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Transcript of A New Construction of the Ricardian Trade Theory KOSIME 2006.6.22 At Pusan Y. Shiozawa (Osaka City...
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)