Topic 4 Labor Demand by qv98Vk7G

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     ECN706


     TOPIC 4


THE DEMAND FOR
    LABOUR
                                                     2


                  Objectives
• To analyse the part played by labour in the firm’s
  production function.
• To define the marginal product of labour and capital
  and analyse how they impact on firm’s production
  decision and profit maximisation.
• To define Value of Marginal Product and Marginal
  Revenue Product and derive the short run labour
  demand curve
• To use isocost-isoquant analysis to derive the long-
  run labour demand curve.
• To analyse the firm’s decision to an optimal
  combination of inputs to maximise profits
                                                         3



                 Objectives
• To distinguish between the short run and long
  run demand for labour.
• To explain the scale and substitution effects of a
  change in input prices.
• To define and calculate elasticity, cross elasticity
  and elasticity of substitution between factor
  inputs.
• To analyse the demand for labour when the
  product market is not competitive.
• To discuss how adjustment costs impact labour
  employment.
                                                  4


              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 how much should they be paid?
                                                       5



 The Firm’s Production Function

• Describes the technical relationship between the
  firm’s uses of inputs in the production of output:
   q = f (E, K)
• The firm’s output is produced by any
  combination of capital and labor
• Assumption:
“All labor and capital are assumed to be
  homogenous”.
                                                     6


 The Firm’s Production Function

• 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 hiring one additional unit
  of capital, holding constant the quantities of
  other inputs
                                                  7



         Production Function

• Marginal products of labor and capital are
  positive, so as more units of each are hired,
  output increases
• When firms hire more workers, total product
  rises
• The slope of the total product curve is the
  marginal product of labor
                                                    8


         Production Function
• Law of Diminishing Returns: eventually, the
  marginal product of labor declines
 ▫ Average Product: the amount of output produced
   by the typical worker
• measured by the amount of total output divided
  by the number of workers used in the production
  of that output
• Marginal Product and Average Product of Labor
  (holding K constant)
                                                                                                             9
The Total Product, the Marginal Product,
    and the Average Product Curves
                  140                                             25

                  120                                                                      Average Product
                                                                  20
                  100




                                                         Output
         Output




                   80                                             15

                   60               Total Product
                                                                  10
                                    Curve
                   40
                                                                   5
                   20                                                          Marginal Product

                    0                                              0
                        0   2   4   6    8    10    12                 0   2     4     6     8    10    12

                            Number of Workers                              Number of Workers



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 gives the output produced by each additional
 worker, and the average product curve gives the output per worker.
                                                 10


            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 firm cannot influence
  prices of output or inputs
                                                      11

Short Run Hiring Decision –the Short
       Run Demand for Labor

• Value of Marginal Product of labor (VMP) is the
  dollar value of what each additional worker
  produces:

  VMP = p x MP

• This indicates the benefit derived from hiring an
  additional worker, holding capital constant
                                                     12

Short Run Hiring Decision –the Short
       Run Demand for Labor
• Value of Average Product is the dollar value of
  output per worker:

 VAP = p x AP

• Note: For a perfectly competitive firm, the VMP of
  labor is equivalent to the Marginal Revenue
  Product (MRP) which is the increase (change) in
  total revenue resulting from the employment of
  each additional labour unit:
•
  So the VMP schedule (Figure 4.2) in slide 15 is also
  the perfectly competitive firm’s MRP schedule.
                                                     13

     Firm’s Hiring Decision in the
              Short Run
• What is the logic underlying the equality of VMP and
  MRP where perfect competition prevails in the
  product market?
• Because the competitive firm is a price taker, it can
  sell as many units of output as it desires at the
  market price (= $2). The sale of each additional unit
  of the product adds the product price (= $2) to the
  firm’s total revenue;
• MR = p (constant)
• the extra revenue to the firm from employing an
  additional labour unit (MRP = MR x MP) equals the
  value of the extra output (VMP = p x MP)
                                                    14


