Lecture 4: The Demand for Labor

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Lecture 4 The Demand for Labor

• The demand for labor is a derived demand.
  Employers 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.

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Two important features of the demand for labor

• 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.

3
When the demand for labor is analyzed, two sets
of distinctions are made

• 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 firms
  capital stock is fixed.
• Long Run A period over which a firm is
  free to vary all factors of production.

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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
  fringe-
• benefit costs for the time being.
• (4) Both a firms labor market and its product
  market
• are competitive.

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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
Average Product
25
120
20
100
15
80
60
10
40
Marginal Product
5
20
0
2
4
6
8
10
2
4
6
8
10
0
Number of workers
Number of workers
The Total Product, the Marginal Product, and the
Average Product Curves
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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
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• 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 Firms Hiring Decision in the Short Run
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• Profit-Maximizing condition Labor should be
  hired
• until its marginal product equals the real
  wage. i.e.,
• MPEW/P

The firms 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.
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• 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, dSR, is
defined as the percentage change in short-run
employment resulting from a 1 percent change in
the wage
dSR (?ESR)/ (?w)
Since the labor demand curves slope downward, an
increase in the wage rate will cause employment
to decrease the (own-wage) elasticity of demand
is a negative number.
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Note dSR gt 1 a 1 increase in wage will
lead to an employment
decline of greater than 1 ? elastic demand
curve dSR lt 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
E
E1
E1
E2
E2
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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.
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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 Maximizations 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.
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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.
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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
MPE/w MPK/ r
0
100
Employment
The Firms Optimal Combination of Inputs
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• The Effect of Change in w

• Increase in w
• 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.

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• 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.

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Capital
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. The size of the substitution effect
directly depends on the magnitude of the
elasticity of substitution.
G
F
J
P
H
P
Q
Q
101
Wage is w1
100
Wage is w0
F
G
H
J
Employment
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• 4. Marshalls Rules of Derived Demand (The
  Hicks-Marshall Law of Derived Demand)
• The factors that influence own-wage
  elasticity can be summarized by the four
  Hicks-Marshall Laws of Derived Demand. These
  laws assert that, other things equal, the
  own-wage elasticity of demand for a category of
  labor is high under the following conditions

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• 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.
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(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.

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(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
• Sometimes collectively bargained or legislated
  restrictions make the demand for labor less
  elastic by reducing substitutability (not
  technically).
• 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.
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(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 firms 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.

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(4) The Share of Labor in Total Costs

• The greater the categorys 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 less-elastic 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.

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(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.,
• djk ?E j / ?Wk
• djk ?Ek / ?Wj

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• 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.