Chapter 5

Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

Chapter 5

The Demand for Labor

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1.Derived Demand for Labor

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Derived Demando The demand for labor is a derived

demand. • That is, it is derived from the demand for

the product or service that the labor is helping produce.

∞The demand for hamburgers leads to the demand for hamburger workers.

• Demand for workers depends on:∞How productive the workers are.∞The price of the product the workers are helping

produce

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2. A Firm’s Short-Run Production Function

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Production Functiono A production function shows the

relationship between inputs and outputs.o Assume that only two inputs are used to

make a product-- labor (L) and capital (K).

o In the short run, at least one input is fixed.

o The total product for a firm in the short run is:• TPSR=f(K,L), where K is fixed.

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Definitionso Total product (TP) is the total product

produced by each combination of labor and the fixed amount of capital.

o Marginal product (MP) is the change in total product associated with the addition of one more unit of labor.

o Average product (AP) is the total product divided by the number of units of labor.

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3 Stages of Production

o Stage 1: as labor increases, total product increases at an increasing rate due to specialization

o Stage 2: as labor increases, total product increases but at a decreasing rate, due to diminishing returns

o Stage 3: as labor increases, total product declines due to extreme fixed constraints

Total Product

0

TotalProduct

54321

• As units of variable input (labor) are added to a fixed input, total product will increase . . .

• First at an increasing rate . . .

• Then at a declining rate . . .

• Note that the Total Product curve is smooth, indicating that labor can be increased by amounts of less than a single unit (it is a continuous function).

20

30

40

50

60

70

80

10

6 7 8

0

9 10

AverageProduct

MarginalProduct

TotalProduct(Output)

Units of Variable

Resource

1 8 2 20 3 34 4 46 5 56 6 64 7 70 8 74 9 75

10 73 Quantity of Labor

Law of Diminishing Returns

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5-9

0

• The Marginal Product curve will initially increase (when TPC is increasing at an increasing rate), reach a maximum, and then decrease (as TPC increases at a decreasing rate).

0

AverageProduct

MarginalProduct

TotalProduct(Output)

Units of Variable

Resource

1 8 2 20 3 34 4 46 5 56 6 64 7 70 8 74 9 75

10 73

-----8

12141210 8 6 4 1- 2

-----

1011.311.511.210.7109.38.37.3

• The Average Product curve will have the same general form except that its maximum point will be at a higher output level.

•Firm will never hire in Stage 1 (costs per unit could be decreased) or in Stage 3

Law of Diminishing Returns

8

5-10

Average Product

Marginal Product

Average and/or Marginal Product

54321

4

8

12

16

6 7 8 9 10

Important Note : MP always crosses AP at its maximum point.

Quantity of Labor

Law of Diminishing Returns

Average Product

Marginal Product

AP & MP

Quantity of Labor

54321

4

8

12

16

6 7 8 9 10

Total Product

TP

54321

20

30

40

50

60

70

80

10

6 7 8 9 10Quantity of Labor

• Graphed together, one can see the relationship between the TP, MP, and AP curves more clearly.

Law of Diminishing Returns

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3. Short-Run Demand for Labor: The Perfectly Competitive Seller

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Hiring Decision

o Profit-maximizing firms will hire additional workers as long as each worker adds more to revenue than she costs.• Marginal revenue product (MRP) is the change

in total revenue that results from hiring an additional worker.

∞MRP= Marginal Revenue (MR) * MP or∞MRP = (change in Total Revenues)/(change in Labor)

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• Marginal Labor Cost (MLC) is the change in total costs of hiring an additional worker.

∞MLC = (change in Total Costs)/(change in Labor)∞MLC = wage package + extra supply costs +

raises to existing employees

o The Hiring Rule:• Hire additional workers as long as MRP >=

MLC

MP TP L(3)

TotalProduct

(TP)(units per week)

(2)

Units of Labor

(L)(1)

Sales Price (Per Unit)

(4)

TotalRevenue

(5)

0.0 5.0 9.0 12.014.0

15.516.517.0

5.0 $1,0004.0 $1,8003.0 $2,4002.0 $2,8001.5 $3,1001.0 $3,3000.5 $3,400

----- $ 0 1000 800 600 400 300 200 100

----

• In the numerical example below, a computer company uses both technology and data-entry operators to provide services in a perfectly competitive market. For each unit processed the firm receives $200 (4).• Column (2) shows how total output changes as additional data-entry operators are hired (given a fixed capital level).• The Marginal Revenue Product schedule (6) indicates how hiring an additional operator affects the total revenue of the firm.