Firm’s Hiring Decision in the Short
               Run
Firms should hire the number of workers to the point
 the value of extra production from hiring of the last
 worker (VMP) equals the wage rate (w) and the
 value of marginal product curve is downward
 sloping :

                      VMP = w
                                                                    15

The Firm's Hiring Decision
in the Short-Run - Fig 4.2


38
                                         A profit-maximizing
                                         firm hires workers up
                    VAPE                 to the point where the
                                         wage rate equals the
22
                                         value of marginal
                    VMPE                 product of labor. If the
                                         wage is $22, the firm
                                         hires eight workers.
                8    Number of Workers
     1   4
                                                   16


  The Firm’s Short Run Labor Demand
                Curve
• The short-run demand curve for labour is meant to
  tell what happens to the firm’s employment decision
  as the wage changes, holding capital constant.
  Therefore, the VMP schedule and the curve is
  the firm’s short run labour demand curve.
• It indicates the amount of labour this firm would
  demand at separate competitively determined wage
  rates.
                                                       17

The Firm’s Short Run Labor Demand
              Curve
• The demand curve for labor indicates how the firm
  reacts to wage changes, holding capital constant
• The curve is downward sloping
• Because of the Law of Diminishing Returns
  (marginal and average production declines) and
  therefore VMP decline as more workers are hired
• So if the firm is to employ more workers, the wage
  must fall
                                                                               18



The Short-Run Demand Curve for Labor

                                                Because marginal product
                                                eventually declines, the
                                                short-run demand curve for
                                                labor is downward sloping.
                                                A drop in the wage from
  22
                                                $22 to $18 increases the
  18
                                                firm’s employment. An
                                                increase in the price of the
                                   VMPE
                                                output shifts the value of
                VMPE
                                                marginal product curve
                                                upward, and increases
        8   9          12                       employment.
                            Number of Workers
                                                       19


Maximizing Profits: A General Rule
• 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: this is the
  hiring rule, hire labor up to the point when the
  added value of marginal product equals the added
  cost of hiring the worker (i.e., the wage)
                                                   20


   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 when MC =
  P (for the competitive firm, P = MR)
 ▫ w x 1/MPe = P
 ▫ w = P x MPe
 ▫ w = VMP
                                             21


   The Mathematics of Marginal
       Productivity Theory
• The firm’s hiring decision:

E*: VMP=w is the same as the firm’s output
 decision:

                 q: P (MR) = MC
                                                                         22

       The Short-Run Demand Curve
             for the Industry

Wage                              Wage


                                             T

                                         D
20                                20


10                                10
                                                               D

                                                           T

        15   28 30   Employment                  30   56 60 Employment
                                                   23


     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:
describes the possible combinations of labor and
  capital that produce the same level of output
  (the curve “ISOlates the QUANTity of output).
                                                           24


     The Employment Decision in
           the Long Run
• Isoquants…
 ▫ Must be downward sloping
 ▫ Do not intersect
 ▫ Higher isoquants indicate more output
 ▫ Are convex to the origin
 ▫ Have a slope that is the negative of the ratio of the
   marginal products of capital and labor
 ▫ MPÉ/MPκ
 ▫ The value of this slope is called the marginal
   rate of technical substitution.
                                                                   25


                    Isoquant Curves
 Capital

                                     All capital-labor
                                     combinations that lie along
                                     a single isoquant produce
                                     the same level of output.
           X
                                     The input combinations at
K                                   points X and Y produce q0
                Y
                         q1
                                     units of output. Input
                        q0
                                     combinations that lie on
                                     higher isoquants produce
                                     more output.
           E                 Employment
                                                     26


                   Isocost

• The Isocost line indicates the possible
  combinations of labor and capital the firm can
  hire given a specified budget
• Isocost indicates equally costly combinations of
  inputs
• Higher isocost lines indicate higher costs
                                                                          27


