The Factor-Proportions Model

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# The Factor-Proportions Model - PowerPoint PPT Presentation

The Factor-Proportions Model. International Trade – Session 3 Daniel TRAÇA. Last session. In countries with lower productivity, competitiveness in world markets arises from lower wages. The gains from trade mean potential gains for workers.

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## The Factor-Proportions Model

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### The Factor-Proportions Model

Daniel TRAÇA

Last session
• In countries with lower productivity, competitiveness in world markets arises from lower wages.
• The gains from trade mean potential gains for workers.
• The political argument is due to adjustment costs (specific factors)
• Factors that are specific to import-competing industries will loose out from trade.
• Those that are specific to exporting industries will be winners.
• But the gains of winners always outweigh the loses of losers.
• Compensating losers is a difficult task!
In each sector, workers must be hired until the marginal worker’s cost (the wage) is equal to its marginal product.

Workers must be indifferent between the two sectors

w = MPLF = MPLM x P

Recall that P is the relative price of manufactures

In autarky, the price must equate the relative marginal product, to ensure both goods are produced.

If the trade price (ofmanufactures) is lower than in autarky, the country will specialize completely in Agro/Food

w

MPLM x PAUT

MPLF

total labor force

LF

LM

Once again, the equilibrium entails

w = MPLF = MPLM x P

For any given price (P), we can find out the employment and output of Agro/Food and Manufactures.

If the trade price (ofmanufactures) is lower than in autarky, the country will specialize, but not completely, in Agro/Food

w

MPLF

MPLM x PAUT

total labor force

LF

LM

We can obtain the PPF, for the case of decreasing returns.

The PPF is concave. The opportunity cost of Food is now increasing.

Equilibrium:

P = MPLF/MPLM

For any price (P), we can obtain the Relative Supply of Manuf.

Manuf

-1

+1

-6

+1

Food

Incomplete specialization IIIDecreasing returns and the concavity of the PPF

-1/P

Slope =

-MPLM / MPLF

The prices of manufactures rises in the North,

Due to its comparative advantage in manufacturing

Production of manufactures for export increases;

Effects on consumption of manufactures depend on income (+) and substitution effect.

But there is incomplete specialization,

The North still produces some Food for its own consumption

Manuf

Food

-1/Pw

-1/PN

Exports

Imports

The Hecksher-Ohlin (HO) model
• 2 sectors: Manuf and Food
• 2 factors: Capital (K) and Labor (L)
• Factors can freely move between Manuf and Food. This mobility captures long term (no adjustment costs)
• 2 countries: North(N) and South (S);
• Differ in relative abundance of Capital and Labor
The Kapital/Labor ratio (K/L) used in production depends on the prices of the factors.

FF

The substitutability of factors

ISOQUANT: combinations of inputs that produce the same quantity of the good

T

w/r

Food

w/r

K/L

L

The substitutability of factors
• Manuf is a Capital Intensive sector.
• It uses a higher ratio of K/L, for any given factor prices.

ISOQUANT: combinations of inputs that produce the same quantity of the good

K

w/r

FF

MM

Manuf

Food

w/r1

K/L

L

Manuf

Food

Concavity of the PPF
• With two factors, and different factor intensities the PPF is concave
• similarly to decreasing returns
• For any price, there is incomplete specialization

P1 >P2

-1/P1

-1/P2

Food output falls; Manuf output expands

Food output decline releases too much Labor (excess supply)

Manuf expansion requires mostly Kapital (excess demand)

Real wage must fall due to excess demand

Kapital rents must rise due to excess supply

All sectors become more labor intensive.

Full employment of Kapital and Labor is preserved.

Prices and the real factor-returns- An intuitive scheme

A rise in the relative price of Manuf (P)

What is the effect of a rise in P on w/r?

An increase in the price of a good raises the relative factor-price of the factor that is used intensively in that sector.

e.g. an increase in the relative price of Manuf (Kapital intensive) lower the relative price of labor (w/r)

The factor-price ratio (w/r) and the relative price of manufacture (P)

w/r

SS

P

Prices, relative factor returns and factor intensities

w/r

• For any given relative price of goods, there is an equilibrium relative factor price and a given distribution of factor intensities in production.
• This is independent of the abundance of resources in the economy.