Short-Run Demand for Perfectly Competitive Firm

0 1 2 3 4 5 6 7

$200$200$200$200$200$200$200$200

MRP TR L(6)

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• If the wage is the only component of MLC, then the MRP curve is the firm’s short run demand curve for labor.

• A profit-maximizing firm will only hire an additional worker only if the worker adds more to revenues than she adds to total costs,

Wage Rate

Quantity of Labor

1000

Short-Run Labor Demand

800

600

400

200

1 2 3 4 5 6 7

• In the short-run, it will slope downward because the marginal product of labor falls as more of it is used with a fixed amount of capital, i.e. in Stage 2

MRP=DL

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Example#2: Fixed Price Market

o Click here for an Excel Worksheet that shows the hiring decision for a firm that sells its product at a fixed price (i.e., a perfectly competitive product market firm).

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Value of Marginal Product

o The value of marginal product (VMP) is the extra output in dollar terms that society gains when an extra worker is employed.• VMP=Price * MP

o For a perfectly competitive seller, MR=Price.• As a result, VMP = MRP for such

firms.

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1. “Only that portion of the MP curve that lies below AP constitutes the basis for a firm’s short-run demand curve for labor.” Explain.

Question for Thought

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4. Short-Run Demand for Labor: The Imperfectly Competitive Seller

MP TP L(3)

TotalProduct

(TP)(units per week)

(2)

Units of Labor

(L)(1)

Sales Price (Per Unit)

(4)

TotalRevenue

(5)

0.0 5.0 9.0 12.014.0

15.516.517.0

5.0 $1,0004.0 $1,7103.0 $2,1602.0 $2,3801.5 $2,4801.0 $2,4750.5 $2,380

----- $ 0 1000 710 450 220 100 -5 -95

----

• In the numerical example below, the company uses both technology and data-entry operators to provide services in an imperfectly competitive market. • Since it is in an imperfectly competitive market, the firm faces a downward sloping product demand curve (4). That is, the product price falls as the firm sells more units.

Short-Run Demand for Imperfectly Competitive Firm

0 1 2 3 4 5 6 7

$210$200$190$180$170$160$150$140

MRP TR L(6)

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• For imperfectly competitive firms, the labor demand curve will slope because of a fallingmarginal product of labor and because the firm must decrease the price on all units of output as more output is produced.

• Since it is in an imperfectly competitive market, the firm faces a downward sloping product demand curve (4). That is, the product price falls as the firm sells more units.

• The labor demand curve for an imperfectly competitive firm (MRP) is less elastic than that for a perfectly competitive firm (VMP). As a result, they will hire fewer workers other things equal.

Wage Rate

Quantity of Labor

1000

Short-Run Labor Demand

800

600

400

200

1 2 3 4 5 6 7

MRP=DL

0

VMP

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Example 2: Price Discounter

o Click here for an Excel worksheet that shows the hiring decision for a firm that has to reduce the price as it increases employment and production (i.e., an imperfectly competitive product market firm).

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5. Long-Run Demand for Labor for the Firm

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Long-Run Labor Demand

o In the long run, both labor and capital are variable.

o The total product for a firm in the long run is:• TPLR=f(K,L)

o The long-run labor demand curve is downward sloping because a wage decline has both an output and substitution effect.

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• A decline in the wage rate will reduce the marginal cost of production (MC1 to MC2) and increase the profit maximizing level of output (40 to 70).

Price

Quantity of Output

10

Output Effect

8

6

4

2

10 20 30 40 50 60 70

• To produce the higher output level, the firm will have to hire more workers.

MR

MC1MC2

• This output effect is present in the short run.

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Substitution Effect

o The substitution effect is the change in employment resulting from a change in the relative price of labor, output being held constant.• If a decline in the wage rate occurs, firms

will substitute labor for the now relatively more expensive capital.

• Since capital is fixed in the short run, this effect can’t occur in the short run.

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• A wage decrease from $800 per week to $600 increases the short-run quantity of labor from 3 to 4 (A to B). This is the output effect.