                   Isocost Lines
  Capital

                                              All capital-labor
C1/r                                          combinations that lie along
                                              a single isocost curve are
            Isocost with Cost Outlay C1
C0/r                                          equally costly. Capital-labor
                                              combinations that lie on a
                Isocost with Cost Outlay C0
                                              higher isocost curve are
                                              more costly. The slope of an
                                              isoquant equals the ratio of
                                              input prices (-w/r).
            C0/w      C1/w       Employment
                                                        28


           Cost Minimization

• Profit maximization implies cost minimization
• The firm chooses a 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 price
  ratio of capital to labor
• MPE/MPκ = w/r
                                                                                 29

The Firm's Optimal Combination
           of Inputs
   Capital
                                                 A firm minimizes the costs of
 C1/r
                                                 producing q0 units of output
             A                                   by using the capital-labor
 C0/r
                                                 combination at point P,
                                                 where the isoquant is tangent
                                                 to the isocost. All other
                       P
 175                                             capital-labor combinations
                                                 (such as those given by
                           B                     points A and B) lie on a
                               q0
                                                 higher isocost curve.
                 100                Employment
                                                     30


   The Firm's Optimal Combination
              of Inputs
• Cost Minimisation therefore requires that marginal
  rate of technical substitution (MPE/MPκ) equal the
  ratio of input prices (w/r)
• MPE/w = MPκ/r
• MPE/w gives the output yield of the last dollar
  spent on labor.
• MPκ/r gives the output yield of the last dollar spend
  on capital.
                                                    31


  The Firm's Optimal Combination
             of Inputs
• Cost Minimisation requires that the last dollar
  spent on labor yield as much output as the last
  dollar spent on capital.
• Since, we constrain the firm to produce qo units of
  output. The firm must produce this level of output
  (qo) in a cost minimizing way in order to maximise
  profits.
                                                      32


The Firm's Optimal Combination
           of Inputs
• Long-run Profit max:

w = P x MPE and r = P x MPK

• Profit –maximizing conditions imply cost
  minimization

• Note that the ratios of the two marginal
  productivity conditions implies that the ratio of
  input prices equals the ratio of marginal
  products
                                                    33

    Long Run Demand for Labor

•    Consider firm producing profit maximising qo
     (qo*: MC = P [MR=P] and

Firm is minimising costs:

(K*,L*: MPE/MPK = w/r)

•    WHAT HAPPENS TO THE FIRM’S LONG
     RUN DEMAND FOR LABOUR WHEN WAGE
     CHANGES?
                                                        34



     Long Run Demand for Labor

•     If the wage rate drops, two effects take place:
    i) Firm takes advantage of the lower price of
         labor by expanding production (scale
         effect)
    Scale Effect- the change in employment and
         output resulting solely from the effect of
         the wage change on the employers’ cost
         outlays
                                                   35



   Long Run Demand for Labor

 (ii) Firm takes advantage of the wage change
   by rearranging its mix of inputs (while
   holding output constant; substitution effect)

• Substitution Effect- the change in employment
  and input mix resulting solely from the change
  in the relative price of labor, output held
  constant
                                                                                                      36
The Impact of A Wage Reduction, Holding
Constant Initial Cost Outlay at Co
  Capital

                                                                 A wage reduction flattens the
                                                                 isocost curve. If the firm were to
C0/r
                                                                 hold the initial cost outlay
                                                                 constant at C0 dollars, the
                                                                 isocost would rotate around C0
                          R
 75              P                                               and the firm would move from
                                                                 point P to point R. A profit-
                                                
                                            q0                   maximizing firm, however, will
                                                                 not generally want to hold the
                                           q0                    cost outlay constant when the
                              Wage is w0
                                                    Wage is w1   wage changes.

