1 The Demand and Supply of Factors of Production Principles of Microeconomics Professor Dalton ECON 202 – Fall 2013 Boise State University

1

The Demand and Supply of Factors of

Production

Principles of MicroeconomicsProfessor Dalton

ECON 202 – Fall 2013Boise State University

2

Input Prices and Employment

Input prices and their employment in a market economy depend on the

functioning of input markets – the supply of and demand

for the various inputs.

3

The Market for an InputDerived Demand

The demand for labor (and other factors of production) is a Derived Demand.

A firm’s demand for a factor of production is derived from its decision to supply a good.

4

Production Theory

Since the demand for inputs is a derived demand, production theory is relevant to our consideration of the demand for inputs.

Firms will face diminishing returns to variable inputs, other inputs fixed, – as output increases the marginal product of variable factors diminishes.

5

Typology of Markets

Product markets:•Price-takers •Price-searchers

Input markets:•(Input-price) “wage”-takers•(Input-price) “wage”-searchers

6

Typology of Markets

The four types of relevant factor markets:•Price-taker, “wage”-taker market•Price-searcher, “wage”-taker market•Price-taker, “wage”-searcher market•Price-searcher, “wage”-searcher

market

7

Output and Factor Markets

In a Price-taker market the profit-maximizing firm chooses that output level at which P = MR= MC.

In a Price-searcher market the profit-maximizing firm chooses that output level at which P > MR = MC.

Given the same market demand for output, a price-searcher market produces less output.

8


In a “Wage-taker” market the profit-maximizing firm has to take the market price of inputs as given – it is such a small employer of inputs that its actions alone do not affect market price of the input.

In a “Wage-searcher” market the profit-maximizing firm alters the market price of inputs as its own demand for inputs change – it is a large employer of those inputs.

9

Price-Taker, Wage-Taker Behavior

In a price-taker, wage-taker market as firm output expands the marginal productivity of inputs changes due to greater employment, but the price of inputs do not change.

Changes in the Marginal Cost of production are due solely to changes in MP of inputs.• Marginal costs rise as marginal

productivity falls.

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MPL

LMPL

The marginal cost [MC] is a “mirror” image of the MP function.

Q

$

MPL x w

MCMC = 1MPL

x w

MPL x w

11


The profit-maximizing output of a firm occurs where Px = MCx, and MCx = w/MPL:

Px = w/MPL or

Px (MPL) = w

12


Px (MPL) = w What does this equation mean?

• Px is the price that the output produced by the input is sold for.

• MPL is the additional output produced when an additional unit of the input is employed.

• w is the price (cost) of an additional unit of the input.

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•Px (MPL) is the marginal benefit (in dollar terms) from employing an additional unit of labor.

•w is the marginal cost of employing an additional unit of labor.

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• A firm employs an input until the marginal benefit of employing the input equals the marginal cost of employing the input.

• For a price-taking, wage-taking firm this occurs where the Value of Marginal Product [VMPL = Px (MPL) ] or Marginal Revenue Product [MRPL = MRx (MPL)] equals the wage-rate.

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Price-Taker, Wage-Taker Demand

Px (MPL) = w Since the firm is a wage-taker, as

the wage varies, the quantity of labor demanded will vary.

The demand curve for the firm (other inputs constant) is the VMPL curve (MRPL) curve of the firm.

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wage

Hours of Labor

W1

MRPL = VMPL = dL

Firm Demand for LaborPrice-taker, Wage-taker with other inputs fixed

L1

W2

L2

W3

L3

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Market Demand for LaborPrice-taker, Wage-taker

It would seem natural to get the market demand curve by simply summing the individual firm’s demand curves.

Is the market demand for an input simply the horizontal sum of the individual firm’s demand curves?

NO. Why? When, for example, the wage decreases, an output

effect occurs – since it is cheaper to produce output (MC falls), more output will be produced –

This means that the market supply increases and price of output falls…

Which means in turn that the firm’s demand curves for input shift to the left (because MRPL) is now smaller!

AND BY ALL FIRMS!

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Market Demand for LaborPrice-taker, Wage-taker

wage

L

W1

L1

W2

IL2

firm

dL

dL2

ΣL1

ΣL2

DL

wage

L

market

ΣdL

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Market Supply of Labor

Determinants of Market Labor Supply• money wage rate

(+)• non-labor income

(-)• Price level

expectations (-)

wage

L

marketS

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Market Wage

Market Wages are determined by the interaction of market demand and supply.

wage

L

marketS

DL

w*

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Market Wage and Firm Employment

wage

L

marketS

DL

w*

L

firm

dL

L*

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Determinants ofLabor Demand

Determinants of Labor Demand• real wage - law of demand

(increase w reduces QDL)

• expected price of output - changes in the price of output are positively related to changes in labor demand (increase Px increases DL)

• productivity - changes in productivity are positively related to changes in labor demand (increase productivity increases DL)

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Labor DemandSources of Productivity Change

Physical Capital : when workers work with a larger quantity of equipment and structures, they produce more.