Wage Rate

Quantity of Labor

1000

Long-Run Labor Demand

800

600

400

200

1 2 3 4 5 6 7

• In the long-run, the firm also substitutes labor for capital, resulting in a substitution effect of 2 units (B to C).

DSR

DLR

A

CB

• The long-run demand curve results from both effects and is found by connecting points A and C.

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Other Factorso Product demand

• Product demand is more elastic in the long run than in the short run, making labor demand more elastic the longer the period.

o Labor-Capital interaction• If the wage rate falls, the short-run quantity demanded of

labor rises.∞This will increase the MP (marginal product) of capital and

thus the MRP of capital.∞The higher MRP of capital, the quantity of capital will

increase and thus the MP and MRP of labor. ∞As a result, the long-run response will be greater than the

short-run response.

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Other Factorso Technology

• If the wage rate falls, technological innovators will try to reduce the use of relatively more expensive capital and increase the use of labor.

∞The long run response will be greater than the short-run response.

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E.G.: Declining US Mfg. Jobs

o 1950 30% in Mfg, 2008 10% in Mfg.o Four causes

• Consumer spending shifting away from goods to services (1950 67% on goods, 2008 40%). Rising real wages and women working

• Increased US investment in capital equipment, leading to 3.3% annual increase in APL, leading to decreased labor needs

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o Growing international trade: US has a comparative advantage in high capital, high skill industries and disadvantage in low capital, low skill industries

o Growing use of outsourcing and temps• Temps working in manufacturing counted as

service workers, not manufacturing. Half of 1979 – 2000 decline due to increased use of temps

• Manufacturers have also outsourced support functions like payroll processing, cleaning, which are counted as services

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1. Referring to the output and substitution effects, explain why an increase in the wage rate for autoworkers will generate more of a negative employment response in the long run than in the short run. Assume there is no productivity increase and no change in the price of nonlabor resources.

Question for Thought

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6. Market Demand for Labor

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• The market demand curve for labor is less elastic than a horizontal summation of the demand curves of individual firms (D).

Wage Rate

Quantity of Labor

1000

Market Labor Demand

800

600

400

200

10 20 30 40 50 60 70

• A lower wage induces all firms to hire more labor and produce more output, causing the supply of the product to increase.

DMARKET

D

A

CB

• The resulting decline in the product price shifts the firms’ labor demand to left.

• As a result, total employment rises to A to B rather than from A to C.

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7. Elasticity of Labor Demand

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Wage Elasticity Coefficient

o The wage elasticity coefficient measures the responsiveness of the quantity demanded of labor to the wage rate.

Wage ElasticityCoefficient = =

% Q

% W

% Change in quantity demanded% Change in Wage

- or put simply -)()(

)()(

1010

1010

WWWW

QQQQ

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Determinants of Labor Demand Elasticity

o Elasticity of product demand• The greater the price elasticity of product

demand, the greater the elasticity of labor demand.

∞Firms with market power tend to have more inelastic product demand, and thus a more inelastic labor demand.

∞Product demand tends to be more elastic in the long run and thus labor demand is more elastic in the long run.

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Determinants of DL Elasticity

o Ratio of labor costs to total costs• The larger the share of labor costs in total

costs, the greater will be the elasticity of labor demand.

∞A 10% wage rise if labor accounts for 10% of total costs, will raise total costs by 1%.

∞A 10% rise in wages if labor accounts for 50% of total costs, will raise total costs by 5%.

~ If costs rise more, the price rise must be greater and thus decrease quantity more.

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Determinants of DL Elasticity

o Substitutability of other inputs• The greater the substitutability of other

inputs for labor, the greater will be the elasticity of labor demand.

o Supply elasticity of other inputs• The greater the elasticity of supply of other

inputs for labor, the greater will be the elasticity of labor demand

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Estimates of DL Elasticity

o Most estimates of elasticity indicates the overall long-run elasticity of demand is about -1.0.• A 1% rise in the wage rate will lower

the quantity demanded of labor by 1%.

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Significance of DL Elasticity

o Labor unions• Unions can achieve greater wage

gains when the labor demand curve is more inelastic.

o Minimum wage• The employment decline of a hike in

the minimum wage will be larger when the labor demand curve for affected workers is more elastic.

