Chapter 3 Chapter 3 The Demand For Labor The Demand For Labor
Chapter 3
Jan 03, 2016
Chapter 3. The Demand For Labor. Objectives. Consumers maximize utility subject to a budget constraint Firms maximize profits subject to cost and production constraints. Two types of demand to consider:. Consumer’s demand for goods and services derived from utility maximization - PowerPoint PPT Presentation
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Chapter 3Chapter 3
The Demand For LaborThe Demand For Labor
ObjectivesObjectives
Consumers
• maximize utility subject to a budget constraint
Firms
• maximize profits subject to cost and production constraints
Two types of demand to consider:Two types of demand to consider:Consumer’s demand for goods and services
• derived from utility maximization
Firm’s demand for inputs (labor, capital)
• derived from profit maximization
We will make the following We will make the following assumptions:assumptions:
• All firms wish to maximize profits.• Firms employ only two homogeneous
inputs - Capital (K) and Labor (L).• The only cost of labor is the hourly wage
(W)• The only cost of capital is the hourly
rental cost (C)• Perfectly competitive labor and product
markets
What rule do firms follow What rule do firms follow to maximize profits?to maximize profits?
Marginal Revenue = Marginal CostMarginal Revenue = Marginal Cost
MR = MCMR = MC
Why?Why?
Suppose that MR > MC. What should the firm do?
• The firm should expand output because the unit is worth more to the firm (in terms of additional revenue) than it costs the firm to produce
Suppose that MC > MR. What should the firm do?
• The firm should reduce output because the last unit cost the firm more to produce than it is worth (in terms of additional revenue)
Since a firm can only expand Since a firm can only expand or contract output by or contract output by
changing its level of inputs, changing its level of inputs, we can think of the profit-we can think of the profit-maximization decision in maximization decision in terms of employment of terms of employment of
inputs:inputs:
• If the revenue generated by hiring an additional unit of an input > additional expense of hiring that unit, the firm should add that unit (because it will increase profit)
• If the revenue generated by hiring an additional unit of an input < additional expense of hiring that unit, the firm should reduce employment of that input (because that unit will decrease profit)
• If the revenue generated by hiring an additional unit of an input = additional expense of hiring that unit, no further changes in that input should be made (profits are maximized)
Short-Run Demand for Short-Run Demand for LaborLabor
Let’s do an example:Let’s do an example:
The Short-Run Demand for Labor The Short-Run Demand for Labor When When BothBoth the Product Market the Product Market
and the Labor Market Are and the Labor Market Are Perfectly CompetitivePerfectly Competitive
Definition of the Short-Run:Definition of the Short-Run:
• Capital is fixed at K*
• Note that the length of the short-run will vary across different firms
What happens to output as we What happens to output as we add more labor?add more labor?
• Marginal Product of Labor
• MPL = Q/L
Suppose we are running an apple Suppose we are running an apple farmfarm
• Two inputs: capital (fixed at K*) and labor
• Apples sell in a competitive market for $4/bushel
• We hire apple pickers in a competitive labor market for $8/hour (This implies that the Marginal Expense [MEL] of hiring a worker is equal to $8.)
• HOW MANY WORKERS DO WE HIRE?
Output for Apple FarmOutput for Apple Farm
L (#pickers) Q (bushels/hour)
0 0
1 7
2 12
3 15
4 17
5 18
Measuring Output of LaborMeasuring Output of Labor
L Q
0 0
1 7
2 12
3 15
4 17
5 18
MPL
----
7
5
3
2
1
Law of Diminishing Marginal ReturnsLaw of Diminishing Marginal Returns
• after some point, each additional unit of labor will result in smaller increases in output
• eventually, marginal product can become negative (implying that hiring an additional unit of input will result in a decrease in output)
• this is true for any input in the short-run (because at least one other input is fixed)
How much is that How much is that additional output worth?additional output worth?
We need to include information on We need to include information on the price of apples.the price of apples.
