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Labour Market Economics 5e
Labour Market Economics, 5/e
Dwayne Benjamin, University of Toronto
Morley Gunderson, University of Toronto
Craig Riddell, University of British Columbia

Demand for Labour in Competitive Labour Markets

Chapter Notes

Introduction

  • to determine the demand for a particular factor of production, such as labour, we assume that profit-maximizing (or cost-minimizing) firms choose the optimal quantity of the factor to employ given the price of that factor, the price of substitute factors, and the value of output produced by that factor
  • thus, the demand for labour depends on the wage rate, the cost of substitute factors (such as capital), and the value of output produced by labour
    • the demand for labour is a derived demand and depends on the demand for output that labour is used to produce
  • we analyze the demand for labour in the short run and in the long run
    • the short run is defined as a period during which one or more of the factors of production cannot be varied
    • in the long run the firm can adjust all of the factors of production
  • in the following analysis, we assume that there is perfect competition in the labour market; the firm faces a horizontal labour supply curve and can purchase as much labour as it desires at the given wage rate
    • the next chapter considers the interesting case of monopsony in the labour market (where the firm faces an upward-sloping labour supply curve)
    • Chapter 15 considers the case where the firm and a union negotiate a wage-employment contract

The Short-run Demand for Labour

  • assume that the production function Q = f(L,K) describes the technological possibilities facing the firm
    • the maximum amount of output (Q) which can be produced from various quantities of labour (L) and capital (K), given the existing state of technology
  • in the short-run the stock of capital is assumed to be fixed (at Ko)
  • the upper diagram in Figure 5-1 plots the production function Q = f(L,Ko) for a fixed capital stock
    <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_01a_250_182.gif','popWin', 'width=266,height=198,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>  Figure 5-1a
  • output (Q) increases as the amount of labour (L) increases but the Marginal Product of Labour (MPL, the increase in Q when an additional unit of labour is added to the production process) decreases as more labour is added to the production process
    • hiring more labour is subject to diminishing marginal returns as each additional worker is not provided with additional capital equipment and thus has a lower productivity level
    • the marginal product of labour is the slope (first derivative) of the production function
      • diminishing marginal returns implies that the first derivative of the production function is positive and the second derivative is negative; as the firm moves up the production function the positive slope decreases in value
  • the lower diagram in Figure 5-1 plots the value of the marginal physical product of labour (VMPL)
    <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_01b_250_178.gif','popWin', 'width=266,height=194,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>  Figure 5-1b
  • if the output market is characterized by perfect competition, then the firm is a price taker and can sell additional units of output at the given market price (P)
    • if perfect competition exists in the product market, VMPL = P*MPL
  • the VMPL will decline as more labour is hired because of diminishing returns to hiring labour (the MPL declines as more L is added to the production process)
  • the profit-maximizing firm will continue to operate as long as it can cover the variable costs of production (such as the wage rate paid to labour)
    • as we shall see in the next chapter, the demand for labour will also be affected by labour costs which are independent of the number of hours worked by labour (quasi-fixed labour costs)
  • thus, the profit-maximizing firm will keep adding additional units of labour to the production process as long as the value of the marginal product of labour (VMPL) is greater than the marginal cost of hiring labour (which is the wage rate W)
  • in the short run a profit-maximizing firm will keep hiring additional units of labour up to the point where VMPL = W
    • for the given wage rate Wo in Figure 5-1, the profit-maximizing firm will hire Lo units of labour
  • the VMPL is the short-run demand for labour and identifies the quantity of labour demanded at various wage rates
    • if the market wage rate increases from Wo to W1, then the profit-maximizing firm will reduce the quantity of labour demanded from Lo to L1
    • the short-run demand for labour slopes down because of diminishing returns (a declining MPL) to hiring more labour
  • in the short-run, the quantity of labour demanded depends on the wage rate (W), the price of output (P) and the marginal productivity of labour (MPL); thus, in the short run labour demand depends on the real wage rate (W/P) and the (the first derivative of the) production function
  • an increase in the price of output or an increase in the marginal productivity of labour (say from technological progress) will shift the short-run demand for labour curve to the right
  • in a non-competitive product market (for example, a monopoly), the demand for labour curve also depends on the price elasticity of the demand for output
    • given a downward-sloping product demand (average revenue) curve, the demand for labour depends on the Marginal Revenue (MR) from selling an additional unit of output and the Marginal Product of Labour (MPL)
    • for a non-competitive product market, the demand for labour curve is given by the Marginal Revenue Product of Labour (MRPL) curve, where MRPL = MR*MPL
    • compared to a perfectly competitive firm, the demand for labour curve for a non-competitive firm, such as a monopolist, will be steeper
      • since the MR declines as output increases, an increase in the quantity of labour causes both the MPL and the MR to decline (making the labour demand curve steeper)

