure the sensitivity in the demand for a particular input to the prices of other inputs, we define the cross-elasticity of factor demand as Crosselasticity of factor demand = Percent change in xi
Percent change in wj (3-20) The cross-elasticity of factor demand gives the percentage change in the demand for input i resulting from a 1 percent change in the wage of input j.
The sign of the cross-elasticity in equation (3-20) provides one definition of whether any two inputs are substitutes or complements in production. If the cross-elasticity is posi- tive, so that the demand for input i increases when the wage of input j rises, the two inputs i and j are said to be substitutes in production. After all, the increase in w j increases the demand for input i at the same time that it reduces the demand for input j. The two inputs
15 Hamermesh, Labor Demand, Chapter 3.
are substitutes because they respond in different ways to the change in the wage; the firm is getting rid of the more expensive input and replacing it with the relatively cheaper input.
If the cross-elasticity of factor demand is negative, the demand for input i falls as a result of the increase in w j , and inputs i and j are said to be complements in production. The inputs are complements when they both respond in exactly the same way to a rise in w j . Put differently, the two inputs “go together.”
Figure 3-16 illustrates this definition of substitutes and complements in terms of shift- ing demand curves. In Figure 3-16 a , the demand curve for input i shifted up when the price of input j increased. In this case, the two inputs are substitutes. As input j became more expensive, employers substituted toward input i. Hence the demand curve for input i shifted up. In Figure 3-16 b , the demand curve for input i shifted down when the price of input j rose. In other words, the demand for both inputs fell when input j became more expensive. The two inputs go together in production and are, therefore, complements.
A number of empirical studies suggest that unskilled labor and capital are substitutes, and that skilled labor and capital are complements. 16 In other words, as the price of machines FIGURE 3-16 The Demand Curve for a Factor of Production Is Affected by the Prices of Other Inputs The labor demand curve for input i shifts when the price of another input changes. (a) If the price of a substitutable input rises, the demand curve for input i shifts up. (b) If the price of a complement rises, the demand curve for input i shifts down.
Price of Input i
Employment of Input i
(a) Demand Curve Shifts Up When the Price of a Substitute Increases
D0
D1
Price of Input i
Employment of Input i
(b) Demand Curve Shifts Down When the Price of a Complement Increases
D1
D0
16 Zvi Griliches, “Capital-Skill Complementarity,” Review of Economics and Statistics 51 (November 1969): 465–468. See also Ann P. Bartel and Frank Lichtenberg, “The Comparative Advantage of Edu- cated Workers in Implementing New Technology,” Review of Economics and Statistics 69 (February 1987): 1–11; and Claudia Goldin and Lawrence F. Katz, “The Origins of Technology-Skill Complemen- tarity,” Quarterly Journal of Economics 113 (August 1998): 693–732. Although there is some debate over the validity of this finding, the evidence makes a strong case that, at the very least, skilled workers and capital are much more complementary (or less substitutable) than unskilled workers and capital.
falls, employers substitute away from unskilled workers. In contrast, as the price of machines falls and employers increase their use of capital equipment, the demand for skilled workers rises because skilled workers and capital equipment “go together.” It has been found that a 10 percent fall in the price of capital reduces the employment of unskilled workers by 5 percent and increases the employment of skilled workers by 5 percent. 17
This result has come to be known as the capital-skill complementarity hypothesis.
This hypothesis has important policy implications. It suggests that subsidies to investments in physical capital (such as an investment tax credit) will have a differential impact on dif- ferent groups of workers. Because an investment tax credit lowers the price of capital to the firm, it increases the demand for capital, reduces the demand for unskilled workers, and increases the demand for skilled workers. An investment tax credit, therefore, spurs invest- ment in the economy, but also worsens the relative economic conditions of less-skilled workers. The capital-skill complementarity hypothesis also suggests that technological progress—such as the substantial reduction in the price of computing power in the 1980s and 1990s—can have a substantial impact on income inequality, again because it increases the demand for skilled workers and reduces the demand for unskilled workers.
3-9 Overview of Labor Market Equilibrium
We have analyzed the factors that encourage workers to supply a particular number of hours to the labor market and that encourage firms to demand a particular number of workers. The labor market is the place where the workers looking for jobs and the firms looking for workers finally meet each other and compare wage and employment offers.
The interaction between workers and firms that occurs in the labor market determines the equilibrium wage and employment levels: the wage and employment levels that “bal- ance” the number of hours that workers wish to work with the number of employee-hours that firms wish to employ. In this section, we briefly describe this equilibrium. Chapter 4 analyzes the properties of labor market equilibrium in greater detail.
