Chapter 3
Labor Demand
“The laborer is worthy of his hire.”
-The Gospel of St. Luke
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Introduction
Firms hire workers because consumers want to purchase a
variety of goods and services.
Demand for workers is derived from the wants and desires of
consumers.
Central questions: how many workers are hired and what are
they paid?
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The Firm’s Production Function
Describes the technology that the firm uses to produce goods
and services.
The firm’s output can be produced by a variety of capital–labor
combinations.
The marginal product of labor is the change in output resulting
from hiring an additional worker, holding constant the quantities
of other inputs.
The marginal product of capital is the change in output resulting
from employing one additional unit of capital, holding constant
the quantities of other inputs.
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The Total Product, the Marginal Product, and
the Average Product Curves
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The total product curve gives the relationship between output and the number of workers
hired by the firm (holding capital fixed). The marginal product curve shows the output
produced by each additional worker, and the average product curve shows output per worker.
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Profit Maximization
Objective of the firm is to maximize profits.
The profit function is:
• Profits = pq – wE – rK
• Total Revenue = pq
• Total Costs = (wE + rk)
Perfectly competitive firms cannot influence prices of output or
inputs.
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Short Run Hiring Decision
Value of Marginal Product of Employment (VMPE) is the marginal
product of labor times the dollar value of the output.
VMPE indicates the dollar benefit derived from hiring an
additional worker, holding capital constant.
Value of Average Product of Employment is the dollar value of
output per worker.
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The Firm’s Hiring Decision in the Short-Run
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A profitmaximizing
firm
hires workers up to
the point where
the wage rate
equals the value of
marginal product
of labor. If the
wage is $22, the
firm hires eight
workers.
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Labor Demand Curve
The demand curve for labor indicates how many workers the
firm hires for each possible wage, holding capital constant.
The labor demand curve is downward sloping. This reflects the
fact that additional workers are costly and alter average
production due to the Law of Diminishing Returns.
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The Short-Run Demand Curve for Labor
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Because marginal product
eventually declines, the
short-run demand curve
for labor is downward
sloping. A drop in the wage
from $22 to $18 increases
the firm’s employment. An
increase in the price of the
output shifts the value of
marginal product curve
upward (to the right), and
increases employment.
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Maximizing Profits: Two Rules
The profit maximizing firm should produce up to the point where
the cost of producing an additional unit of output (marginal cost)
is equal to the revenue obtained from selling that output
(marginal revenue).
Marginal Productivity Condition: hire labor up to the point where
the value of marginal product equals the added cost of hiring the
worker (i.e., the wage).
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The Mathematics of Marginal Productivity Theory
The cost of producing an extra unit of output:
• MC = w x (1 / MPE)
The condition: produce to the point where MC = P (for the
competitive firm, P = MR)
• W x (1 / MPE) = P
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Critiques of Marginal Productivity Theory
A common criticism is that the theory bears little relation to the
way that employers make hiring decisions.
Another criticism is that the assumptions of the theory are not
very realistic.
However, employers act as if they know the implications of
marginal productivity theory (hence, they try to make profits and
remain in business).
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The Short-Run Demand Curve for the Industry
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The Firm’s Output Decision
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A profit-maximizing
firm produces up to
the point where the
output price equals
the marginal cost of
production.
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The Employment Decision in the Long Run
In the long run, the firm maximizes profits by choosing how
many workers to hire AND how much plant and equipment to
invest in.
Isoquant curves describe the possible combinations of labor and
capital that produce the same level of output
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Isoquant Curves
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All capital-labor
combinations that lie on a
single isoquant produce the
same level of output. The
input combinations at
points X and Y produce q0
units of output.
Combinations of input
bundles that lie on higher
isoquants must produce
more output.
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Isocost Lines
The isocost line indicates all labor–capital bundles that exhaust a
specified budget for the firm.
Isocost lines indicate equally costly combinations of inputs.
Higher isocost lines indicate higher costs.
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Isocost Lines
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All capital-labor
combinations that lie on a
single isocost curve are
equally costly. Capitallabor
combinations that lie
on a higher isocost curve
are more costly. The slope
of an isoquant equals the
ratio of input prices (-w/r).
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The Firm’s Optimal Combination of Inputs
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A firm minimizes the cost of
producing q0 units of output
by using the capital-labor
combination at point P,
where the isoquant is
tangent to the isocost. All
other capital-labor
combinations (such as those
given by points A and B) lie
on a higher isocost curve.
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Cost Minimization
Profit maximization implies cost minimization.
The firm chooses the least-cost combination of capital and labor.
This least-cost choice is where the isocost line is tangent to the
isoquant.