Human Capital : when workers are more educated/better trained, they produce more.

Technology : when workers have access to more sophisticated technologies, they produce more.

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w

Labor

w

DL

Labor-Market EquilibriumComparative Statics

L*

SL(Pe0)

D1L

An increase in productivity or product prices...

…increases the demand for labor...

…increasing the market wage...

…and increasing the quantity of labor employed.

w**

L**

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Growth Rates in Productivityand Real Earnings

1960 - 1970 2.33 2.89

1970 - 1980 0.84 0.79

1980 - 1990 1.38 1.15

1990 - 2000 1.89 1.92

Observations• Greater growth in labor productivity increases

the demand for labor and causes higher real wage growth

Annual Growth Rate (%)

Productivity Real Earnings

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W

Labor

w*

DL

Labor-Market EquilibriumComparative Statics

L*

SL

S1L

An decrease in non-labor income or price level expectations, or increase in number of workers...…increases the supply of labor...

…decreasing the market wage...

…and increasing the quantity of labor employed.

w**

L**

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Profit-maximizing Employment

For a firm maximizing profits, the least cost-combination of inputs must be employed.

The least cost condition occurs when:

MPK/r = MPL/w

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A price-taker, wage-taker maximizes profits when it employs resources such that the MP per dollar spent per resource is equal to the inverse of the Marginal Cost of output (equal to the inverse of the Price of output).

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Profit-maximizing Employment

Generalizing, the least-cost combination of inputs occurs when:

MPK = MPL = MPa = MPb = … = MPn

r w Pa Pb

Pn

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Why has the gap between the wages of skilled and unskilled workers widened in recent years?

Explaining the Trends in Real Wages and Employment

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The Effect of Globalization on the Demand for Workers in Two

Industries

Employment

Rea

l Wag

e

Employment

Importing industry Exporting industry

Stextiles

Dtextiles

w

N textiles

Ssoftware

Dsoftware

Nsoftware

Initially, wages are equal

D’textiles

w’textiles

N’textiles

Demand for workers in importing industry (textiles) declines, lowering wages and employment

D’software

w’software

N’software

Demand for workers in exporting industry (software) increases, raising wages and employment.

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Increasing Wage Inequality: The Effects of Globalization• When wages in “losing” industries fall and wages in

“winning” industries rise, wage inequality increases.• Low-skill industries in the U.S. face the toughest

international competition. High-skill industries in the U.S. tend to do the best in international competition.

• This relationship between low-skill and high-skill industries exacerbates the wage inequality created by increasing trade.

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Why has the gap between the wages of less-skilled and higher-skilled workers widened in recent years?


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The Effect of Skill-Biased Technological Change on Wage

Inequality

Employment

Rea

l Wag

e

Employment

Unskilled workers Skilled workers

D’unskilled

w’unskilled

N’unskilled

The demand for unskilled workers decreases and reduces their wages.

The increase in demand for skilled workers, due to technological change, raises their wages.

D’skilled

N’skilled

w’skilled

Sunskilled

Dunskilled

N unskilled

Sskilled

Nskilled

Initially, wages are equal.

wunskilled w’skilled

Dskilled

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Typology of Markets


market

36




Given the same market demand for output, a price-searcher market produces less output.

37


In a “Wage-taker” market the profit-maximizing firm has to take the market price of inputs as given – it is such a small employer of inputs that its actions alone do not affect market price of the input.


38

Price-Searcher, Wage-Taker Behavior

In a price-searcher, wage-taker market as firm output expands the marginal productivity of inputs changes due to greater employment, but the price of inputs do not change.

Changes in the Marginal Cost of production are due solely to changes in MP of inputs.• Marginal costs rise as marginal

productivity falls.

39


The profit-maximizing, least-cost combina-tion of inputs remains:

MPK = MPL = MPa = MPb = 1 = 1

r w Pa Pb MCx

MRx

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A price-searcher, wage-taker maximizes profits when it employs resources such that the MP per dollar spent per resource is equal to the inverse of the Marginal Cost of output (equal to the inverse of the Marginal Revenue of output).

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MRx (MPL) = w What does this equation mean?

• MRx is the marginal revenue obtained from the output produced by the input.

• MPL is the additional output produced when an additional unit of the input is employed.

• w is the price (cost) of an additional unit of the input.

42



•MRx (MPL) is the marginal benefit (in dollar terms) from employing an additional unit of labor.

•w is the marginal cost of employing an additional unit of labor.

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• A firm employs an input until the marginal benefit of employing the input equals the marginal cost of employing the input.

• For a price-taking, wage-taking firm this occurs where the Marginal Revenue Product [MRPL = MRx (MPL)] equals the wage-rate.

44

Price-Searcher, Wage-Taker Demand

MRx (MPL) = w Since the firm is a wage-taker, as

the wage varies, the quantity of labor demanded will vary.

The demand curve for the firm (other inputs constant) is the MRPL curve of the firm.