            25       40
                                                                                   37
The Impact of a Wage Reduction on the
             Output and
Employment of a Profit-Maximizing Firm
 Dollars                                Capital


                MC0      MC1




 p                                                              R
                                                       P


                                                                           150


                                                                             100
             100        150    Output             25       50       Employment


 •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.
                                                                                                   38


       Substitution and Scale Effects
  Capital
                                                                     A wage cut generates
            D
                                                                     substitution and scale effects.
C1/r
                                                                     The scale effect (the move from
                      Q                                              point P to point Q) encourages
C0/r                                                                 the firm to expand, increasing
                               R
                                                                     the firm’s employment. The
             P                                                       substitution effect (from Q to
                                                  200
                                                                     R) encourages the firm to use a
                                   D
                                                                     more labor-intensive method of
                                                                     production, further increasing
                                            100
                                                                     employment.
                                                        Wage is w1
                               Wage is w0



        25       40       50                                Employment
                                                                            39

   The Short- and Long-Run Demand
          Curves for Labor
Dollars


          Short-Run
          Demand Curve                      In the long run, the firm can
                                            take full advantage of the
                                            economic opportunities
                                            introduced by a change in
                         Long-Run
                         Demand Curve       the wage. As a result, the
                                            long-run demand curve is
                                            more elastic than the short-
                                            run demand curve.
                               Employment
                                                       40


        Elasticity of Substitution


• Intuitively, elasticity of substitution is the
  percentage change in capital to labor (a ratio)
  given a percentage change in the input price
  ratio (wages to real interest)
• %∆K/L%∆w/r
• This is the percentage change in the capital:labor
  ratio given a 1% change in the relative price of
  the inputs
                                                              41


          Elasticity of Substitution

• For eg as the relative price of labour (w/r) increases,
  substitution effect tells us the that K/L ratio increases
  (firm replaces labour with capital)
• Elasticity of substitution measures the curvature of the
  isoquant.
• When two inputs can be substituted at a constant rate
  (MRTS is constant), the two inputs are called perfect
  substitutes ;isoquant is linear: σ = α (infinite)
• The substitution effect is large when the two inputs are
  perfect substitutes
                                                        42


        Elasticity of Substitution
• If σ = 0, there would be no change in the relative
  amounts of K and L when there is a change in the
  relative input prices w/r. The isoquant is right
  angled and therefore inputs are perfect
  complements in production
• There is no substitution effect when the inputs are
  perfect complements (since both inputs are
  required for production)
• If σ = 3, a 1% rise in the relative price of labor
  (w/r) would lead to a 3% rise in the K/L ratio. The
  isoquant is strictly convex and inputs are
  substitutes in production.
                                                                                    43
Isoquants: When inputs are either
   perfect substitutes or perfect
           complements
 Capital                             Capital




100

                     q 0 Isoquant                     q 0 Isoquant
                                     5


                         200 Employment        20                    Employment

 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.
                                                      44


Factor Demand with Many Inputs

• There are many different inputs and categories
  of workers
 ▫ Skilled and unskilled labor
 ▫ Old and young
 ▫ Old and new machines
 What will happen to the demand for unskilled
   labour if the price of skilled labour increases?
                                                       45


  Factor Demand with Many Inputs

• Cross-elasticity of factor demand:
• Gives the percentage change in the demand for
  input i resulting from a 1% change in the price of
  input j

                       % Δ Li
                  ηij=
                       % Δ wj
                                                        46



 Factor Demand with Many Inputs
• ηij > 0 – if the price of unskilled labor (j) rises, the
  employer will consequently use more skilled labor
  (i); inputs i and j are said to be substitutes in
  production
• ηij < 0 – if the price of factor (j) rises, the
  employer would use less of factor (i).
  ▫ two inputs are complements in production
                                                                                              47

The Demand Curve for a Factor of Production
  is Affected by the Prices of Other Inputs
         Price of                                Price of
         input i                                 input i


                          (a)
                                                                        (b)



                                    D1                                      D0
                              D0                                      D1

                             Employment of                           Employment of
                             input i                                 input i


   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.
                                                           48


