A New Construction of the Ricardian Trade Theory

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

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Core ideas

• Ricardian theory
• Countries are characterized by technology.
• Technology matters.
• Technology gap explains the big difference of
  wages between countries.
• Hecksher-Ohlin theory
• Countries are characterized by capital/labor
  ratio.
• Technology gap is not most important.
• Capital/labor ratio aminly determines wage
  difference.

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Policy implications

• Ricardian theory
• Technology development
• gtgttechnology importation
• gtgtRD and innovation
• Hecksher-Ohlin theory
• Capital accumulation, capital importation
• Technology development is only a windfall.
• No necessity of innovation management

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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.

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Present state of Ricardian theory

• J. S. Mill Mutual demand theory
• Graham Multi-commodity multi-country case
• McKenzie Grahams theory in the light of GE
  theory.
• Jones(1960) Discovery of the formula to
  determine complete specialization pattern.
• Minabe, Ikema, and others examination of
  numerical examples, 33 cases.

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Ricardos original model a recapitulation
Labor input Cloth Wine
England 100 120
Portugal 90 80
Portugal has absolute advantage both n cloth and
wine.
Comparative advantage
120/100 gt 80/90 Portugal has comparative
advantage in wine and England in cloth.
Specialization pattern England exports cloth
and Portugal exports wine.
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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
• 100/901.11 ? wp/we ? 120/801.5
• Portuguese wage is always higher than that of
  England.
• Existence of wage difference is presupposed.

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Ricardos 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 ? 90/109 In this case English workers
gains at least 6.67 times of Portuguese workers.
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Problems to break through

• Extensions to M country N commodity case
• Choice of techniques
• Intermediate input goods
• The new construction satisfies all these three
  requirements.
• A substantial step up since 40 years.

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3-country 3-commodity case 1
No intermediate goods
Wage simplex
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3-country 3-commodity case 2
No intermediate goods. A modal decomposition of
production possibility set. Seen from the origin.
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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.

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Trade of intermediate goods
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3-country 3-commodity case 3
With intermediate goods
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3-country 3-commodity case 4
A modal decomposition of wage simplex
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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).

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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
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A modal decomposition of wage simplex 1
Patterns of specialization For each 2 cell
(domain)
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A modal decomposition of wage simplex 2
Types of specializations of each crosspoints
Each crosspoint corresponds to a facet of
production Possibility set
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Crosspoints of a modal decomposition of wage
simplex
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A modal decomposition for production possibility
set
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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)

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Supply conditions or demand conditions a good
question?

• Mill
• Mutual demand theory
• Graham
• Supply conditions predominate.
• Demand vs. supply conditions
• gtgtPrice adjustment or quantity adjustment

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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.

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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 homotopy theory
  

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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.

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Production possibility set

• Convex polytope P
• Includes the origin
• Polar relationship
• PolarPp p ltx,pgt ?1, for all x ?Pp
• PolartPolartPpPp
• PolarPpa part of modal decomposition of price
  space
• Correspondense with modal decomposition of wage
  space

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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
  trade.
• The same is true for industrials who have lost
  their market by the increase of trade.

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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.

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References

• A summery in English
• A 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???????(?????)
• English paper
• Evolutionary and Institutionary Economics Review
  (JAEE)