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Labor Demand
Sellers’ view of Labor
• Sellers view labor as a source of income (potential
for increase in consumption of goods and services).
• Labor Supply: – Labor as hours devoted to work (T – leisure).
– Leisure is a ‘good’, work is a ‘bad’. • Find individual labor supply curves, then aggregate them to
find market labor supply curve.
– Hours supplied (per period) is an increasing function of wages.
– Backward bending labor supply: Hours may decline at very high levels of wages. Chapter 3
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Demand for Labor is «derived demand»
Buyers’ view of Labor
• Buyers view labor as a factor of production. • Borjas: «workers … differ from other inputs in a number of important ways.» (p.84)
• Econ 320 Syllabus: • 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.
– Quality is not easily discrenable (Ch.6, 7)
– Worker may not apply his/her labor as responsibly
as the employer will like (Ch.11) Presently we abstract from these information
problems.
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• Central questions: how many workers are hired and what are they paid?
3
Labor is an important input!
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The Firm’s Production Function
• Describes the technology that the firm uses to produce goods and services.
• The firm’s output can be produced by a variety of capital–labor combinations.
• 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 employing one additional unit of capital, holding constant the quantities of other inputs.
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The Total Product, the Marginal Product, and the Average Product Curves, Fig. 3‐1
Profit Maximization
• Objective of the firm is to maximize profits.
• Production function: Q = f(E, K)
• Profit function: π = pQ – wE – rK
• Total Revenue = pQ
• Total Costs = (wE + rK)
• Perfectly competitive firms cannot influence prices of output or inputs.
• Take p, w, r as given, choose input (E, K) and
output (Q) levels to maximize profits.
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 shows the output produced by each additional worker, and the average product curve shows output per worker.
See Table 3‐1 for a numerical illustration. 7
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Short Run Hiring Decision
• E = employee‐hours
= no. of workers x average hours per worker
Consider:
10 workers x 8 hrs/day = 80 hrs/day
20 workers x 4 hrs/day = 80 hrs/day
• Will the employer be indifferent between
these? • If fixed costs of employement are present, the answer is «NO».
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The Firm’s Hiring Decision in the Short‐Run (Fig. 3‐2)
• Optimal E solves
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Employment = employee‐hours
• Short run: K is fixed. • Value of Marginal Product of Employment (VMPE) is the marginal product of labor times the dollar value of the output.
• VMPE indicates the dollar benefit derived from hiring an additional worker, holding capital constant.
• Value of Average Product of Employment is the dollar value of output per worker.
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Labor Demand Curve • The demand curve for labor indicates how many workers the firm hires for each possible wage, holding capital constant.
A profit‐
maximizing firm hires workers up to the point where the wage rate equals the value of marginal product of labor. If the wage is $22, the firm hires eight workers.
• The labor demand curve is downward sloping. This reflects the fact that additional workers are costly and alter average production due to the Law of Diminishing Returns.
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The Short‐Run Demand Curve for Labor (Fig. 3‐3)
The Firm’s Output Decision
Fig. 3‐5
Because marginal product eventually declines, the short‐run demand curve for labor is downward sloping. A drop in the wage from $22 to $18 increases the firm’s employment. An increase in the price of the output shifts the value of marginal product curve upward (to the right), and increases employment.
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A profit‐maximizing firm produces up to the point where the output price equals the marginal cost of production.
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The Mathematics of Marginal Productivity Theory
Maximizing Profits: Two Rules
• Choice of optimal Q: 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).
• The cost of producing an extra unit of output:
MC = w x (1 / MPE)
• The condition: produce to the point where MC = MR = p (for the competitive firm)
• Choice of optimal E: (Marginal Productivity Condition) hire labor up to the point where the value of marginal product equals the added cost of hiring the worker (= wage).
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w x (1 / MPE) = p or w = VMPE
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Critiques of Marginal Productivity Theory
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The Short‐Run Demand Curve for the Industry (Fig. 3‐4)
• A common criticism is that the theory bears little relation to the way that employers make hiring decisions.
1. In response to a wage reduction, and individual firm would like to
increase employment and increase output. 2. If all firms did this, output increase will reduce the output price, and
the labor demand curve of the individual firm will shift in.
Wage
• Another criticism is that the assumptions of the theory are not very realistic.
Wage
T
D
• However, employers act as if they know the implications of marginal productivity theory (hence, they try to earn profits and remain in business).
