A New Construction of the Ricardian Trade Theory

KOSIME 2006.6.22 At Pusan

Y. Shiozawa(Osaka City University)

Two competing theories:

Ricardian theory: 2 countries, 2 goods, 1 factor (labor) Linear technology (Leontief-Sraffa type) Graham, McKenzie, Jones, & Others

Hecksher-Ohlin theory 2 countries, 2 goods, 2 factors (labor & capital) Homotetic, smooth substitution Samuelson, Vanek, & Others

Others Marxian trade theory

Core ideas:

Ricardian theory Countries are characterized by technology. Technology matters. Technology gap explains the big difference of wa

ges between countries.

Hecksher-Ohlin theory Countries are characterized by capital/labor ratio. Technology gap is not most important. Capital/labor ratio aminly determines wage differe

nce.

Policy implications:

Ricardian theory Technology development

>>technology importation

>>R&D and innovationHecksher-Ohlin theory

Capital accumulation, capital importation Technology development is only a windfal

l. No necessity of innovation management

Provisional conclusion

Those who knows the crucial role of technology and innovation must feel unhappy with the base vision which underlies the main stream trade theory.

Unfortunately, Ricardian trade theory stayed so far in a very crude level.

It is necessary to re-activate Ricardian tradition and develop general theory in such a way that the new theory can supersede HO theory and its varieties.

Present state of Ricardian theory

J. S. Mill: Mutual demand theory Graham ： Multi-commodity multi-country ca

se McKenzie: Graham’s theory in the light of GE

theory. Jones （ 1960 ） : Discovery of the formula to

determine complete specialization pattern. Minabe, Ikema, and others: examination of n

umerical examples, 3×3 cases.

Ricardo’s original model: a recapitulation

Labor input Cloth Wine

England 100 120

Portugal 90 80

Comparative advantage: 120/100 > 80/90Portugal has comparative advantage in wine and England in cloth. Specialization pattern: England exports cloth and Portugal exports wine.

Portugal has absolute advantage both n cloth and wine.

A hidden assumption: Commodities are traded by comparing prices.

International currency: silver or gold. Fixed exchange rate

Wage rates: we, wp measured in a common currency Trade conditions:

cloth 100 we 90 wp≦ wine 　 120 we 80 wp ≧

Specialization pattern 100/90=1.11 wp/we 120/80=1.5≦ ≦ Portuguese wage is always higher than that of England.

Existence of wage difference is presupposed.

Ricardo’s original model: a revised one

Labor input Cloth Wine

England 10 12

Portugal 90 80

Trade conditions: cloth 10 we ≦ 90 wp wine 　 12 we 80 wp≧Wages must satisfy: 6.67 =80/12 ≦ we/wp ≦ 90/10=9In this case English workers gains at least 6.67 times of Portuguese workers.

Problems to break through

Extensions to M country N commodity case

Choice of techniquesIntermediate input goods

The new construction satisfies all these three requirements.

A substantial step up since 40 years.

3-country 3-commodity case 1

A B

C

U1

U2

U3

No intermediate goods:

Wage simplex:

3-country 3-commodity case 2

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

41

46

56

142

169

No intermediate goods.A modal decomposition of production possibility set.Seen from the origin.

Importance of intermediate goods:

Materials are traded widely and extensively.

Capital goods can be treated as intermediate goods.

Greater profit from trade. See the next sheet.

Trade of intermediate goods

3-country 3-commodity case 3

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

With intermediate goods

3-country 3-commodity case 4

A15 0 13 8 44 3 5

A26 1 2

1 1 01 3 8

A38 5 0

5 4 04 4 3

A modal decomposition of wage simplex

Questions on wage simplex?

Are there always a open domain with full specialization ?

No, for some special cases.Strong existence theorem

Yes, for almost all cases. Weak existence theorem

There is at least a point with full specialization (weak specialization).

A result of numerical experiments

DimensionFields

Diagonal elements

Non-diagonal elements

Number of cases examined

Non-existent cases

Probability

3

Integer

[1,9] [0,5] 100,000 487 0.005

3

Integer

[1,18] [0,10] 100,000 0 0

3

Real

[1,9] [0,5] 100,000 0 0

Experiments by Mathematica

A modal decomposition of wage simplex 1

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

a, a, aa, b, a

a, c, a

b, b, ab, b, bb, b, c

b, c, ab, c, c

c, c, a c, c, c

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1 Patterns of specializationFor each 2 cell (domain)

A modal decomposition of wage simplex 2

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

1, 3,2, 3,31, 3,2,2, 31, 2, 3,2,21,2, 3,1, 31,2,1, 2, 3

1,1, 2, 3,10.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1 Types of specializations of each crosspoints:

Each crosspoint corresponds to a facet of production Possibility set

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

22

32

34

75

139

180

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Crosspoints of a modal decomposition of wage simplex

-0.5 -0.25 0.25 0.5 0.75 1 1.25 1.5

-0.5

-0.25

0.25

0.5

0.75

1

1.25

1.5

22

32

34

75

139

180

A modal decomposition for productionpossibility set

Dual relations between two modal decompositions:

3 country 3 commodity case

Faces of production possibility set

Faces of wage vector

point Facet (2-polytope, open domain)

Line segment Line segment

Facet (2-dim polytope) Point (cross point of at least)

Supply conditions or demand conditions: a good question?

Mill Mutual demand theory

Graham Supply conditions predominate.

Demand vs. supply conditions

>>Price adjustment or quantity adjustment

Which is dominant: price adjustment or quantity adjustment?

All points of a facet of efficient production point (maximal point) corresponds to a point of wages and prices.

All points of a facet of the wage space modal decomposition can generate only one efficient/maximal point of the production possibility set.

Mathematical feature of RTT

Existence theorem (Weak version) Fare partition theorem Combinatorial discussion Existence of equilibrium

Existence theorem (Strong version) New theorem Combinatorial 　 discussion + simple hom

otopy theory

Modal decomposition

Each domain is a locus of system of linear inequalities.

Check all possible combinations. Suitable for computers but not for human calculation.

Computable in principle, but for M and N bigger than 3 there is no visual method to display the solution.

Production possibility set

Convex polytope P Includes the origin

Polar relationship: Polar[Pp]= {p: <x,p> 1, for all x Pp}≦ ∈ Polart[Polart[Pp]]=Pp

Polar[Pp]=a part of modal decomposition of price space Correspondense with modal decompositio

n of wage space

Topics to be treated:

Financial flow （ trade balance ） Balance is not a simple function of exchange rate.

Non-equilibrium state can be analysed. Profit from trade

Different interest: consumers benefit from trade, but not unemployed.

Trade conflict Unemployed people cannot enjoy the profit from t

rade. The same is true for industrials who have lost thei

r market by the increase of trade.

Some concluding remarks:

Ricardian trade theory can be generalized to a real size economy, with many countries and many commodities.

Some new features appear by the generalization.

New approach to dis-equilibrium state becomes possible.

References:

A summery: in EnglishA paper (preprint version) :in Japanese

Very preliminary draft. Do not quote from these papers. Please wait the following papers now in preparation.

To appear Japanese paper:『経済学雑誌』 (大阪市立大 )

English paper:Evolutionary and Institutionary Economics

Review (JAEE)