Chapter 3 presented a framework for thinking about the demand side of the labor market.
The framework explained why the quantity of labor demanded is inversely related to the
wage both in the short run and the long run. It also explained what causes labor demand
to increase or decrease when the prices of other inputs change. Knowing why these
things happen provides a foundation for correctly analyzing the effects of different
policies (e.g., payroll taxes) on the direction of employment and wages. Chapter 4
extends the labor demand framework to look at the issue of how responsive the quantity
of labor demanded is to changes in the wage or the price of other inputs. Does the
quantity firms demand change by a little or a lot when the wage changes? Under what
circumstances is the substitution effect accompanying a change in the price of capital
likely to be large and the scale effect small? These are the types of questions taken up in
Chapter 4.
The main measure of how responsive employment is to changes in the wage or the price
of other inputs is the elasticity of demand, which is denoted by the Greek letter eta (η).
An elasticity is simply the ratio of two percentage changes. If the focus is how responsive
the quantity of labor demanded is to a change in the wage rate, the elasticity is called the
own-wage elasticity of demand. Letting E stand for employment, W the wage, the
subscript i a particular category of labor, and %Δ a percentage change, the own-wage
elasticity is defined as
The elasticity can be interpreted as the percentage change in employment induced by a
one percentage point change in the wage. Since the own-wage elasticity will always have
a negative sign (since demand curves slope downward), usually reference is made to just
the magnitude (the absolute value) of the elasticity. When the magnitude of η is less than
one, demand is said to be inelastic, meaning employment is relatively unresponsive to
changes in the wage. A magnitude greater than one is called elastic and means that
employment is relatively responsive to changes in the wage.
What factors lead the own-wage elasticity to be elastic or inelastic? In the case of a
straight line demand curve, whether the own-wage elasticity is elastic or inelastic depends
in part on the current position along the curve. Straight line demand curves exhibit the
same unit changes throughout the entire curve. For example, a demand curve with a
slope of -1 will show an increase of employment by one unit for every one-unit fall in the
wage. The same curve, however, will have changing elasticities as wages change. In
particular, demand will be more elastic towards the top and get less elastic as wages fall.
The logic behind this is simple: when wages are high and employment low (at the top of
the curve), any given wage change will be small in percentage terms while a given change
in employment will be large in percentage terms. The reverse is true when wages are low
and employment high (at the bottom of the curve). So, although slope alone is not a good
universal indicator of elasticity, when comparing two demand curves, it is still usually
possible to generalize whether one tends to be more elastic than another. For example, in
Figure 4-1, for any small change at a given wage rate, say from $25 to $26, curve D1 will
always be more elastic (η11 = -1.67 at $25) than curve D2 (η22 = -1 at $25), even though
each will eventually exhibit an inelastic range if the wage goes low enough.
Secondly, the size of the own-wage elasticity can be explained by the size of the
substitution and scale effects resulting from a change in the wage. The size of the
substitution and scale effects, in turn, are influenced primarily by four factors. These
factors have come to be known as the Hicks-Marshall laws of derived demand. These
laws state that the elasticity of demand for labor will be greater (more elastic):
- the greater the elasticity of demand for output,
- the easier it is to substitute other factors of production for labor,
- the more elastic is the supply of other factors, and
- the greater is labor’s share in the total costs of the firm.
To understand the Hicks-Marshall laws, consider a situation where the wage increases,
holding all else constant. What kinds of things would tend to diminish the substitution
and scale effects, and hence result in a very unresponsive (inelastic) labor demand curve?
Considering the substitution effect first, the substitution effect will be small if
circumstances exist that make it difficult to substitute capital for labor. For example, in a
production process where labor and capital are used in fixed proportions, there can be no
substitution effect. Alternatively, union rules may limit firms from undertaking certain
tasks with less than some minimum number of workers. Supposing that the firm can and
does try to substitute capital for labor, are there any factors that could limit this
substitution? Usually we think of the firm being able to buy as much or as little capital as
it wants at the going price. This would be the case if the supply of capital is perfectly
elastic (horizontal). But suppose instead that the supply of capital is actually upward
sloping and relatively inelastic. As the firm tries to substitute capital for labor, the
demand for capital will be shifting outward along a relatively inelastic supply curve. This
bids up the price of capital significantly and limits the firm’s incentive to continue
substituting additional units of capital for labor. So, substitution can be limited or
perhaps even unfeasible due to either technical or economic factors.
What would lead to a small scale effect? The best way to answer this is to think of the
linkages through which the scale effect occurs. When the wage increases, the marginal
cost of production (MC) rises, and a rise in the MC destroys the equality between
marginal revenue (MR) and MC. That forces the firm to adjust its output downward to
restore the MR = MC condition for profit maximization. As the optimal output (Q*) is
adjusted downward, the firm’s use of labor (L) and capital inputs (K) are reduced. This
chain of reasoning is summarized schematically below.
The important thing to realize is that if the first two links in the chain are weak, the last
can not help but be weak. But what would cause the MC of production not to rise much
as the wage increases? The answer is if the cost of employing labor is a small share of
total cost. As an extreme example of this, suppose a firm did not use any labor to begin
with (so that labor’s share of total cost was 0 percent). In such a case, an increase in the
wage would have no effect on the MC. (See the discussion accompanying footnote 5 in
the text for a situation where a category of labor could still be highly elastic even when it
accounts for a very small share of total costs.) What about the second link? What would
make the level of output not fall very much for a given increase in MC? The answer here
is an inelastic demand for the final product the firm sells. The more unresponsive
quantity demanded is to changes in price, the more the MC increase can be passed along
in the form of higher prices, and the less output has to adjust downward.
