The Factor-Proportions ModelInternational 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.

• 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!

MPLFMPLM x PAUT

Incomplete specialization IThe equilibrium with constant returns

• 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 PRecall 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 (of manufactures) is lower than in autarky, the country will specialize completely in Agro/Food

LF LM

w

total labor force

MPLM x PTRADE

Incomplete specialization IIThe equilibrium with decreasing returns

• 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 (of manufactures) is lower than in autarky, the country will specialize, but not completely, in Agro/Food LF

MPLF

LM

MPL M x P AUT

w

total labor force

MPL M x P TRADE

Incomplete specialization IIIDecreasing returns and the concavity of the PPF

• 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.

-6

+1

Food

Manuf

+1

-1

Slope = -MPLM / MPLF

-1/P

Incomplete specialization IIIThe gains from trade in the North

• 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

Food

Manuf

-1/PN-1/Pw

Gains from trade

Imports

Ex

po

rts

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 substitutability of factors

• The Kapital/Labor ratio (K/L) used in production depends on the prices of the factors.

T

L

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

Food

w/r

K/L

w/r

FF

The substitutability of factors

K

L

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

Foodw/r1

K/L

w/rFF

Manuf

• Manuf is a Capital Intensive sector. – It uses a higher ratio of K/L, for any

given factor prices.

MM

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 specializationP1 >P2

Food

Manuf

-1/P1

-1/P2

Prices and the real factor-returns- An intuitive scheme

A rise in the relative price of Manuf (P)

Food output falls; Manuf output expands

Full employment of Kapital and Labor is preserved.

Food output decline releases too much Labor (excess supply)Manuf expansion requires mostly Kapital (excess demand)

Real wage must fall due to excess demandKapital rents must rise due to excess supply

All sectors become more labor intensive.

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

w/r

P

SS

Prices, relative factor returns and factor intensities

w/r

SS

PK/L

MM FF

K/LM1 K/LF1

w/r1

P2

K/LM2 K/LF2 P1

w/r2

• 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.

An interesting theorem (Rybczinsky)

• 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

declinesFood

Manuf

F1

M1

F2

M2

An interesting theorem (Rybczinsky)

• 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

M F M M F F

M F M F

K K K L K LK

L L L L L L L

The effects of international trade demand

• 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 relatively LABOR ABUNDANT and has Comparative Advantage in the LABOR INTENSIVE sectors.

Manuf/Food

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

PRSS

RSN

PS

PN

PW

RSW

Resource Abundance, Comparative Advantage and the Pattern of Trade

• If technologies are

identical, a country

has comparative

advantage in the

sectors that use

relatively INTENSIVELY

the factors that are

relatively ABUNDANT.

SOUTHRelatively Labor Abundant

Specializes in Food

NORTHKapital Abundant

Specializes in Manuf

MA

NU

FK

apital In

tensive

FO

OD

Lab

or In

tensive

Econom

ic Developm

ent

Education, Investm

ent, Infrastructure

Dynamic Comparative Advantage- Accumulating Skills and Capital

Knowledge Intensive(Aeronautics)

Skilled labor Intensive(Electronics)

Capital Intensive(Machinery)

Unskilled labor Intensive(Textiles)

Resource Intensive(Rice, Oil)Natural Resources

Labor Unskilled

Capital

Skilled Labor

Knowledge & R&D

Prices and real factor returns

w/r

SS

PK/L

FFMM

K/LM2 K/LF2

w/r2

P1

K/LM1 K/LF1 P2

w/r1

• 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

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,…• …raising the return to capital and lowering the wage

– 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.

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

Low returns for unskilled labor

High returns for unskilled labor

Abundance in unskilled labor

Abundance in skilled labor and capital

Rich countries

Poor countries

Good working conditions

High unskilled wages

Poor working conditions

Low unskilled wages

Unfair Competition and Comparative Advantage

• Low wage competition is comparative advantage in goods that are intensive in educated/skill labor for industrialized countries– Trade creates value because returns to unskilled workers are

lower in developing countries

• The mix between wages and working conditions is mostly market driven.– Legal constraints have a cost that depends on how restrictive

they are, relative to market outcomes.– Part of this cost is borne by workers in the form of

unemployment and lower net wages.– It is a cost that rich, industrialized societies have accepted to

pay to promote social justice and avoid exploitation.

Summary

• Comparative Advantage (and gains from trade) may arise from differences in the relative abundance of factors, if they are used with different intensities across sectors

• Comparative advantage in sectors the used intensively the abundant factor.

– Changes in factor abundance due to economic development will affect the country’s comparative advantage.

• Low wages in poor countries are due, in part, to low capital abundance.– These low wages are the source of gains from trade and

not unfair competition