The Long-run Demand for Labour

  • in the long run, the profit-maximizing firm can vary the inputs of both labour (L) and capital (K)
    • we assume that there are diminishing marginal returns to adding more units of K (holding L constant) and to adding more units of L (holding K constant)
      • we assume that the first derivatives of Q = f(L, K) are positive and the second derivatives are negative
  • an isoquant-isocost diagram can be used [i] to determine the optimal combination of L and K and [ii] to derive the demand for labour when K is a variable input into the production process

Isoquants

  • each isoquant depicts the various combinations of L and K which can be used to produce a particular level of output, say Qo in Figure 5-2
    • isoquants depicting larger quantities of output (such as Q1 in Figure 5-2) will be further from the origin (they require greater quantities of inputs)
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_02_250_191.gif','popWin', 'width=266,height=207,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a>  Figure 5-2
  • the shape of the isoquant reflects the technological possibilities for substituting L and K in the production process
  • isoquants are convex to the origin
    • the slope of the isoquant is equal to MPL/MPK, where MPL is the marginal product of labour and MPK is the marginal product of capital
    • given diminishing returns to hiring each factor, the slope of the isoquant exhibits a diminishing marginal rate of technical substitution between L and K
      • larger and larger amounts of L must be substituted for each unit of K as the amount of K used in the production process decreases

Isocost Lines

  • assume that factor prices are given: 'W' is the wage paid to labour and 'r' is the implicit (rental) cost of using capital
  • for a given COST outlay, a firm can purchase different quantities of L and K according to the following equation:
    COST = WL + rK,
  • an isocost line depicts the various quantities of L and K which can be purchased for a particular COST outlay
  • re-arranging the COST equation produces the following equation for an isocost line:
    K = COST/r – (W/r)L
  • as shown in Figure 5-2, the slope of the solid isocost line is – (W/r), the horizontal intercept is COST/W and the vertical intercept is COST/r
  • the greater the COST outlay, the further the isocost line will be from the origin (more of both L and K can be purchased)
    • in Figure 5-2, the dashed isocost line has a higher cost outlay than the solid isocost line; the dashed isocost line is parallel to the solid isocost line (both isocost lines have slope –W/r)

The Optimal Quantities of L and K

  • a profit-maximizing firm will choose the least cost combination of L and K to produce a particular level of output, such as Qo
  • the least cost factor input combination will be determined by the tangency of an isocost line with the Qo isoquant
    • the closer the isocost line to the origin, the smaller the cost
  • as shown in Figure 5-2, the optimal tangency position is given by point Eo
    • given factor prices (W, r), the optimal combination of inputs to produce Qo is Lo and Ko
  • at this optimal tangency point, the slope (W/r) of the isocost line is equal to the MPL/MPK slope of the isoquant
    • the ratio of factor marginal products is equal to relative factor prices; the firm's internal rate of factor substitution is equal to the rate at which the factors can be substituted in the market place
  • to summarize, in the short run the firm hires labour up to the point where the VMPL (of MRPL) is equal to the wage rate and in the long run the firm hires labour up to the point where the relative value of the MPL (in terms of the MPK) is equal to the relative price of labour (W/r)