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20
10
10
D
T
15 28 30
Employment
Firm
17
30
56
60
Employment
Industry
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Elasticity of Labor Demand
The Employment Decision in the Long Run
• As a result, the demand curve for the industry
(b) is steeper (less elastic) than the demand
curve for an individual firm (a). • Short run elasticity of labor demand: • In the long run, the firm maximizes profits by choosing how many workers to hire AND how much plant and equipment to invest in.
%
%
• In figure (b):
56
10
∆ /
∆ /
30 /30
20 /20
• Isoquant curves describe the possible combinations of labor and capital that produce the same level of output
1.73
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Isoquant Curves (Fig. 3‐6)
X
K
Y
q1
q0
E
Isocost Lines
All capital‐labor combinations that lie on a single isoquant produce the same level of output. The input combinations at points X and Y produce q0
units of output. Combinations of input bundles that lie on higher isoquants must produce more output.
Capital
• The isocost line indicates all labor–capital bundles that exhaust a specified budget for the firm.
• Isocost lines indicate equally costly combinations of inputs.
• Higher isocost lines indicate higher costs.
Employment
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Capital
C1/r
Isocost with Cost Outlay C1
Isocost with Cost Outlay C0
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All capital‐labor combinations that lie on a single isocost curve are equally costly. Capital‐
labor combinations that lie on a higher isocost curve are more costly. The slope of an isoquant equals the ratio of input prices (‐w/r).
Capital
C1/r
A
C0/r
P
175
B
q0
C0/w
100
C1/w
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The Firm’s Optimal Combination of Inputs (Fig. 3‐8)
Isocost Lines (Fig. 3‐7)
C0/r
20
23
A firm minimizes the cost of producing q0 units of output by using the capital‐labor combination at point P, where the isoquant is tangent to the isocost. All other capital‐labor combinations (such as those given by points A and B) lie on a higher isocost curve.
Employment
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Cost Minimization
Long Run Demand for Labor
• When the wage drops, two effects arise.
• Profit maximization implies cost minimization.
• The firm chooses the 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 ratio of input prices, w / r, at the least‐cost choice.
– The firm takes advantage of the lower price of labor by expanding production (the scale
effect).
– The firm takes advantage of the wage change by rearranging its mix of inputs, by employing more labor and less of other inputs, even if holding output constant (the substitution
effect)
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The Impact of a Wage Reduction Holding Costs Constant (Fig. 3‐9)
Capital
C0/r
R
P
75

q0
The Impact of a Wage Reduction on the Output and Employment of a Profit‐
Maximizing Firm (Fig. 3‐10)
A wage reduction flattens the isocost curve. If the firm were to hold the initial cost outlay constant at C0 dollars, the isocost would rotate around C0
and the firm would move from point P to point R. A profit‐
maximizing firm, however, will not generally want to hold the cost outlay constant when the wage changes.
Dollars
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.
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Capital
D
C1/r
Q
C0/r
R
P
200
D
100
Wage is w1
Wage is w0
A wage cut generates substitution and scale effects. The scale effect (from P to Q) encourages the firm to expand, increasing the firm’s employment. The substitution effect (from Q
to R) encourages the firm to use a more labor‐
intensive method of production, further increasing employment.
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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.
Employment
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Two Special Cases of Isoquants
(Fig. 3‐12)
50
R
P
150
Substitution and Scale Effects
40
MC1
p
40
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Capital
MC0
Wage is w1
Wage is w0
25
26
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Elasticity of Substitution
Elasticity of Substitution
• The elasticity of substitution is the percentage change in the capital to labor ratio given a percentage change in the price ratio (wages to real interest).
• Example:
If the elasticity of substitution is 5, then a 10% increase in the ratio of wages to the price of capital would result in the firm increasing its capital‐
to‐labor ratio by 50%.
– Formula: %∆(K/L)  %∆(w/r).
– Interpret a particular elasticity of substitution number as the percentage change in the capital–
labor ratio given a 1% change in the relative price of labor to capital
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The Short‐ and Long‐Term Demand Curves for Labor
Long Run Demand Curve for Labor
(Fig. 3‐11)
Dollars
Dollars
Short-Run
Demand Curve
The long‐run demand curve for labor gives the firm’s employment at a given wage and is downward sloping.
w0
w1
Long-Run
Demand Curve
In the long run, the firm can take full advantage of the economic opportunities introduced by a change in the wage. As a result, the long‐run demand curve is more elastic than the short‐
run demand curve.
