Prof. Dr. Volker Clausen Universität Duisburg-Essen Campus Essen 1 Ricardo, David (1817): On the Principles of Political Economy and Taxation. London.

Prof. Dr. Volker ClausenUniversität Duisburg-EssenCampus Essen

1

Ricardo, David (1817): On the Principles of Political Economy and Taxation. London.

Heckscher, Eli (1919): The Effect of Foreign Trade on the Distribution of Income, Ekonomisk Tidskrift, 497-512.

Ohlin, Bertil (1933): Interregional and International Trade. Cambridge, Mass.

Krugman, Paul (1980): Scale Economies, Product Differentiation, and the Pattern of Trade. American Economic Review 70, 950-959.

Markusen, James R. (1981): Trade and the Gains from Trade with Imperfect Competition. Journal of International Economics 11, 531-551.

Markusen, James R. (2002): Multinational Firms and the Theory of International Trade. Cambridge, Mass.

Helpman, Elhanan (1984): A Simple Theory of International Trade with Multinational Corporations. Journal of Political Economy 92, 451-471.

Source: van Marrewijk, C. (2002): International Trade and the World Economy. Oxford et al.


2

Differences in Endowments: The Heckscher-Ohlin Model

Ricardo-Model: Trade due to differences in labor productivity

Heckscher-Ohlin Model: Trade due to differences in factor endowments, technologies identical across countries

Assumptions:

• perfect competition in all markets

• two countries

• two homogenous goods, computer and clothes

linear homogenous production technologies, identical for both countries:

0

dada

a,afd,0

dada

a,afd

,0da

a,afd,0

da

a,afd

,0a

a,af,0

a

a,af

,a,afx

KkLk

LkKkk2

LkKk

LkKkk2

2Lk

LkKkk2

2Kk

LkKkk2

Lk

LkKkk

Kk

LkKkk

LkKkkk

k, computer, clothes


3

• two homogenous factors of production, capital K and labor L, supply completely price

inelastic

• factors of production mobile between sectors, but immobile between countries

• general equilibrium model: goods and factor prices lead to an equilibrium on all goods and

factor markets

• homothetic preferences, identical across countries


4

Notation:

factor input coefficients: first index: factor of production, second index: good

LCa

KCa

LKa

KKa

labor per unit computer

capital per unit computer

labor per unit clothes

capital per unit clothes

factor endowments:

DL labor, Germany

capital, Germany

labor, China

capital, China

DK

CL

CK


5

iso-cost line

per unit production isoquant

w

ra

w

Ca KKLK

LKKKK a,af1

LKa

KKa

•*LKa

*KKa

*KK

*LK

a

a

w

r

Figure 1

0

Deriving the factor input coefficients:

graphical:

Minimize per unit cost, given that one unit of output is produced:


6

With Cobb-Douglas production technologies:

,aaQ

,aaQ

LCKCC

LKKKK

1

1

LKKKLKKK aaawar 11

KK

LK

a

a

w

r

1

1

1 1

w

raa KKKK

1

1

1

w

ra

r

wa

LK

KK

11

1 11

w

r

wr

wr

a

a

KK

LK

1wr

aa KKLK

10

10


7

...and for computer:

1wr

aa KCLC

Assumption: ,

computers more capital intensive in production, compared to clothes

computer capital intensive, clothes labor intensive

11

KK

LK

a

a

w

r

clothes, slope

computer, slope

KC

LC

a

a

1

1

no reversal in factor intensities

figure 2

0


8

relative goods prices and relative factor prices

perfect competition on goods and factor markets

zero profit conditions hold:

,pr,wawr,war

pr,wawr,war

CLCKC

KLKKK

in the example:

C

K

pw

rw

r

wr

pw

rw

r

wr

1

1

1

1

1

1

C

B

K

A

pwr

pwr

11

11

1

1

1

1


9

wr

wr

A

B

p

p

K

C

1

1

w

r

A

B

p

p

K

C

K

C

p

p

w

r

Stolper-Samuelson Theorem (weak version):

In a neoclassical framework with two final goods and two factors of production, an increase in the relative price of a final good increases the relative price of the factor of production used intensively in the production of that good and reduces the reward to the other factor, provided both goods are produced.

Opening up a country to international trade may generate conflicts between households

figure 3

0

1

w

r

A

B

wr

pp KC > 0

012

2

2

w

r

A

B

wrd

ppd KC

2


10

Merging both figures:

clothes

computerw

r

K

C

p

p

KK

LK

a

a,

a

a

KC

LC

unique relationship between relative goods prices and factor input ratio:

An increase in the relative price to leads to an increase in the labor intensity

in producing both goods.