Valuing Output of LaborValuing Output of Labor
L Q MPL P
0 0 ---- 4
1 7 7 4
2 12 5 4
3 15 3 4
4 17 2 4
5 18 1 4
We can use information on MPWe can use information on MPLL
and P to calculate the Marginal and P to calculate the Marginal Revenue Product of Labor (MRPRevenue Product of Labor (MRPLL))
• MRPL is the additional revenue a firm earns by hiring an additional unit of labor
• MRPL = MPL X MR (general case)
• MRPL = MPL X P (competitive output market)
Valuing Output of LaborValuing Output of Labor
L Q MPL P
0 0 ---- 4
1 7 7 4
2 12 5 4
3 15 3 4
4 17 2 4
5 18 1 4
MRPL
----
28
20
12
8
4
So, how many workers would we hire So, how many workers would we hire if we have to pay them a wage of if we have to pay them a wage of
$8/hour?$8/hour?
L Q
0 0
1 7
2 12
3 15
4 17
5 18
MPL P MRPL
---- 4 ----
7 4 28
5 4 20
3 4 12
2 4 8
1 4 4
We would hire workers up to the We would hire workers up to the point where the last worker point where the last worker adds nothing to profits.adds nothing to profits.
• That is where the additional revenue from hiring that worker equals the addition to total costs (“expense”) of hiring him/her
• The firm hires workers to the point where MRPL = MEL
MRPL = MEL
Since the labor market is competitive (in our example):
• MEL = w
Since the product market is competitive (in our example):
• MRPL = P * MPL
MRPL = MEL is the same thing as
MRPL = w which is the same thing as
P X MPL = w
Dividing both sides by P, we get:
MPL = w/P
Thus, we can express the profit-maximization decision in terms of the nominal wage:
MRPL = w
Or in terms of the real wage:
MPL = w/P
Let’s do another example: Let’s do another example:
Competitive firm producing ping-pong balls Competitive firm producing ping-pong balls that sell for $0.50 each. Hourly output:that sell for $0.50 each. Hourly output:
K* L Q
10 0 0
10 1 14
10 2 46
10 3 84
10 4 116
10 5 130
10 6 140
Let’s calculate MPLet’s calculate MPLL::
K* L Q
10 0 0
10 1 14
10 2 46
10 3 84
10 4 116
10 5 130
10 6 140
MPL
----
14
32
38
32
14
10
Now, let’s calculate MRPNow, let’s calculate MRPLL. We need to . We need to
include information on price:include information on price:
K* L Q MPL
10 0 0 ----
10 1 14 14
10 2 46 32
10 3 84 38
10 4 116 32
10 5 130 14
10 6 140 10
P MRPL
0.50 ----
0.50 7
0.50 16
0.50 19
0.50 16
0.50 7
0.50 5
If the wage is $7/hour, how many workers If the wage is $7/hour, how many workers do we hire?do we hire?
K* L Q MPL
10 0 0 ----
10 1 14 14
10 2 46 32
10 3 84 38
10 4 116 32
10 5 130 14
10 6 140 10
P MRPL
0.50 ----
0.50 7
0.50 16
0.50 19
0.50 16
0.50 7
0.50 5
Let’s graph MRPLet’s graph MRPLL::
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6
The firm’s demand for The firm’s demand for labor curve is the labor curve is the
downward sloping portion downward sloping portion of the MRPof the MRPLL curve. curve.
The market demand for The market demand for labor is a horizontal labor is a horizontal
summation of the firms’ summation of the firms’ demand for labor.demand for labor.
MonopolyMonopoly
• What happens to the firm’s short-run labor demand when the firm is a monopoly in its output market?
A monopoly has the same goal A monopoly has the same goal as a competitive firm. It wishes as a competitive firm. It wishes
to maximize profit.to maximize profit.
• However, P MR (indeed, MR < P at all output rates except Q=1)
• This means that we must use the general formula to calculate MRPL.
MRPL = MR X MPL
For a monopoly, MR always lies For a monopoly, MR always lies below P. below P.