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wage

Hours of Labor

W1

MRPL = dL

Firm Demand for LaborPrice-searcher, Wage-taker with other inputs fixed

L1

W2

L2

W3

L3

46

Market Demand for LaborPrice-searcher, Wage-taker

It would seem natural to get the market demand curve by simply summing the individual firm’s demand curves.

Is the market demand for an input simply the horizontal sum of the individual firm’s demand curves?

NO. Why? When, for example, the wage decreases, an output

effect occurs – since it is cheaper to produce output (MC falls), more output will be produced –

This means that the market supply increases and price of output falls…

Which means in turn that the firm’s demand curves for input shift to the left (because MRPL) is now smaller!

AND BY ALL FIRMS!

47

Market Demand for LaborPrice-searcher, Wage-taker

wage

L

W1

L1

W2

IL2

firm

dL

dL2

ΣL1

ΣL2

DL

wage

L

market

ΣdL

48

Marshall’s Laws of Derived Demand

The demand for a factor of production is more elastic when • demand for the final product is more

elastic • the degree of substitutability with other

inputs is higher • the supply of other factors is more

elastic

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Typology of Markets


market

50

Wage-Searcher Factor Markets


51

Wage-Searcher Factor Markets

What is the consequence of being a wage-searcher on the cost of employing additional units of labor?

Let’s take the extreme case of wage-searcher activity – a monopsony.• A monopsony is a single buyer of an

item – in this context a monopsony is the only buyer of labor.

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Monopsony Factor Markets

If the firm is a monopsony it faces the entire market supply curve of labor.

Wage rate

Hrs. Labor

SL

53


If the firm wants to hire H0 hours of labor, it has to pay w0 per hour.

If the firm wants to hire H1 hours of labor it has to pay w1 per hour.

Wage rate

Hrs. Labor

SL

w0

H1

w1

H0

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What happens to the marginal cost of hiring labor (marginal factor cost) in this situation?

When the additional labor is hired, the firm not only has to pay w1 to the additional labor, but also has to increase the wage paid to “previous” units of labor from w0 to w1 also.

Wage rate

Hrs. Labor

SL

w0

H1

w1

H0

55


Suppose that H1 = 11 and H0 = 10, and w1 = $10 and w0 = $9 .

When H1 is hired, the marginal factor cost of hiring the 11th hour of labor is the $10 paid for the 11th hour plus the $1 that has to be paid for each of the previous 10 hours ( = $10) so that the marginal factor cost = $20!

Wage rate

Hrs. Labor

SL

$9

H1

$10

H0

$20

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For a monopsony (and for a wage-searcher in general) the marginal factor cost curve will lie everywhere above the supply curve of labor…

Wage rate

Hrs. Labor

SL

$9

H1

$10

H0

$20

MFCL

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… because when a the amount of labor is increased the cost of hiring labor increases due to 2 reasons – (1) having to pay a higher wage to induce additional labor to be employed and (2) having to pay a higher wage to previous units.

Wage rate

Hrs. Labor

SL

$9

H1

$10

H0

$20

MFCL

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MFC > w

for a wage-searcher

Wage rate

Hrs. Labor

SL

$9

H1

$10

H0

$20

MFCL

59




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Price-Taker, Wage-Searcher Behavior

A price-taker’s marginal benefit from hiring additional labor is the VMPL.

If the price-taker is also a wage-searcher, it’s marginal cost of hiring additional labor is it’s MFCL.

A price-taker, wage-searcher hires that amount of labor where VMPL = MFCL.

61

wage

Hours of Labor

VMPL = dL

Firm Demand for LaborPrice-taker, Wage-searcher with other inputs fixed

L*

w*

MFCL

SL

MFC = VMP determines L

L determines w as read off S

62

Price-Searcher, Wage-Searcher Behavior

A price-searcher’s marginal benefit from hiring additional labor is the MRPL (and MR < P).

If the price-taker is also a wage-searcher, it’s marginal cost of hiring additional labor is it’s MFCL.

A price-taker, wage-searcher hires that amount of labor where MRPL = MFCL.

63

wage

Hours of Labor

VMPL

Firm Demand for LaborPrice-searcher, Wage-searcher with other inputs

fixed

L*

w*

MFCL

SL

MFC = MRP determines L

L determines w as read off S

MRPL = dL

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wage

Hours of Labor

VMPL

Comparing Outcomeswith other inputs fixed – the short run

MFCL

SL

In a PTWT market, VMP = w

In a PTWS market, VMP = MFC

In a PSWS market, MRP = MFCMRPL

wPTWT

LPTWT

wPTWS

wPSWS

LPSWS LPTWS

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Comparing Outcomeswith other inputs fixed – the short run

• Price-searcher behavior reduces the employment of inputs below that which a price-taker would employ, certeris paribus, because MR < P (marginal benefits are lower).

• Wage-searcher behavior reduces the employment of inputs below that which a wage-taker would employ, ceteris paribus, because MFC > w (marginal costs are higher).

Documents

1 The Demand and Supply of Factors of Production Principles of Microeconomics Professor Dalton ECON 202 – Fall 2013 Boise State University