MM

FF

w/r2

w/r1

SS

K/L

K/LM2

K/LM1

K/LF2

K/LF1

P2

P1

P

An increase in Abundance of Kapital

The PPF becomes larger, but the change is not parallel:

Since Manuf is the main user of Kapital, the difference is relatively larger in Manuf.

For the same price, the output of Manuf rises and that of Food declines

M2

F2

An interesting theorem (Rybczinsky)

Manuf

M1

F1

Food

An increase in the supply of a factor, with prices unchanged, raises the output of sectors that use intensively that factor and lowers the output of sectors that do not use intensively

A rise in L lowers K/L (right-hand side).

With given prices, factor intensities (in square brackets) do not change.

Since K/LF < K/LM , employment in Food (LF/L) must rise, and in Manuf (LM/L) must fall.

Since LM falls and TM= [T/LM]xLM falls, the production of Manuf must fall

An interesting theorem (Rybczinsky)

RSW

RSN

PW

PN

The effects of international trade demand

P

• If the North has more Capital, the relative supply of Manuf is higher than in the South.
• Use the Rybczinsky theorem
• The autarky price of Manuf (P) is higher in the South.
• This means that the South has the Comparative Advantage in Food.
• With trade, relative price of Manuf rises in the North
• Comparative Advantage arises because the South is relativelyLABOR ABUNDANT and has Comparative Advantage in the LABOR INTENSIVE sectors.

PS

RD is the same for both countries and for the World, as a whole.

Manuf/Food

If technologies are identical, a country has comparative advantage in the sectors that use relatively INTENSIVELY the factors that are relatively ABUNDANT.

SOUTH

Relatively Labor Abundant

Specializes in Food

MANUF

Kapital Intensive

FOOD

Labor Intensive

NORTH

Kapital Abundant

Specializes in Manuf

Knowledge Intensive

(Aeronautics)

Knowledge & R&D

Skilled labor Intensive

(Electronics)

Skilled Labor

Economic Development

Education, Investment, Infrastructure

Capital Intensive

(Machinery)

Capital

Unskilled labor Intensive

(Textiles)

Labor Unskilled

Resource Intensive

(Rice, Oil)

Natural Resources

Prices and real factor returns

w/r

FF

• All else constant, a higher relative price of a good…
• … means a higher relative factor-price of the factor used intensively in that good
• … and a lower intensity in that factor in both sectors.
• This has implications for real factor returns:
• Factor intensity  Marginal Product  Factor returns

MM

w/r1

w/r2

SS

K/L

K/LM1

K/LM2

K/LF1

K/LF2

P1

P2

P

Factor returns: Prices vs. Factor abundance
• The HO model establishes a unique relationship between goods’ prices and factor prices.
• The Stolper-Samuelson theorem
• An increase in the relative price of the good raises the real return to the factor used intensively, and lowers the relative return to the factor not used intensively
• Changes in P causes lower in K/LM and K/LF,…
• In this context, if goods prices are constant, an increase in the abundance of a given factor does not affect factor returns, it simply affects the relative output of the goods (remember the Rybczinsky effect)
Factor abundance and factor prices in autarky
• Comparing Real Factor Returns in the North, with the South
• Due to higher Kapital abundance, the North has comparative advantage in K-intensive goods (Manuf).
• The autarky relative-price of Manuf is lower in the North, than in the South.
• Kapital intensity in Manuf and Food is higher in the North, than in the South.
• This is necessary to ensure that the higher abundance of Kapital is used up.
• Real (Labor) Wages are higher and (Kapital) Rents are lower in the North, than in the South.

Good working conditions

Rich countries

Abundance in skilled labor and capital

High returns for unskilled labor

High unskilled wages

Poor working conditions

Poor countries

Abundance in unskilled labor

Low returns for unskilled labor

Low unskilled wages

Unfair Competition
• If the items entering this country in such volumes were better designed or more attractive, more durable or more efficiently produced, we would have little reason to object. But the vast majority of imports sell here primarily because they are cheaper; and they are cheaper for one reason only - they are made at wages and under working conditions that would be illegal and intolerable in this country’.
• from the President of American Textile Manufacturers Institute