If the focus is how responsive the quantity demand of labor input i is to a change in the
price of another input j, the elasticity is called the cross-price elasticity of demand
(cross-wage elasticity of demand when the other input is a different category of labor) and
is defined as
Similarly, one could define a cross-price elasticity ηji (though readers should note that the
two elasticities will not have the same value). Unlike the own-wage elasticity where the
sign is typically ignored, both the sign and magnitude of the cross-price elasticities are
important. If the sign is positive, the employment of input i moves together with the price
of input j (and hence presumably opposite to that of the quantity of input j) indicating that
i and j are gross substitutes. If the sign is negative, inputs i and j are gross
complements.
What factors lead two inputs to be gross substitutes or gross complements? When
focusing on the long-run demand for labor, the size of the substitution and scale effects
are again the determining factors in whether demand will be relatively elastic or inelastic,
and whether any two inputs will be gross substitutes or gross complements. (In the short
run only the scale effect is relevant to the choice between capital and labor since there can
be no substitution effect. However, if the focus is on two types of labor, there often can
be substitution between the two types even in the short run.)
Focusing on these four factors (the ease of substitutability between labor and other inputs,
the supply elasticity of the other inputs, the share of total costs that are labor costs, and
the product demand elasticity) provides a good place to start in assessing the likely
consequences for employment of different changes that may take place in the labor
market. By assembling evidence on each of these factors, one would be in a strong
position to gauge the magnitude of the employment change due to a change in the wage.
Also these four factors can provide focus when assessing the employment effects of
changes in the price of other inputs. In the problems and applications that follow, these
four factors will be employed in a number of different contexts to assess and explain a
variety of labor market phenomena. Proper use of the Hicks-Marshall laws is one of the
most important and versatile tools for anyone interested in being a serious thinker about
labor market issues.
The next section of the chapter uses the concept of elasticity to look at the effects of
minimum wage legislation. The basic model of labor demand under competitive labor
market conditions predicts that the minimum wage will produce both winners and losers.
The winners are those who retain their jobs at the higher wage. The losers include those
covered by the law who lose their jobs, and those not covered by the law who experience
lower wages because of the rightward supply shift that accompanies the migration of
these unemployed workers to the uncovered sector. The key issue is the degree of the
employment loss among low-wage workers and the resulting impact on poverty levels,
and ultimately this is a question of labor demand elasticity. Factors that can complicate
the empirical estimation of the employment effects of the minimum wage are reviewed
and an overview of recent empirical results is presented. Empirical findings have been
sensitive to the design of the study, and overall it is difficult to reach a definite conclusion
as to the effects of the minimum wage on employment.
The chapter also applies the labor demand framework to the issue of how technological
change affects employment. Technological change can affect the demand for labor in
two ways. Technological change involving the introduction of new or improved products
causes demand shifts in the product markets—an outward shift for the newly created
product, an inward shift for the product that is superseded—which in turn translates into
shifts in labor demand. Labor demand will increase in the sectors producing the new
product, and decrease in the sectors producing the outdated product. New and improved
products also tend to increase competition in the product markets as consumers have
more substitution possibilities. Increased competition means each firm faces a more
elastic product demand. A more elastic product demand, according to the Hicks-Marshall
laws, results in a more elastic labor demand curve for the firm. An elastic labor demand
greatly diminishes the ability of unions to bargain for wage increases since employment
losses are greater for a given wage increase when labor demand is elastic.
Technological change can also affect employment by reducing the price of capital
directly, or making available a new type of capital that can serve as a substitute for labor.
The latter occurrence can be treated as a reduction in the price of capital since when
something is unavailable it essentially has an infinite price. When the capital does
become available through technological change, it is as if its price has fallen to a point
where at least some firms can afford to buy it. Direct or indirect price changes like these
induce the firm to substitute capital for labor, but also create a scale effect that causes the
firm to use more capital and more labor. By examining the factors listed in the Hicks-
Marshall laws, the likely size of the substitution and scale effects can be determined,
thereby providing a solid foundation for assessing the likely employment effects of the
technological change on particular industries. Even when employment falls in a
particular industry, however, it is important to keep in mind that these labor resources are
now free to flow to those industries that will be expanding because of the technological
change.
Freeing up resources so that they can be used more productively in other industries is also
the logic behind international trade, and so the chapter concludes with an appendix that
analyzes the employment effects of international trade. The basis for trade lies in
differences in the internal costs of producing each good in each country, without trade.
Those costs are opportunity costs, which arise because the same resources can only be
used once. Resources used to grow food, for example, are then no longer available to
produce clothing, and the cost of the food is best measured by the amount of clothing the
same resources could have produced. The relative costs of each good can be represented
by the slope of each country’s production possibilities curve. Such a curve shows (for
two goods) all the different combinations of goods that can be produced when a country
efficiently uses all of its resources. Trade will cause shifts in employment between
industries, but countries with high living standards and high wages need not fear
permanent employment losses because of trade. While shifts in employment
opportunities associated with free trade can cause temporary unemployment and hardship
for those workers producing goods that will no longer be produced domestically, the
overall effects of trade are higher living standards for both trading partners. The reason
for this gain, and the irrelevance of a country’s internal wage rates to the process of trade,
is explored in the following example.
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