1K

C

p

p

2K

C

p

p

1

w

r

2

w

r

1KK

LK

a

a

2KK

LK

a

a

1KC

LC

a

a

2KC

LC

a

a

2K

C

p

p

1K

C

p

p

figure 4

0


11

Stolper-Samuelson Theorem (strong version):

In a neoclassical framework with two final goods and two factors of production, an increase in the relative price of a final good increases the real reward - in units of both goods - of the factor of production used intensively in the production of that good and reduces the real reward - in units of both goods - to the other factor, provided both goods are produced.

Example:see figure 2:

clothes

computer

see figure 3:

KK

LK

K

C

a

a

A

B

p

p 1

1

1 B

A

p

p

a

a

K

C

KK

LK

KC

LC

K

C

a

a

A

B

p

p 1

1

1 B

A

p

p

a

a

K

C

KC

LC

KC

LC

KK

LK

a

a

w

r

a

a

w

r

1

1

w

r

A

B

p

p

K

C


12

Furthermore, due to profit maximizing factor input of firms,

factor price = marginal value product

LK

LKKKFK

LC

LCKCCC

KK

LKKKFK

KC

LCKCCC

a

a,afpw

a

a,afpw

a

a,afpr

a

a,afpr

see figure 4

KC

LC

KC

LCKCC

a

a

a

a,af1

1

LC

KC

LC

LCKCC

a

a

a

a,af

KK

LK

KK

LKKKK

a

a

a

a,af1

1

LK

KK

LK

LKKKK

a

a

a

a,af

KC

LC

C a

a

p

r1

KK

LK

K a

a

p

r1

An increase in (pC/pK) leads to an increase in (aLC/aKC) as well as (aLK/aKK) - capital gains in units of computer as well as in units of clothes

1

LC

KC

C a

a

p

w

1

LK

KK

K a

a

p

w

Stolper-Samuelson Theorem (strong version):

An increase in (pC/pK) leads to a decline in (aKC/aLC) as well as (aKK/aLK) - labor looses in units of computer as well as in units of clothes

0

1

1

11

B

A

B

A

p

p

pp

aa

K

C

KC

KKLK

0

1

1

11

B

A

B

A

p

p

pp

aa

K

C

KC

KCLC


13

Factor endowments and goods production

Assumption: relative goods prices constant

w

r

A

B

p

p

K

C (see previous slide) relative factor prices constant

Edgeworth-Box for a country, e. g. Germany:

0C

0K

CK

KK

CL

KL

KC

LC

a

a

KK

LK

a

a

*CL

*KK

*KL

*CK

figure 5


14

Increase in the relative and absolute capital endowment of Germany:( decrease in the relative labor endowment of Germany)

0C

0K

CK

KK

CL

KL

KC

LC

a

a

KK

LK

a

a

*CL

*KK

*KL

*CK

figure 6

0KC

0K‘

*KL

*CK

*KK

*CL

*K

*K

*K

*K

*C

*C

*C

*C

KK

LL

KK

LLabsolute and relative production of computer increases, absolute and relative production of clothes declines

KK

LK

a

a


15

Rybczynski-Theorem:

In a neoclassical framework with two final goods, two factors of production, and constant prices of the final goods, an increase in the supply of one of the factors of production results in an increase of the output of the final good that uses this factor of production intensively and a reduction in the output of the other final good, provided both goods are produced in equilibrium.

Expansion to two countries, Germany and China:

• identical homothetic preferences: identical relative demand for computer and clothes, if relative prices are identical

• identical production technologies: identical factor input leads to identical output

• different relative factor endowments: C

C

D

D

L

K

L

K

Germany is relatively well endowed with capital (“relative” to labor, “well” in comparison to China), China is relatively well endowed with labor (“relative” to capital, “well” in comparison to Germany).

Heckscher-Ohlin Theorem:

In a neoclassical framework with two final goods, two factors of production, and two countries which have identical homothetic preferences, a country will export the

good which intensively uses the relatively abundant factor of production.