D
MR
P
Q
The rule to find the profit-maximizing The rule to find the profit-maximizing level of labor hired is the same for level of labor hired is the same for allall firms (whether the product market firms (whether the product market perfectly competitive or not):perfectly competitive or not):
• Hire labor up to the point where MRPL = w
For a monopolist: MR X MPL = w
For a competitive firm: P X MPL = w
Since MR < P for a monopolist:Since MR < P for a monopolist:
• MRPL for a monopolist will be lower than MRPL for a competitive firm
• this implies that the monopolist’s demand for labor would lie below (or to the left) of the competitive firm’s demand for labor
Since the labor demand Since the labor demand curve for a monopolist lies curve for a monopolist lies below and to the left of the below and to the left of the labor demand curve for a labor demand curve for a
competitive firm, then competitive firm, then at any at any given wage the monopolist given wage the monopolist will hire less labor than the will hire less labor than the
competitive firm.competitive firm.
Therefore, just as output Therefore, just as output is lower for a monopolist, is lower for a monopolist,
so is the level of so is the level of employment.employment.
Let’s do an example:Let’s do an example:
• Suppose we own the only pizzeria in town
• Thus, we face the market demand curve for pizza (which is downward-sloping)
• We do, however, hire labor in a competitive labor market
• Let’s see how we would decide how many workers to hire
Output per day as the amount of Output per day as the amount of labor varies:labor varies:
L Q
0 0
1 45
2 75
3 95
4 102
5 105
6 106
Let’s calculate MPLet’s calculate MPLL::
L Q
0 0
1 45
2 75
3 95
4 102
5 105
6 106
MPL
----
45
30
20
7
3
1
Now let’s add information and Now let’s add information and calculate MR:calculate MR:
L Q MPL
0 0 ----
1 45 45
2 75 30
3 95 20
4 102 7
5 105 3
6 106 1
P TR MR
---- ---- ----
4.75 213.75 4.75
4.50 337.50 4.13
4.30 408.50 3.55
4.15 423.30 2.11
4.05 425.25 0.67
4.00 424.00 -1.25
Now let’s calculate MRPNow let’s calculate MRPLL::
L Q MPL P TR MR
0 0 ---- ---- ---- ----
1 45 45 4.75 213.75 4.75
2 75 30 4.50 337.50 4.13
3 95 20 4.30 408.50 3.55
4 102 7 4.15 423.30 2.11
5 105 3 4.05 425.25 0.67
6 106 1 4.00 424.00 -1.25
MRPL
----
213.75
123.90
71.00
14.77
2.00
-1.25
Again, we should be able to determine Again, we should be able to determine how many workers we would hire at how many workers we would hire at
different values of the daily wagedifferent values of the daily wageL Q MPL P TR MR
0 0 ---- ---- ---- ----
1 45 45 4.75 213.75 4.75
2 75 30 4.50 337.50 4.13
3 95 20 4.30 408.50 3.55
4 102 7 4.15 423.30 2.11
5 105 3 4.05 425.25 0.67
6 106 1 4.00 424.00 -1.25
MRPL
----
213.75
123.90
71.00
14.77
2.00
-1.25
So far, we have been assuming So far, we have been assuming that the that the labor marketlabor market is is
competitive. But, what if it is not?competitive. But, what if it is not?
• Remember that profit-maximization requires the firm to hire labor until MRPL = MEL
• We have used the rule: MRPL = w because we have assumed a perfectly competitive labor market (MEL = w).
