The Demand for Labor
The demand for labor is a derived
demand. Employer’s demand for labor
is a function of the characteristics of
demand in the product market. It is
also a function of the characteristics of
the production process.
Two important features of the demand
for labor:
1.
2.
It can be shown theoretically and empirically
that labor demand curves slope downward.
The quantity of labor demanded has varying
degrees of responsiveness to changes in the
wage.
When the demand for labor is analyzed,
two sets of distinctions are made:
1.
2.
Demand by firm v.s. the demand curves for an
entire market.
Note: Firm and market labor demand curves have
different properties although both slope downward.
The time period for which the demand curve is
drawn.
Short Run: A period over which a firm’s capital
stock is fixed.
Long Run: A period over which a firm is free to
vary all factors of production.
A Simple Model of Labor Demand
Assumptions:
(1) Employers seek to maximize profit.
(2) Firms employ two homogeneous factors of
production, employee-hours (E) and capital (K), in
their production of goods and services. Their
production function can be written as:
Q = f (E, K)
(3) Hourly wage cost is the only cost of labor.
Note: We ignore hiring, training cost and fringebenefit costs for the time being.
(4) Both a firm’s labor market and its product market
are competitive.
1. Short-Run Demand for Labor by Firms
Defn. Marginal Product of Labor: The change in output
resulting from hiring an additional worker, holding
constant the quantities of all other input.
Output
Output
140
120
20
100
80
15
60
40
10
5
20
0
Average Product
25
2
4
6
8
Number of workers
10
0
Marginal Product
2
4
6
8
Number of workers
The Total Product, the Marginal Product, and the Average Product Curves
10
Defn. Law of Diminishing Returns: Eventually each
additional increment of labor produces
progressively smaller increments of output.
Defn. Value of the Marginal Product (VMP): The dollar
values of the additional output produced by an
additional worker.
VMP = P × MPE
 The profits are maximized by the competitive firm
when the value of marginal product of labor is just
equal to its marginal cost.
Dollars
38
VAPE
22
VMPE
0
1
4
8
Number of Workers
The Firm’s Hiring Decision in the Short Run
 Profit-Maximizing condition: Labor should be hired
until its marginal product equals the real wage. i.e.,
MPE=W/P
The firm’s demand for labor in the short run is
equivalent to the downward-sloping segment of its
marginal product of labor schedule.
Note: The downward-sloping nature of the short-run
labor demand curve is based on an assumption that
MPE declines as employment is increased.
 Elasticity of Labor Demand
We measure the responsiveness of labor demand to changes
in the wage rate by using an elasticity. The short-run
elasticity of labor demand, δSR, is defined as the percentage
change in short-run employment resulting from a 1 percent
change in the wage:
δSR = (%△ESR)／ (%△w)
Since the labor demand curves slope downward, an increase in
the wage rate will cause employment to decrease; the (ownwage) elasticity of demand is a negative number.
Note: | δSR | > 1: a 1% increase in wage will lead to an employment
decline of greater than 1% → elastic demand curve
| δSR | < 1: a 1% increase in wage will lead to a proportionately
smaller decline in employment → inelastic demand curve
Elastic demand: aggregate earnings↓ when w↑
Inelastic demand: aggregate earnings↑ when w↑
W
D2
D1
D1: elastic demand
D2: inelastic demand
W’
W
E1’
E1 E2’ E2
E
2. Market Demand Curve
A market demand curve is just the summation of
the labor demanded by all firms in a particular
labor market at each level of the real wage.
Note: When aggregating labor demand to the market
level, product price can no longer be taken as given,
and the aggregation is no longer a simple summation.
However, the market demand curves drawn against
money wages, like those drawn as functions of real
wages, slope downward.
3. Long-Run Demand for Labor by Firms
In the long run, employers are free to vary their capital stock as
well as the number of workers they employ.
 Profit Maximization’s Dual Problem – Cost Minimization
Defn. Isoquant: An isoquant describes the possible combination of
labor and capital which produce the same level of output.
Defn. The Marginal Rate of Technical Substitution: The slope of
an isoquant is the negative of the ratio of marginal products. The
absolute value of the slope of an isoquant is called the marginal
rate of technical substitution.
Defn. Isocost: The isocost line gives the menu of different
combinations of labor and capital which are equally costly.
A profit-maximizing firm that is producing q0 units of
output wants to produce these units at the lowest possible
cost.
