A New Construction of the Ricardian Trade Theory

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

2. 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

3. 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.

4. Policy implications: • Ricardian theory • Technology development >>technology importation >>R&D and innovation • Hecksher-Ohlin theory • Capital accumulation, capital importation • Technology development is only a windfall. • No necessity of innovation management

5. 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.

6. Present state of Ricardian theory • J. S. Mill: Mutual demand theory • Graham： Multi-commodity multi-country case • 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 numerical examples, 3×3 cases.

7. Ricardo’s original model: a recapitulation Portugal has absolute advantage both n cloth and wine. Comparative advantage: 120/100 > 80/90 Portugal has comparative advantage in wine and England in cloth. Specialization pattern: England exports cloth and Portugal exports wine.

8. 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 • wine120 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.

9. Ricardo’s original model: a revised one • Trade conditions: • cloth 10 we ≦ 90 wp • wine12 we ≧ 80 wp • Wages must satisfy: • 6.67 =80/12 ≦ we/wp ≦90/10=9 • In this case English workers gains at least 6.67 times of Portuguese workers.

10. 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.

11. 3-country 3-commodity case 1 No intermediate goods: Wage simplex:

12. 3-country 3-commodity case 2 No intermediate goods. A modal decomposition of production possibility set. Seen from the origin.

13. 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.

14. Trade of intermediate goods

15. 3-country 3-commodity case 3 With intermediate goods

16. 3-country 3-commodity case 4 A modal decomposition of wage simplex

17. 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).

18. A result of numerical experiments Experiments by Mathematica

19. A modal decomposition of wage simplex 1 Patterns of specialization For each 2 cell (domain)

20. A modal decomposition of wage simplex 2 Types of specializations of each crosspoints: Each crosspoint corresponds to a facet of production Possibility set

21. Crosspoints of a modal decomposition of wage simplex

22. A modal decomposition for production possibility set

23. Dual relations between two modal decompositions: 3 country 3 commodity case

24. 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

25. 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.

26. Mathematical feature of RTT • Existence theorem (Weak version) • Fare partition theorem • Combinatorial discussion • Existence of equilibrium • Existence theorem (Strong version) • New theorem • Combinatorialdiscussion + simple homotopy theory

27. 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.

28. 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 decomposition of wage space

29. 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.

30. 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.

31. 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:『経済学雑誌』(大阪市立大) • English paper: Evolutionary and Institutionary Economics Review (JAEE)