MONOPSONYMONOPSONY
• exists when only one firm is the buyer of labor in a particular market
• Some examples may include coal mining and nursing
If the firm is the only buyer of labor, it If the firm is the only buyer of labor, it faces the entire labor supply curve.faces the entire labor supply curve.• No longer can the firm hire all of the labor it
chooses at the going market wage• Since the market labor supply curve is
upward-sloping, the firm must raise the wage to hire additional workers
• Thus, when hiring an additional worker, labor costs rise in 2 parts: (a) the additional worker’s wages and (b) the increase in wages paid to all workers
Let’s do an example:Let’s do an example:
Suppose we are running a coal Suppose we are running a coal mine which is the major employer mine which is the major employer
of the regionof the region
The table below shows how wages paid The table below shows how wages paid (per day) increase as the firm hires (per day) increase as the firm hires
additional workersadditional workers
L w
100 40
101 41
102 42
103 43
104 44
105 45
106 46
Let’s calculate Total Expenditure on Let’s calculate Total Expenditure on Labor (TELabor (TELL = w X L) = w X L)
L w
100 40
101 41
102 42
103 43
104 44
105 45
106 46
TEL
4000
4141
4284
4429
4576
4725
4876
Now, let’s calculate MENow, let’s calculate MELL::
L w TEL
100 40 4000
101 41 4141
102 42 4284
103 43 4429
104 44 4576
105 45 4725
106 46 4876
MEL
----
141
143
145
147
149
151
Note that MENote that MELL > w at every level > w at every level
of labor (for L>1)of labor (for L>1)
• This implies that when we graph MEL , it will lie above the labor supply curve
• Let’s draw a graph showing a monopsony:
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
To maximize profit, the firm sets To maximize profit, the firm sets MRPMRPLL = ME = MELL to find the quantity to find the quantity
of labor they should hire. The of labor they should hire. The wage rate that the firm must wage rate that the firm must
pay can be found by following pay can be found by following the quantity of labor hired up to the quantity of labor hired up to
the supply curve.the supply curve.
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Thus a monopsony hires Thus a monopsony hires less labor than firms in a less labor than firms in a competitive labor market competitive labor market and pays a lower wage.and pays a lower wage.
Monopsony and Monopsony and MinimumWage LawsMinimumWage Laws
Suppose the government Suppose the government sets the minimum wage at sets the minimum wage at
$10/hr. How will the $10/hr. How will the monopsony react?monopsony react?
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Minimum Wage
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Minimum Wage
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Minimum Wage
Let’s try another example Let’s try another example where the minimum wage where the minimum wage
is set at $8/hr:is set at $8/hr:
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Minimum Wage
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Minimum Wage
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D = MRPL
MEL
Minimum Wage
The government was able to The government was able to force the monopsony to act as force the monopsony to act as
if it were operating in a if it were operating in a competitive labor market by competitive labor market by setting the minimum wage setting the minimum wage equal to the competitive equal to the competitive
market wage!market wage!
Long-Run Demand for Long-Run Demand for LaborLabor
In the long-run, employers can In the long-run, employers can vary vary bothboth capital and labor. capital and labor.
• This implies that changes in wages will bring about both a scale effect and a substitution effect.
• Suppose a firm is currently maximizing profit. This means that MR = MC.
• An increase in the wage raises MC without affecting MR ( MR < MC).
• THE FIRM IS LOSING MONEY ON THE LAST UNITS PRODUCED.
• It can increase its profits by cutting back on production . This implies SCALING DOWN and reducing both K and L.
• A SUBSTITUTION EFFECT also occurs.
• To maximize profits, the firm must minimize costs to produce whatever level of output it produces.
• This occurs when the last dollar the firm spends employing capital yields the same increment to output as the last dollar spent on labor
• This is sometimes referred to as the equi-marginal principle
Remember that C is the Remember that C is the rental rate of capital.rental rate of capital.
The firm will hire levels of The firm will hire levels of K and L so that: K and L so that:
MPMPLL/w = MP/w = MPKK/C/C
What happens when the What happens when the wage rises? How does the wage rises? How does the
firm adjust so that it firm adjust so that it returns to this equality?returns to this equality?
When the wage increases:When the wage increases:
• In the short-run the firm will cut back on labor hired.
• In the long-run, the firms will cut back on output (scale effect). This means lowering the level of both K and L.
• As L falls, MPL rises. As K falls, MPK rises. (But, keep in mind that MPL and MPK will both also be affected by the drop in each other.)
Eventually, the firm will keep adjusting K and L until the equi-marginal principle is satisfied.