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o Total Wages depend on the labor demand elasticity• w/ inelastic demand, higher wages lead to

increased total wages• w/ elastic demand, higher wages lead to

decreased total wages

o Labor will work to make labor demand more inelastic, which makes it possible to increase wages, decrease hours & preserve employment

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Total Wages Example

total hours total Hours/ Pay/

wage desired wages workers Week weekElastic Demand 10 400 4000 10 40 400

12 300 3600 9 40 480

12 300 3600 10 30 360Inelastic Demand 10 400 4000 10 40 400

12 360 4320 9 40 480

12 360 4320 10 36 432

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8. Determinants of Demand for Labor

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Determinants of Labor Demand

o Product demand• A change in product demand will shift labor

demand in the same direction.

o Productivity• Assuming that it does not cause an offsetting

decrease in the product price, a change in marginal product will shift labor demand in the same direction.

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Determinants of Labor Demand

o Number of employers• Other things equal, a change in the number of

firms employing a particular type of labor will change labor demand in the same direction.

o Prices of other resources• Normally labor and capital are substitutes in

production.• Labor and capital can also be complements in

production

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What Happens if the Cost of Capital Decreases to Labor Demand?

• If labor and capital are substitutes for each other, then labor demand could increase or decrease depending on whether they are Gross Substitutes or Gross Complements

• Gross substitutes∞Gross substitutes are inputs such that when the price of one changes, the demand for the other changes in the same direction.

∞Implies substitution effect outweighs the output effect.∞Example: the decline in the price of security camera and sensor equipment has decreased the demand for night guards

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• Gross complements∞Gross complements are inputs such that when the price of one changes, the demand for the other changes in the opposite direction.

∞Implies output effect outweighs the substitution effect.

∞Example: the decline in the price of computing software has increased the demand for workers who work with software (i.e., programmers, accountants, analysts)

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• If labor and capital cannot be substituted for each other, then they are considered Pure Complements∞Pure complements in production are inputs that are used in direct proportion to each other.

∞Since no substitution effect occurs, the inputs must be gross complements, i.e., if the cost of capital decreases, the demand for labor increases.

∞Example: if crane prices decrease, the demand for crane operators will increase.

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Application: Outsourcing

o Concern with outsourcing jobs to foreign countries is increasing• A recent study states that 11% of US jobs

could be outsourced, mainly data entry, call centers, programmers & operators

• Another study states that 3.3 million jobs will leave US by 2015

o Are concerns warranted? Researchers say no for 3 reasons

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• 3.3 million jobs is small stuff relative to total employment. 8 million jobs are normally eliminated every 3 months in US but new job creation exceeds that. 1998-2008 11 million increase in total jobs

• Jobs eliminated are low-wage jobs which would be eliminated by technology even w/o outsourcing, e.g., automated call centers.

• Outsourcing decreases production costs which then increases overall employment, e.g., globalization decreased computer costs 30% which lead to greater APL & GDP.

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1. Use the concepts of (a) substitutes in production versus pure complements in production and (b) gross substitutes versus gross complements to assess the likely impact of the rapid decline in the price of computers and related office equipment on the labor demand for secretaries.

Question for Thought

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9. Other Real-World Applications

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Employment in Textiles and Apparel• Employment in the textile and apparel industries has fallen in one-half since 1973.

0

0.5

1

1.5

2

2.5

3

Empl

oym

ent (

mill

ions

)

• Demand for American textile and apparel workers has fallen because the share of sales due to imports has risen from 5% in 1970 to 40% now.

• Robots and assembly-line labor are gross substitutes. The price of robots has fallen and so labor demand has fallen.

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Declining Computing Costs

o Falling computing costs and technological innovation has increased the demand for network analysts and software engineers• Rising demand for internet services due to

falling prices• Increased productivity for these workers

because of tech change• Falling equipment costs have created an

output effect that dwarfs the substitution effect

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Minimum Wage

o Labor demand for low wage workers is inelastic, i.e., -.1 to -.3. A 10% increase in wage leads to a 1 to 3% decrease in employment

o If the minimum wage is increased, total wages to minimum wage workers will increase. Hence tradeoff between the jobless and higher total incomes for low wage workers

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Contingent Workers

o Temp Employment doubled between 1990 and 2008 (1.2 million to 2.4 million)

o Why?• Wages are lower & so are fringes• Competitive pressures are increasing both

domestically and internationally• Greater flexibility in altering production