→The firm chooses the combination of labor and
capital where the isocost is tangent to the isoquant. i.e.,
MPE/MPK = w/r
→Cost-minimization requires that the marginal rate of
technical substitution equal the ratio of prices.
Capital
Note: To be minimizing
cost, the cost of
producing an extra unit
of output by adding
only labor must equal
the cost of producing
that extra unit by
employing only
additional capital. i.e.,
C1/r
A
C0/r
P
175
B
0
100
Employment
The Firm’s Optimal Combination of Inputs
MPE/w = MPK/ r
 The Effect of Change in w
Increase in w:
(1)Substitution Effect
As w increase, labor cost rises, and more capital and less
labor are used in the production process.
(2) Scale effect
The new-profit-maximizing level of production will be
less. How much less cannot be determined unless we
know something about the product demand curve.
Both the substitution effect and the scale effect work
in the same direction. So these effects lead us to
assert that the long-run demand curve for labor slopes
downward.
Note: In general, if a firm is seeking to minimize costs,
in the long run it should employ all inputs up until the
point that the marginal cost of producing a unit of
output is the same regardless of which input is used.
Capital
G
F
J
H
P’
Q’
P
Wage is w1
Q
Wage is w0
F
G
Defn. The Elasticity of
Substitution: The
elasticity of substitution
gives the percentage
change in the
capital/labor ratio
resulting from a 1
percent change in the
relative price of labor.
101
The size of the
100
substitution effect
directly depends on the
H
J
magnitude of the
Employment
elasticity of substitution.
4. Marshall’s Rules of Derived Demand (The
Hicks-Marshall Law of Derived Demand)
The factors that influence own-wage elasticity
can be summarized by the four “HicksMarshall Laws of Derived Demand.” These
laws assert that, other things equal, the ownwage elasticity of demand for a category of
labor is high under the following conditions:
1)
2)
3)
4)
When the price elasticity of demand for the product
being produced high;
When other factors of production can be easily
substituted for the category of labor;
When the supply of other factors of production is
highly elastic;
When the cost of employing the category of labor is
a large share of the total cost of production.
Note: (1), (2) and (3) can be shown to always hold. There
are conditions, however, under which the final law does
not hold.
(1) Demand for the Final Product
The greater the price elasticity of demand for
the final product, the larger will be the decline
in output associated with a given increase in
price and the greater the decrease in output, the
greater the loss in employment (other things
equal). Thus the greater the elasticity of
demand for the product, the greater the
elasticity of demand for labor will be.
(2) Substitutability of Other Factors
Other things equal, the easier it is to substitute other
factors in production, the higher the wage elasticity
of demand will be.
Note:
a. Sometimes collectively bargained or legislated
restrictions make the demand for labor less elastic by
reducing substitutability (not technically).
b.
Substitution possibility that are not feasible in the
short run may well become feasible over longer
periods of time, when employers are free to vary
their capital stock.
→ The demand for labor is more elastic in the longer run
than in the short run.
(3) The supply of Other Factors
As the wage rate increased and employers attempted
to substitute other factors of production for labor, the
prices of these inputs were bid up substantially. Such
a price increase would dampen firm’s appetites for
capital and thus limit the substitution of capital for
labor.
Note:
Prices of other inputs are less likely to be bid up in the
long run than in the short run. → Demand for labor
will be more elastic in the long run.
(4) The Share of Labor in Total Costs
The greater the category’s share in total costs, the
higher the wage elasticity of demand will tend to be.
If the share of labor cost is large, cost increase due to
wage increase is larger. The employer would have to
increase their product prices by more, output and
hence employment would fall more.
Note:
This law, relating a smaller labor share with a lesselastic demand curve, holds only when it is easier for
customers to substitute among final products than it is
for employers to substitute capital for labor.
(5) The Cross-Wage Elasticity of Demand
The elasticity of demand for input j with
respect to the price of input k is the percentage
change in the demand for input j induced by 1
percent change in the price of input k. i.e.,
δjk = %△E j / %△Wk
δjk = %△Ek / %△Wj
If the cross elasticities are positive (with an increase in
the price of one increasing the demand for the other)
the two are said to be gross substitutes. If the cross
elasticities are negative (and increase in the price of one
reduces the demand for the other), the two are said to be
gross complements.
Note:
Whether two inputs are gross substitutes or gross
complements depends on both the production function
and the demand conditions.
→ Knowing that two groups are substitutes in production
is not sufficient to tell us whether they are gross
substitutes or gross complements.