Chapter 3 Specific Factors and Income Distribution

Chapter 3Specific Factors and Income Distribution

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The Specific Factors Model International Trade in the Specific Factors Model Income Distribution and the Gains from Trade The Political Economy of Trade: A Preliminary View

Kernel of the Chapter

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Assumptions of the Model• One economy that can produce two goods, manufactures and

food.

• three factors of production; labor (L), capital (K) and land (T for terrain).

• Manufactures are produced using capital and labor (but not land).

• Food is produced using land and labor (but not capital).

– Labor is therefore a mobile factor

– Land and capital are both specific factors.

• Perfect Competition prevails in all markets.

The Specific Factors Model

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• The production function for good X gives the maximum quantities of good X that a firm can produce with various amounts of factor inputs.

– For instance, the production function for manufactures (food) tells us the quantity of manufactures (food) that can be produced given any input of labor and capital (land).


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• The production function for manufactures is given by QM = QM (K, LM) (3-1)

• The production function for food is given by

QF = QF (T, LF) (3-2)


• The full employment of labor conditionLM + LF = L (3-3)

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Production Possibilities• To analyze the economy’s production possibilities, we

need only to ask how the economy’s mix of output changes as labor is shifted from one sector to the other.

• Figure 3-1 illustrates the production function for manufactures.


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QM = QM (K, LM)

Figure 3-1: The Production Function for Manufactures


Labor input, LM

Output, QM

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• The shape of the production function reflects the law of diminishing marginal returns.

• Figure 3-2 shows the marginal product of labor, which is the increase in output that corresponds to an extra unit of labor.


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MPLM

Figure 3-2: The Marginal Product of Labor


Labor input, LM

Marginal product of labor, MPLM

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QF =QF(K, LF)

QM =QM(K, LM)

L2M

L2F

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1

L

LAA

1'

3'

PP

Economy’s production possibility frontier (PP)

Production functionfor manufacturesEconomy’s allocation

of labor (AA)

Production functionfor food

Q2F

Q2M

2'

Labor input in food, LF (increasing )

Output of manufactures, QM (increasing )

Labor input in manufactures, LM (increasing )

Output of food, QF (increasing )

Figure 3-3: The Production Possibility Frontier in the Specific Factors Model


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Prices, Wages, and Labor Allocation• How much labor will be employed in each sector?

• Demand for labor:


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• The demand curve for labor in the manufacturing sector can be written:

MPLM x PM = w (3-4)

• The demand curve for labor in the food sector can be written:

MPLF x PF = w

(3-5)


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The wage rate must be the same in both sectors, because of the assumption that labor is freely mobile between sectors.

The wage rate is determined by the requirement that total labor demand equal total labor supply:

LM + LF = L (3-6)


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PM X MPLM

(Demand curve for labor in manufacturing)

PF X MPLF

(Demand curve for labor in food)

Wage rate, W Wage rate, W

W1

1

L1M L1

F

Total labor supply, L

Labor used in manufactures, LM

Labor used in food, LF

Figure 3-4: The Allocation of Labor


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At the production point

-MPLF/MPLM = -PM/PF (3-7)


Slope = -(PM /PF)1

1Q1

F

Q1M

Output of manufactures, QM

Output of food, QF

PP

Figure 3-5: Production in the Specific Factors Model

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• What happens to the allocation of labor and the distribution of income when the prices of food and manufactures change?

• Two cases:– An equal proportional change in prices

– A change in relative prices


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W1 1

PF increases 10%

Wage rate, WWage rate, W

PF 1 X MPLF



10% wage increase

PM increases 10%

PM 1 X MPLM

W2

2

PF 2 X MPLFPM 2 X MPLM

Figure 3-6: An Equal Proportional Increase in the Prices of Manufactures and Food


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• When both prices change in the same proportion, no real changes occur.

– The real incomes of capital owners and landowners also remain the same.


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• When only PM rises, the wage rate (w) does not rise as much as PM since manufacturing employment increases and thus the marginal product of labor in that sector falls.


