Lecture The Demand for Labor

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					        Lecture 4:
   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.    It can be shown theoretically and empirically
      that labor demand curves slope downward.
2.    The quantity of labor demanded has varying
      degrees of responsiveness to changes in the
 When the demand for labor is analyzed,
   two sets of distinctions are made:
1.   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.
2.   The time period for which the demand curve is
     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
(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 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                                      25                  Average Product
     80                                      15

     60                                      10
                                              5    Marginal Product

             2     4     6    8   10           0     2     4     6    8       10

             Number of workers                           Number of workers

    The Total Product, the Marginal Product, and the Average Product Curves
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.




         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.,

    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 (own-
wage) 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’                                D1: elastic demand
                                            D2: inelastic demand

                     E1’    E1 E2’ E2
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

→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.
                                                   Note: To be minimizing
C1/r                                               cost, the cost of
             A                                     producing an extra unit
C0/r                                               of output by adding
                                                   only labor must equal
                                                   the cost of producing
                   P                               that extra unit by
                                                   employing only
                                    B              additional capital. i.e.,

       0         100                                   MPE/w = MPK/ r

       The Firm’s Optimal Combination of Inputs
  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

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.
                                                 Defn. The Elasticity of
                                                 Substitution: The
                                                 elasticity of substitution
                                                 gives the percentage
                                                 change in the
J                  P’                            capital/labor ratio
                                                 resulting from a 1
              P         Q’                       percent change in the
      Wage is w1    Q
                                                 relative price of labor.
                                  100            The size of the
       Wage is w0
                                                 substitution effect
                                                 directly depends on the
                        F    G    H       J
                                                 magnitude of the
                                                 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 “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:
 1)   When the price elasticity of demand for the product
      being produced high;
 2)   When other factors of production can be easily
      substituted for the category of labor;
 3)   When the supply of other factors of production is
      highly elastic;
 4)   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.
 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
 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.
  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.
(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.
   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.

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