Figure 3-17 illustrates the labor demand and labor supply curves in a particular labor market. As drawn, the supply curve slopes up, so that we are assuming that substitution effects dominate income effects. The demand curve is negatively sloped. The equilibrium wage and employment levels in this market are given by the point where the supply and demand curves intersect. A total of E * workers are employed and each receives the market wage of w * . To see why this intersection represents a labor market equilibrium, suppose that workers were getting paid a wage of w high , which is above the equilibrium wage. At this wage, the demand curve indicates that firms are only willing to hire E D workers, and the supply curve indicates that E S workers are looking for work. A wage above the equilibrium level, therefore, implies that there is a surplus of workers competing for the few available jobs. This competition puts downward pressure on the wage. When the wage is above the equilibrium level, therefore, the competition for jobs drives down the wage.
If firms were offering a wage below the equilibrium level, such as w low in Figure 3-17 , the situation would be exactly reversed. Employers want to hire a lot of workers, but few persons are willing to work at the going wage. The competition among employers for the
17 Kim Clark and Richard B. Freeman, “How Elastic Is the Demand for Labor?” Review of Economics and Statistics 62 (November 1980): 509–520.
few available workers puts upward pressure on the wage and moves the wage up toward equilibrium.
Once the labor market attains the equilibrium wage, the conflicting wishes of employers and workers have been balanced. At this wage, the number of workers who are looking for work exactly equals the number of workers that employers want to hire. In the absence of any other economic shocks, the equilibrium level of the wage and employment can then persist indefinitely.
3-10 Policy Application: The Employment Effects of Minimum Wages
The U.S. federal government introduced mandatory minimum wages in the labor market in 1938 as one of the provisions of the Fair Labor Standards Act (FLSA). 18 In 1938, the nominal minimum wage was set at 25 cents an hour, and only 43 percent of nonsupervi- sory workers were covered by the minimum wage provisions of the FLSA. Workers in such industries as agriculture and intrastate retail services were exempt from the legislation. As Figure 3-18 shows, the nominal minimum wage has been adjusted at irregular intervals in the past six decades. The wage floor was increased to $5.85 an hour in 2007, and it now stands at $7.25 an hour. The coverage of the minimum wage also has been greatly expanded. Most workers who are not employed by state or local governments are now covered by the legislation.
FIGURE 3-17 Wage and Employment Determination in a Competitive Market
In a competitive labor market, equilibrium is attained at the point where supply equals demand. The “going wage”
is w* and E* workers are employed.
Dollars
Supply
Demand
Employment
ED E* ES
whigh
w*
wlow
18 Other provisions of the FLSA include an overtime premium for persons who work more than 40 hours a week and regulations on the use of child labor.
Figure 3-18 illustrates an important characteristic of minimum wages in the United States: They have not been indexed to inflation or productivity growth. As a result, the real minimum wage declines between the time that the nominal floor is set and the next time that Congress raises it. For instance, the minimum wage was set at $3.35 per hour in 1981, or 42 percent of the average wage in manufacturing. In 1989, the nominal minimum wage was still $3.35 per hour, but this wage was only 32 percent of the average wage in manufacturing. The “ratcheting” in the real minimum suggests that the economic impact of minimum wages declines the longer it has been since it was last raised.
Figure 3-19 illustrates the standard model economists use to analyze the impact of the minimum wage on employment. 19 Initially, the competitive labor market is in equilibrium at wage level w * and employment E * . The government imposes a minimum wage of w. Let’s assume initially that this minimum wage has universal coverage, so that all workers in the labor market are affected by the legislation, and that the penalties associated with paying less than the minimum wage are sufficiently stiff that employers comply with the legislation.
Once the government sets the wage floor at w, firms move up the labor demand curve and employment falls to E. As a result of the minimum wage, therefore, some workers (E* E ) are displaced from their current jobs and become unemployed. In addition, the higher wage encourages additional persons to enter the labor market. In fact, E S workers would like to be employed, so an additional E S E * workers enter the labor market, cannot find jobs, and are added to the unemployment rolls.
FIGURE 3-18 Minimum Wages in the United States, 1938–2010
Source: U.S. Bureau of the Census, Statistical Abstract of the United States, Washington, DC: Government Printing Office, various issues; U.S. Bureau of the Census, Historical Statistics of the United States, Colonial Times to 1970, Washington, DC: Government Printing Office, 1975; and U.S. Bureau of Labor Statistics, Employment and Earnings, Washington, DC: Government Printing Office, January 2006.
0.2 0.3 0.4 0.5 0.6
0 1 2 3 4 5 6 7 8
1938 1944 1950 1956 1962 1968 1974 1980 1986 1992 1998 2004 2010 Year
Ratio
Nominal Wage
Nominal Minimum Wage Ratio of Minimum Wage to
Average Manufacturing Wage
19 The standard model was first presented in George J. Stigler, “The Economics of Minimum Wage Legislation,” American Economic Review 36 (June 1946): 358–365.