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Chapter 5: Demand for Labour in Competitive Labour Markets
Introduction
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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
o 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
o the short run is defined as a period during which one or more of the factors of
production cannot be varied
o 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
o the next chapter considers the interesting case of monopsony in the labour
market (where the firm faces an upward-sloping labour supply curve)
o Chapter 15 considers the case where the firm and a union negotiate a wageemployment contract
The Short-Run Demand for Labour
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assume that the production function Q = f(L,K) describes the technological possibilities
facing the firm
o 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
o please note that in the textbook (see for example, equation 5.1 on page 153),
the abbreviation N is used for labour instead of L since L is most often used to
denote leisure; thus consider MPPN in the textbook equivalent to MPL in the
discussion below
in the short-run the stock of capital is assumed to be fixed (at Ko)
the upper diagram in Figure 5a plots the production function Q = f(L,Ko) for a fixed
capital stock
Figure 5a
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output (Q) increases as the amount of labour (L) increases but the Marginal Physical
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
(note that it is conventional that Marginal Product of Labour is frequently used
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synonymously with Marginal Physical Product of labour; you will notice that below as
well as in the textbook)
o 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
o 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
Figure 5b plots the value of the marginal physical product of labour (VMPL)
o Note that because the VMPL is an equivalent term for the marginal revenue
product of labour when the product or output market is perfectly competitive
(see page 155)
Figure 5b
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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)
o 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)
o 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
o for the given wage rate Wo in Figure 5b, 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
o 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
o 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 physical product of labour (MPL); thus, in the
short run labour demand depends on the real wage rate (W/P) and the (first derivative
of the) production function
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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
o 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)
o 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
o 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
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in the long run, the profit-maximizing firm can vary the inputs of both labour (L) and
capital (K)
o 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, (1) to determine the optimal combination of
L and K, and (2) to derive the demand for labour when K is a variable input into the
production process
Isoquants
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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 5c
o isoquants depicting larger quantities of output (such as Q1 in Figure 5c) will be
further from the origin (they require greater quantities of inputs)
Figure 5c
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the shape of the isoquant reflects the technological possibilities for substituting L and
K in the production process
isoquants are convex to the origin
o 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
o given diminishing returns to hiring each factor, the slope of the isoquant
exhibits a diminishing marginal rate of technical substitution between L and K
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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
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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 5c, 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)
o in Figure 5c, 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
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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
o the closer the isocost line to the origin, the smaller the cost
as shown in Figure 5c, the optimal tangency position is given by point Eo
o 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
o 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
(which is often instead referred to as the marginal revenue product of labour) 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
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as illustrated in Figure 5d and 5e, 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
Figure 5d
Figure 5e
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given a wage rate Wo the firm maximizes profits at point A
o 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
o 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
o 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)
o 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
o the firm now minimizes costs at point B in the Figure 5d, 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
o 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 5d) 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)
o in Figure 5d 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
o to produce the same output level Qa at the higher wage rate W1, the profitmaximizing firm will use less labour (Lc) and more capital
o 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
o in Figure 5d the scale effect is represented by the movement from point C to B
o 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
o 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
o 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
o
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Factors Affecting the Elasticity of the Long-Run Demand for Labour
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workers (and their unions) are keenly interested in the elasticity of labour demand
o 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; if the elasticity is between 0 and -1, the demand curve is termed
inelastic, implying that the percentage increase in wages is larger than the
percentage decrease in employment
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
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as shown in the upper diagram in Figure 5f, if the production process permits a high
degree of substitution between the factors of production, the isoquant will not exhibit
much curvature
o a wide range of L,K combinations can produce Qo in the upper diagram
Figure 5f
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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 5g)
o 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
Figure 5g
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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 Figure 5f, 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 Figure 5g, 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)
o 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
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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 Elasticity of Supply of Substitute Inputs
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the substitution of alternative inputs can be affected the changes in price of these
inputs
if the substitutes are relatively inelastic in supply, so that an increase in the demand
for the inputs will lead to an increase in their price, then this price increase may chock
off some of the increased usage of the substitutes
o for example, consider the use of unskilled workers as substitutes for skilled
labour; if the wages of unskilled workers rose rapidly with an increase in
demand (this would correspond to relatively inelastic labour supply), then this
would limit the use of unskilled workers as substitutes
The Price Elasticity of the Demand for Output
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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)
o 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
o 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
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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
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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 substitutes are relatively
inelastic in supply (i.e., quantity of labour supplied is unresponsive to changes in their
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wage rate), (3) if the product demand curve is price inelastic, and/or (4) if 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
o 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)
o 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 168-9 in the textbook) suggests that the
wage elasticity of labour demand likely lies between – 0.15¾ and -0.75; in other
words, a 10% increase in the wage rate likely results in a 1.5% to 7.5% decrease in
employment
the final section of Chapter 5 examines changing labour demand conditions, global
competition, and outsourcing
o 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
o in considering the effects of globalization and outsourcing 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