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PF 1 X MPLF


PM 1 X MPLM

2W 2


Labor used in manufactures, LM Amount of labor

shifted from food to manufactures

Wage rate rises by less than 7%

7% upward shift in labor demand

PM 2 X MPLM1

W 1

Figure 3-7: A Rise in the Price of Manufactures


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PP

Slope = - (PM /PF)1


Output of food, QF

Slope = - (PM /PF) 2

1Q1

F

Q1M

2Q2

F

Q2M

Figure 3-8: The Response of Output to a Change in the Relative Price of Manufactures


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Relative quantityof manufactures, QM/QF

Relative price of manufactures, PM /PF

RD

RS

Figure 3-9: Determination of Relative Prices

1 (PM /PF )1

(QM /QF )1


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Relative Prices and the Distribution of Income

• Suppose that PM increases by 10%. Then, we would expect the wage to rise by less than 10%, say by 5%.

• What is the economic effect of this price increase on the incomes of the following three groups?

– Workers

– Owners of capital

– Owners of land


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• Workers:– We cannot say whether workers are better or worse off;.

• Owners of capital:– They are definitely better off.

• Landowners:– They are definitely worse off.


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Assumptions of the model• Assume that both countries (Japan and America) with

the same relative demand.

• The only source of international trade is the differences in relative supply which arises from the difference in:

– Technology

– Factors of production (capital, land, labor)

International Trade in the Specific Factors Model

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Resources and Relative Supply• What are the effects of an increase in the supply of

capital stock on the outputs of manufactures and food?


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PM X MPLM2

PF 1 X MPLF


PM X MPLM1

W 1

1

2W 2

Increase in capital stock, K

Amount of labor shifted from food to

manufactures


Labor usedin food, LF


Figure 3-10: Changing the Capital Stock

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• An increase in the supply of capital would shift the relative supply curve to the right.

• An increase in the supply of land would shift the relative supply curve to the left.

• The effect of an increase in the labor force? – The effect on relative output is ambiguous, although

both outputs increase.


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Trade and Relative Prices• Suppose that Japan has more capital per worker than

America, while America has more land per worker than Japan.

• International trade leads to a convergence of relative prices.


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Relative quantity of manufactures, QM/QF

Relative price of manufactures, PM /PF

(PM /PF )W

(PM /PF )A

(PM /PF )J


Figure 3-11: Trade and Relative Prices

RDWORLD

RSA

RSWORLD

RSJ

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The Pattern of Trade• In a country that cannot trade, the output of a good

must equal its consumption.

• International trade makes it possible for the mix of manufactures and food consumed to differ from the mix produced.

• A country cannot spend more than it earns.


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Budget constraint (slope = -PM/PF)

Consumption of manufactures, DM


Consumption of food, DF

Output of food, QF

Production possibility curve

International Trade in the Specific Factors ModelFigure 3-12: The Budget Constraint for a Trading Economy

Q1M

1Q1

F

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QJF

QAF

DAFDJ

F

QAM DA

MQJMDJ

M

Japan’s food

imports

America’s food

exports

Japan’s manufactures

exports

America’s manufactures

imports

Quantity of manufactures

Quantity of manufactures

Quantity of food

Quantity of food

Japanese budget constraint American budget constraint


Figure 3-13: Trading Equilibrium

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Income Distribution and the Gains from Trade

To assess the effects of trade on particular groups, the key point is that international trade shifts the relative price of manufactures and food.

Trade benefits the factor that is specific to the export sector of each country, but hurts the factor that is specific to the import-competing sectors.

Trade has ambiguous effects on mobile factors.

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Could those who gain from trade compensate those who lose, and still be better off themselves?

The fundamental reason why trade potentially benefits a country is that it expands the economy’s choices.• This expansion makes it possible to redistribute

income in such a way that everyone gains from trade.


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Budget constraint(slope = - PM/PF)

PP

Consumption of manufactures, DM


Consumption of food, DF

Output of food, QF

Q1M

Q1F

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Figure 3-14: Trade Expands the Economy’s Consumption Possibilities


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Trade often produces losers as well as winners. Optimal Trade Policy

• The government must somehow weigh one person’s gain against another person’s loss.

• Any realistic understanding of how trade policy is determined must look at the actual motivations of policy.

The Political Economy of Trade: A Preliminary View

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Income Distribution and Trade Politics• Those who gain from trade are a much less

concentrated, informed, and organized group than those who lose.

– Example: Consumers and producers in the U.S. sugar industry

The Political Economy of Trade: A Preliminary View

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Chapter 3 Specific Factors and Income Distribution

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