Marginal rate of substitution equals the ratio of input prices, w /
r, at the least-cost choice.
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Long Run Demand for Labor
When the wage drops, two effects arise.
• The firm takes advantage of the lower price of labor by
expanding production (the scale effect).
• The firm takes advantage of the wage change by rearranging its
mix of inputs, by employing more labor and less of other inputs,
even if holding output constant (the substitution effect)
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The Impact of a Wage Reduction Holding Costs
Constant
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A wage reduction flattens the
isocost curve. If the firm were to
hold the initial cost outlay
constant at C0 dollars, the
isocost would rotate around C0
and the firm would move from
point P to point R. A profitmaximizing
firm, however, will
not generally want to hold the
cost outlay constant when the
wage changes.
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The Impact of a Wage Reduction on the Output and
Employment of a Profit-Maximizing Firm
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•A wage cut reduces the marginal cost of production and encourages the firm to
expand (from producing 100 to 150 units).
•The firm moves from point P to point R, increasing the number of workers hired
from 25 to 50.
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Substitution and Scale Effects
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A wage cut generates
substitution and scale
effects. The scale effect
(from P to Q) encourages
the firm to expand,
increasing the firm’s
employment. The
substitution effect (from Q
to R) encourages the firm
to use a more laborintensive
method of
production, further
increasing employment.
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Two Special Cases of Isoquants
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Capital and labor are perfect substitutes if the isoquant is linear (so that two
workers can always be substituted for one machine). The two inputs are perfect
complements if the isoquant is right-angled. The firm then gets the same output
when it hires 5 machines and 20 workers as when it hires 5 machines and 25
workers.
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Elasticity of Substitution
The elasticity of substitution is the
percentage change in the capital to labor
ratio given a percentage change in the price
ratio (wages to real interest).
• Formula: %∆(K/L)  %∆(w/r).
• Interpret a particular elasticity of substitution number
as the percentage change in the capital–labor ratio
given a 1% change in the relative price of labor to
capital
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Elasticity of Substitution
Example:
If the elasticity of substitution is 5, then
a 10% increase in the ratio of wages to the
price of capital would result in the firm
increasing its capital-to-labor ratio by 50%.
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The Short- and Long-Term Demand Curves for Labor
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In the long run, the firm can
take full advantage of the
economic opportunities
introduced by a change in
the wage. As a result, the
long-run demand curve is
more elastic than the shortrun
demand curve.
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Marshall’s Rules
Labor Demand is more elastic when:
• The elasticity of substitution is greater.
• The elasticity of demand for the firm’s output is greater.
• Labor’s share in total costs of production is greater.
• The elasticity of supply of other factors of production such as
capital is greater.
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Factor Demands When There Are Several Inputs
There are many different inputs.
• Skilled and unskilled labor
• Old and young
• Old and new machines
Cross-elasticity of factor demand.
• Percent change in xi  Percent change in wj
• If cross-elasticity is positive, the two inputs are said to be
substitutes in production.
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The Demand Curve for a Factor of Production Affected by
the Prices of Other Inputs
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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.
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Labor Market Equilibrium
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In a competitive labor
market, equilibrium is
attained at the point
where supply equals
demand. The marketclearing
wage is w* at
which E* workers are
employed.
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Application: The Employment Effects of Minimum
Wages
The unemployment rate is higher the higher the minimum wage
and the more elastic are the labor supply and demand curves.
The benefits of the minimum wage accrue mostly to workers
who are not at the bottom of the distribution of permanent
income.
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The Impact of the Minimum Wage on Employment
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A minimum wage set at w
results in employers
cutting employment from
E* to E. The higher wage
also encourages ES – E*
workers to enter the
market. Thus, under a
minimum wage, ES – E–
workers are unemployed.
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Minimum Wages in the United States, 1938-2011
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The Impact of Minimum Wages on the Covered and
Uncovered Sectors
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If the minimum wage applies only to jobs in the covered sector, the displaced
workers might move to the uncovered sector, shifting the supply curve to the
right and reducing the uncovered sector’s wage. If it is easy to get a minimum
wage job, workers in the uncovered sector might quit their jobs and wait in the
covered sector until a job opens up, shifting the supply curve in the uncovered
sector to the left and raising the uncovered sector’s wage.
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Estimating Labor Demand
One can identify the slope of the labor demand curve, which can
be used to calculate the elasticity of labor demand, when the
supply curve shifts.
Problem: Must make sure the labor demand curve is not also
changing.
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Problems with Estimating Labor Demand
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The Impact of Wartime Mobilization of Men on
Female Labor Supply
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The Impact of Wartime Mobilization of Men on
Female Wages
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