We have been assuming that We have been assuming that there are only two inputs in there are only two inputs in
the production process (K and the production process (K and L). What if there are more L). What if there are more
than two?than two?
When more than two inputs When more than two inputs are used in production then are used in production then
the inputs may be either the inputs may be either gross complementsgross complements or or
gross substitutesgross substitutes..
Inputs are Inputs are gross substitutesgross substitutes when the increase in the when the increase in the
price of one input increases price of one input increases the demand for the other the demand for the other
input, for example:input, for example:
Price of backhoes Price of backhoes Demand for shovels Demand for shovels
Inputs are Inputs are gross gross complementscomplements when an when an
increase in the price of one increase in the price of one input results in a decrease in input results in a decrease in
the demand for the other the demand for the other input, for example:input, for example:
Price of computers Price of computers Demand for computer Demand for computer operators operators
Keep in mind that labor Keep in mind that labor can be divided into two can be divided into two
categories -- Skilled and categories -- Skilled and Unskilled.Unskilled.
Policy Application: Policy Application: Incidence of a Payroll TaxIncidence of a Payroll Tax
We are going to once again We are going to once again assume that the labor market is assume that the labor market is
perfectly competitive.perfectly competitive.
The incidence of the The incidence of the payroll tax is unaffected by payroll tax is unaffected by whether the tax is placed whether the tax is placed
on the employer or on the employer or whether it is placed on the whether it is placed on the
employee.employee.
Example One: Payroll Example One: Payroll Tax Placed on EmployersTax Placed on Employers
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
Demand shifts down by $2
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
Demand shifts down by $2
wr
wp
Example Two: Payroll Tax Example Two: Payroll Tax Placed on EmployeesPlaced on Employees
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
Supply decreases by $2
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
Supply decreases by $2
wp
wr
It does not matter who the It does not matter who the tax is placed on!tax is placed on!
Employers end up paying the Employers end up paying the same amount and employees same amount and employees
end up receiving the same end up receiving the same amount.amount.
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
Tax on employers: Supply decreases by $2
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
Tax on Employees: Demand shifts down by $2
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W S
D
wp
wr
More inelastic supply or More inelastic supply or more elastic demand more elastic demand implies the higher the implies the higher the
incidence of a payroll tax on incidence of a payroll tax on the worker.the worker.
The opposite would be true if we were The opposite would be true if we were concerned with the incidence of the tax on concerned with the incidence of the tax on
the employer.the employer.
Let’s look at elasticity of Let’s look at elasticity of demand first.demand first.
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W
DE
DI
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W
DE
DI
S0
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W
DE
DI
S0S1
$3 tax paid by employees
0
2
4
6
8
10
12
14
16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15L
W
DE
DI
S0S1
$3 tax paid by employees
wr
wr
Now, let’s look at elasticity of Now, let’s look at elasticity of supply.supply.
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
SI
SE
w
L
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
SI
SE
w
L
D
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
SI
SE
w
L
D
$3 tax paid by employers
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
SI
SE
w
L
D
$3 tax paid by employers
wr
wr
Figure 3A.1Figure 3A.1 A Production FunctionA Production Function
Figure 3A.2 Figure 3A.2
The Declining Marginal Productivity of LaborThe Declining Marginal Productivity of Labor
Figure 3A.3Figure 3A.3 Cost Minimization in the Production of Cost Minimization in the Production of Q*Q* (Wage = (Wage =
$10 per Hour; Price of a Unit of Capital = $20)$10 per Hour; Price of a Unit of Capital = $20)
Figure 3A.4Figure 3A.4 Cost Minimization in the Production of Cost Minimization in the Production of Q*Q*
(Wage = $20 per Hour; Price of a Unit of Capital = $20)(Wage = $20 per Hour; Price of a Unit of Capital = $20)
Figure 3A.5 Figure 3A.5
The Substitution and Scale Effects of a Wage IncreaseThe Substitution and Scale Effects of a Wage Increase
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