 Marshall’s Rules –Determinants of
             Elasticity
• Labor Demand is more elastic when:
 ▫ Elasticity of substitution is greater
 ▫ Elasticity of demand for the firm’s output is
   greater
 ▫ The greater labor’s share in total costs of
   production
 ▫ The greater the supply elasticity of other factors of
   production (such as capital)
                                                      49


The Demand for Labor in Non
 competitive Product Market
• What is the logic underlying the equality of VMP
  and MRP where perfect competition prevails in
  the product market?
• Because the competitive firm is a price taker, it
  can sell as many units of output as it desires at
  the market price (= $2). The sale of each
  additional unit of the product adds the product
  price (= $2) to the firm’s total revenue;
• MR = p (constant)
• the extra revenue to the firm from employing an
  additional labor unit (MRP = MR x MP) equals
  the value of the extra output (VMP = p x MP)
                                                       50


The Demand for Labor in Non
competitive Product Market
• Because of product uniqueness or
  differentiation, the imperfectly competitive
  seller’s product demand curve is downward
  sloping rather than perfectly elastic. This means
  that the firm must lower its price to sell the
  output contributed by each successive worker.
• It must lower the price not only on the last unit
  produced but also on all other units which would
  otherwise have commanded a higher price.
• The sale of an extra unit of output therefore does
  not add its full price to the firm’s marginal
  revenue.
                                                       51


The Demand for Labor in Non
competitive Product Market

• Because the marginal revenue is les than the
  product price, the imperfectly competitive sellers
  Marginal Revenue Product is less than that of
  the perfectly competitive seller .
• Recall that perfectly competitive firm suffers no
  decline in marginal revenue as it sells the extra
  output of added workers.
                                                   52

The Demand for Labor in Non
competitive Product Market
• To see how the demand for labor would change if
  the product market is non-competitive, let’s turns
  to an example.
• The MRP or labor demand curve of the purely
  competitive seller falls for a single reason –
  marginal product diminishes as more units of labor
  are employed.
• But the MRP or labor demand of the imperfectly
  competitive seller declines for two reasons –
  marginal product falls as more units of labor are
  employed and product price declines as output
  increases.
                                                   53

The Demand for Labor in Non
competitive Product Market
The lower price accompanying each increase in
 output applies not only to the output produced by
 each additional worker but also to all prior units
 that otherwise could have been sold at a higher
 price.
For example, the 5th worker’s marginal product is 12
 units, and these 12 units can be sold at $2.40 each
 ($28.80).
                                                     54

    The Demand for Labor in Non
     competitive Product Market
• This is the value of VMP- value of added output
  from the society’s perspective. But the MRP of the
  5th worker is only $25.80.
• Why the $3.00 difference? Because in order to sell
  the 12 units associated with the 5th worker, the firm
  must accept a $0.20 price cut on each of the 15 units
  produced by the previous workers – units that could
  have been sold for $2.60 each. Thus, the MRP of the
  5th worker is only ($25.80) [$28.80 – (15x 0.20)].
• So for a firm in non-competitive product market,
  the VMP no longer measures the true worth of the
  marginal worker but the MRP.
                                                   55

    The Demand for Labor in Non
     competitive Product Market

Therefore, for a non competitive seller the
 application of the MRP = w rule to the MRP will
 yield the conclusion that the MRP curve is the
 imperfectly competitive seller’s labour demand
 curve.
                                                        56

     The Demand for Labor in Non
      competitive Product Market
• Comparing the MRP curves, all else being equal, the
  imperfectly competitive sellers labor demand curve is
  less elastic than that of a purely competitive seller.
  Thus a firm that has monopoly power is less
  responsive to wage rate changes.
• This is merely the labor market reflection of the firm’s
  reduction in output in the product market (as
  compared to perfectly competitive seller).
• In producing less output, the seller with monopoly
  power will employ fewer workers.
• Therefore, the marginal revenue accruing to an
  imperfectly competitive seller from hiring an
  additional unit of labor is less then the market value of
  the extra output the unit of labor helps produce [(MRP
  = MR x MP) < (VMP = P x MP).
          57




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