DLR
25
50
Employment
Employment
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Factor Demands When There Are Several Inputs
Marshall’s Rules
• Labor Demand is more elastic when:
• There are many different inputs.
– The elasticity of substitution is greater.
– Skilled and unskilled labor
– Old and young
– Old and new machines
– The elasticity of demand for the firm’s output is greater. (Remember: The demand for labor
is derived demand.)
– Labor’s share in total costs of production is greater.
• Cross‐elasticity of factor demand.
– Percent change in xi  Percent change in wj
– If cross‐elasticity is positive, the two inputs are said to be substitutes in production.
– The elasticity of supply of other factors of production such as capital is greater.
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The Demand Curve for a Factor of Production Affected by the Prices of Other Inputs
Labor Market Equilibrium
Dollars
Price of
input i
Price of
input i
In a competitive labor market, equilibrium is attained at the point where supply equals demand. The market‐
clearing wage is w* at which E* workers are employed.
Supply
whigh
w*
D0
D1
D0
wlow
D1
Employment of
input i
Employment of
input i
Demand
ED
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.
E*
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Application: The Employment Effects of Minimum Wages
ES
Employment
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The Impact of the Minimum Wage on Employment
Dollars
• The unemployment rate is higher the higher the minimum wage and the more elastic are the labor supply and demand curves.
S
w
w*
• The benefits of the minimum wage accrue mostly to workers who are not at the bottom of the distribution of permanent income.
D
E
39
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Minimum Wages in the United States, 1938‐2011
0.5
0.4
4
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Evidence from Turkey, 2005
Monthly labor market earnings = real wage x hours
Ratio
5
Employment
Evidence from around the World is mixed! Why? Compliance with the Law is not perfect.
7
6
ES
Employment effects of minimum wages
0.6
8
E*
A minimum wage set at w
results in employers cutting employment from E* to E. The higher wage also encourages ES – E*
workers to enter the market. Thus, under a minimum wage, U = ES – E–
workers are unemployed.
3
0.3
2
Nominal Minimum Wage
1
0.2
0
1938
1944
1950
1956
1962
1968
1974
1980
1986
1992
1998
2004
2010
Year
left axis: min wage
right axis: ratio
ratio = min. wage / average manufacturing wage
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The Impact of Minimum Wages on the Covered and Uncovered Sectors
Employment Protection Legislation
Makes adjustment of employment level costly.
Adjustment costs: • Firing costs
In Turkey if firm wants to fire a «permanent» worker, it must pay penalties («severnace
pay» and «advanced notice pay»).
• Hiring costs
Dollars
Dollars
SU
SC
(If workers migrate to
covered sector)
SU
w
SU
(If workers migrate to
uncovered sector)
w*
w*
DC
E
EC
DU
Employment
EU
EU
EU
Employment
(b) Uncovered Sector
If the minimum wage applies only to jobs in the covered sector, the displaced workers might move to the uncovered sector, shifting the supply curve to the right and reducing the uncovered sector’s wage. If it is easy to get a minimum wage job, workers in the uncovered sector might quit their jobs and wait in the covered sector until a job opens up, shifting the supply curve in the uncovered sector to the left and raising the uncovered sector’s wage.
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Asymmetric Variable Adjustment Costs
Slow Transition to a New Labor Equilibrium
Employment
150
B
100
A
C
50
Changing employment quickly is costly, and these costs increase at an increasing rate. If government policies prevent firms from firing workers, the costs of trimming the workforce will rise even faster than the costs of expanding the firm.
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Variable adjustment costs encourage the firm to adjust the employment level slowly. The expansion from 100 to 150 workers might occur more rapidly than the contraction from 100 to 50 workers if government policies “tax” firms that cut employment.
Time
45
46
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Problems with Estimating Labor Demand
Estimating Labor Demand
S0
• One can identify the slope of the labor demand curve, which can be used to calculate the elasticity of labor demand, when the supply curve shifts.
Dollars
S1
Z
P
w0
R
w2
• Problem: Must make sure the labor demand curve is not also changing.
Z
Q
w1
D1
D0
E0
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E1
E2
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Employment
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The Impact of Wartime Mobilization of Men on Female Labor Supply
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The Impact of Wartime Mobilization of Men on Female Wages
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