16

Example:

• Germany relatively well endowed with capital

China relatively well endowed with labor

• Computer production intensive in capital

clothes production intensive in labor

LF

KF

LC

KC

a

a

a

a

KF

LF

KC

LC

a

a

a

a

Germany exports computer, China exports clothes


17

K

C

p

p

,Q

QD

SK

SC

,

Q

QC

SK

SC

,

Q

QD

DK

DC

C

DK

DC

Q

Q

D

SK

SC

Q

Q

C

SK

SC

Q

Q

D

DK

DC

Q

Q

C

DK

DC

Q

Q

Relative supply of computer, Germany

Relative supply of computer, China

Relative demand for computer, Germany

Relative demand for computer, China

relative demand for computer, identical across countries due to identical homothetic preferences

relative supply of computer, China

Relative supply of computer, Germany, larger than China’s relative supply of computer due to Rybczynski-Theorem

.Aut

CK

CC

p

p

.Aut

DK

DC

p

p

FT

K

C

p

p

I II III IV

I: relative supply of China, free trade

II: relative supply = relative demand of China, autarky

V

III: relative demand of both countries, free trade

IV: relative supply = relative demand of Germany, autarky

V: relative supply of Germany, free trade

figure 8


18

Graphical “proof” of the Heckscher-Ohlin theorem:

A country achieves a higher level of welfare, if it specializes according to the Heckscher-Ohlin theorem (Maintained assumption: Costless restructuring)

.

.

AutDK

AutDK

Q

C

tradefreeDKQ

Germany China

DCQ

DKQ C

KQ

CCQ

tradefree

K

C

p

p

tradefreeDKC

tradefreeU

.AutU

.Aut

DK

DC

p

p

tradefreeDCC

.AutD

C

.AutDC

Q

C

tradefreeDCQ

tradefreeCKQ

tradefree

K

C

p

p

tradefreeCKC

.AutC

K

.AutCK

Q

C

tradefreeCCQ

.AutC

C

.AutCC

Q

C

tradefreeCCC

.Aut

CK

CC

p

p

.AutU

tradefreeU

figure 9


19

Goods trade and intranational income distribution:

Germany:

Opening Germany up to free trade leads to an increase of the relative price of

computer;

Stolper-Samuelson Theorem:

relative and real reward of capital increases, relative and real reward of labor declines

Opening Germany up to free trade leads to an increase in real factor income for

households, which are endowed with the factor the country is relatively well endowed

with. Households, which are endowed with the factor the trade partner is relatively well

endowed with, loose in real factor income, if the country is opened to free trade.


20

Goods trade and factor price equalization:

Trade leads to equalization of relative and absolute goods prices:

Equalization of relative and absolute factor prices:

see figure 3

K

C

p

p

w

r

figure 3

definite relationship between relative goods prices and relative factor prices

goods trade is a perfect substitute to factor trade:

Germany exports capital, which is embodied in the exports of computers,

China exports labor, which is embodied in the exports of clothes


21

No convergence in factor prices;

Reason?

C

DDDDLC

DDDDKC

KDDDD

LKDDDD

KK

DDC

DDDLC

DK

DDDLK

DDC

DDDKC

DK

DDDKK

pwr,warr,wa

pwr,warr,wa

LQr,waQr,wa

KQr,waQr,wa

factor market equilibrium conditions:

Germany:

C

CCCCLC

CCCCKC

KCCCC

LKCCCC

KK

CCC

CCCLC

CK

CCCLK

CCC

CCCKC

CK

CCCKK

pwr,warr,wa

pwr,warr,wa

LQr,waQr,wa

KQr,waQr,wa

zero profit conditions:

Germany: China:

China:

If the number of goods is larger/equal to the number of factors of production ( number

of zero profit conditions is larger/equal to the number of factors), if trade leads to

identical goods prices across countries, and if the production technologies are identical

across countries ( ) identical zero profit condition are solved for the

factor prices in both countries.

CCCij

DDDij r,war,wa

Factor price equalization theorem


22

Factor price equalization results.

Possible reasons for incomplete factor price equalization:

• specialization in production, Germany only produces computer, China produces only

clothes

only one zero profit condition per country, determination of factor prices also requires

factor market equilibrium conditions;

differences in relative factor endowments lead to differences in absolute factor prices

• differences in production technologies,

zero profit conditions may be solved for the factor prices,

however, not identical zero profit conditions are solved for factor prices

• no equalization of goods prices due to tariffs, transport costs, etc.

right hand sides of the zero profit conditions are not identical

CCCij

DDDij r,war,wa

Prof. Dr. Volker Clausen Universität Duisburg-Essen Campus Essen 1 Ricardo, David (1817): On the Principles of Political Economy and Taxation. London.

Documents

factor of production

unit clothes capital

unit computer labor

unit computer capital

unit clothes factor

factor markets

pattern of trade

factor input coefficients