Deriving the Long-run Demand for Labour

  • as illustrated in Figure 5-3, the long-run demand for labour can be derived by determining the optimal combination of L and K for different wage rates, holding the cost of capital (r) constant
    <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_03a_300_242.gif','popWin', 'width=316,height=258,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (8.0K)</a>  Figure 5-3a
    <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_03b_300_282.gif','popWin', 'width=316,height=298,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (5.0K)</a>  Figure 5-3b
  • given a wage rate Wo the firm maximizes profits at point A
    • in the upper diagram, the GF isocost line (with slope Wo/r) is tangent to the Qa isoquant at point A
      • the firm uses La units of labour and Ka units of capital to produce Qa units of output
    • in the lower diagram, in the long run the firm hires La unit of labour when the wage rate is Wo; point A is one point on the long-run demand for labour
  • now suppose that the wage rate increases to W1
    • the GF isocost line will rotate inwards to the dashed line GH (the horizontal intercept COST/W1 is now located closer to the origin) and the new set of dashed isocost lines will be steeper (with slope W1/r)
    • an increase in the wage rate also shifts firms' marginal cost curves upwards, resulting in higher output prices and a lower level of output demanded (say Qb) in the product market
      • as discussed below, the reduction in output depends on the price elasticity of the product demand curve
    • the firm now minimizes costs at point B in the upper diagram of Figure 5-3, where a dashed isocost line with slope W1/r is tangent to the lower Qb isoquant
    • the increase in wage rates from Wo to W1 has resulted in a decrease in the amount of labour (from La to Lb) and an increase in the amount of capital (from Ka to Kb) used in the production process
    • in the lower diagram, the firm hires Lb units of labour when the wage rate is W1 (holding the cost of capital constant)
      • point B is a second point on the long-run demand for labour
  • an increase in the wage rate (from Wo to W1 in Figure 5-3) reduces the long-run demand for labour (from La to Lb)
  • the reduction in the demand for labour from an increase in wage rates can be broken down into a substitution effect and a scale effect
  • the substitution effect measures the effect of a change in an input price on the amount of inputs used to produce a given output level (say Qa)
    • in Figure 5-3 the pure substitution effect from an increase in the wage rate from Wo to W1 is represented by the movement from point A to C
    • to produce the same output level Qa at the higher wage rate W1, the profit-maximizing firm will use less labour (Lc) and more capital
    • an increase in wage rates from Wo to W1 has a pure (output constant) substitution effect equal to La minus Lc
  • the scale effect measures the effect of a change in output levels (the scale of operation) on the amount of inputs used, holding input prices constant
    • in Figure 5-3 the scale effect is represented by the movement from point C to B
    • holding input prices constant, a reduction in output from Qa to Qb results in less labour (Lb) and less capital used in the production process
    • an increase in wage rates from Wo to W1 has a scale effect equal to Lc minus Lb
  • both the substitution and scale effects reduce the quantity of labour demanded when the wage rate increases; the long-run labour demand curve unambiguously slopes down
  • since there is no substitution effect possible in the short run (with a fixed capital stock), the short-run demand for labour will be steeper than the long-run demand for labour
    • in the long run, the firm can respond to an increase in wage rates by substituting capital for labour and thus the long-run effect on the quantity of labour demanded for a given change in the wage rate will be larger than the short-run effect

Factors Affecting the Elasticity of the Long-run Demand for Labour

  • workers (and their unions) are keenly interested in the elasticity of labour demand
    • if the labour demand curve is very inelastic (steep), an increase in wages will have a very small negative effect on the quantity of labour employed (the number of jobs) and will have a very large positive effect on total labour income
  • the elasticity of the labour demand curve depends on the size of the substitution and scale effects

The degree of substitution possible between labour and capital

  • as shown in the upper diagram in Figure 5-4, if the production process permits a high degree of substitution between the factors of production, the isoquant will not exhibit much curvature
    • a wide range of L,K combinations can produce Qo in the upper diagram
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_04a_250_209.gif','popWin', 'width=266,height=225,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>  Figure 5-4a
  • on the other hand, if the production process does not permit much substitution between the factors of production, the isoquant will be more angular (see the isoquant in the lower part of Figure 5-4)
    • if no L, K substitution is possible, the isoquant would be L-shaped (have a 90 degree angle); the production of output requires a fixed amount of L and a fixed amount of K
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif:: ::/sites/dl/free/0070891540/43154/benjamin_05_04b_250_188.gif','popWin', 'width=266,height=204,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>  Figure 5-4b
  • an increase in the wage rate increases the slope of the isocost line; the dashed isocost line in both diagrams represents an increase in the wage rate (compared to the solid isocost line)
  • in the upper part of Figure 5-4, the substitution effect (A to B) is very large; an increase in the wage rate results in a very large substitution of K for L in the production process and a very large reduction in the quantity of labour demanded
  • in the lower part of Figure 5-4, the substitution effect (A to B) is very small; an increase in the wage rate results in very little substitution of K for L in the production process and a very small reduction in the quantity of labour demanded
  • the greater the degree of substitution possible between L and K, the flatter (less steep) the labour demand curve and the greater the wage elasticity of the long-run demand for labour curve
  • while the degree of factor substitution largely depends on the state of technology, workers and their unions try to reduce the degree of K – L substitution (to obtain a more inelastic labour demand schedule)
    • workers typically resist the implementation of new labour-saving technology; for example, 19th century Luddites destroyed textile machinery and 20th century auto workers, worried about robotics and out-sourcing of intermediate goods, shut down General Motors for a prolonged period of time in 1998
    • unions try to negotiate contracts which 'lock-in' a fixed K/L ratio or a fixed Q/L ratio, and thus limit the employer's flexibility to substitute K for L; for example, automobile workers want to regulate the speed of the assembly line and teacher unions want to limit class size

The price elasticity of the demand for output

  • since labour demand is a derived demand, the wage elasticity of the demand for labour depends on the price elasticity of the demand for output
  • the scale effect in the derivation of the demand for labour depends on the price elasticity of the demand for output in the product market
  • an increase in the wage rate causes a firm's marginal cost curve to rise and equilibrium will occur at a higher point on the product demand curve
  • if the product demand curve is very inelastic (steep), there will be a very small reduction in output and a very small-scale effect on labour demand
  • on the other hand, if the product demand curve is very elastic (flatter), there will be a very large reduction in output and a very large-scale effect on labour demand
  • the greater the price elasticity of the demand for output, the larger the scale effect, and the greater the elasticity of the labour demand curve
  • again workers and their unions are interested in promoting policies which make the product demand curve more inelastic (and therefore make the labour demand curve steeper and more inelastic)
    • the labour movement was strongly opposed to the signing of a Free Trade Agreement (FTA) with United States and Mexico; a FTA permits the importation of foreign substitute products without tariffs or quotas, thus making the domestic product demand curve and the labour demand curve more elastic
    • protectionist policies, such as buy Canadian, make both the product demand curve and the labour demand curve more inelastic, which allows a union to negotiate larger wage settlements without risking many jobs

The ratio of labour costs to total costs

  • if the ratio of labour costs to total costs is very low, then an increase in the wage rate will have a very small effect on total costs and thus have a very small scale effect
  • thus, the labour demand curve tends to be very inelastic when labour costs are a small share of total costs (the importance of being unimportant)

Summary

  • in the long run the labour demand curve will be inelastic (1) if there is a low degree of substitution possible between labour and other inputs, (2) if the product demand curve is price inelastic, and/or (3) labour costs are a small share of total costs
  • the wage elasticity of labour demand will vary from occupation to occupation depending on the relative magnitude of these three factors
    • for example, the demand for airline pilots is likely very inelastic; there is little possibility of substituting K for L and pilot salaries are a very small share of total costs (prior to de-regulation and 'open skies' policies, the demand for airline services was also very price inelastic)
    • on the other hand, the demand for garment workers may be very elastic; with the signing of the FTA the product demand curve has become more price elastic and there is a high degree of K,L substitution possible
  • thus, some labour groups will be able to exploit a very inelastic labour demand curve to obtain large wage increases (without fear of job loss), while other labour groups facing a very elastic labour demand curve will be fearful of losing jobs if they push for higher wages
  • as discussed in Chapter 7, in a competitive labour market the employment effects following an increase in the minimum wage also depend on the elasticity of the labour demand curve
  • econometric evidence (reviewed on pages 156-7 in the textbook) suggests that the wage elasticity of labour demand likely lies between – 1/4 and – 3/4; in other words, a 10% increase in the wage rate likely results in a 2.5% to 7.5% decrease in employment
  • the final section of Chapter 7 examines changing labour demand conditions and global competition
    • employment in Canada depends on labour productivity and labour costs in Canada compared to labour productivity and labour costs in the rest of the world
    • in considering the effects of globalization and free trade on a country's labour demand, the appropriate cross-country comparison is unit labour costs (the wage rate divided by labour productivity) expressed in a common currency
      • international competitiveness depends on relative wage rates, relative productivity rates, and the foreign exchange rate




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