This post continues a previous numericexample. The firms in each of three countries are assumed to know a technology for producing corn, wine, and linen. The technology is such that each commodity can be produced in each country. The technology varies among countries.

Each of these small open economies can specialize and obtain non-produced commodities through foreign trade. I confine myself to patterns of specialization in which:

  • Each country produces exactly one commodity domestically.
  • Each commodity is produced in one country.

Six patterns of specializations meet these criteria. Table 1 lists the commodity produced in each country for each pattern of specialization.

Table 1: Patterns of Specialization
EnglandPortugalGermany
ICornWineLinen
IICornLinenWine
IIIWineCornLinen
IVWineLinenCorn
VLinenCornWine
VLinenWineCorn

I have found out that, in my example, each specialization is consistent with a long period position. I take the international price of corn as numeraire. That is, p1 = 1. Table 2 lists the prices of the other commodities, p2 and p3, that are traded domestically. It also lists rates of profits, r1, r2, and r3, in each country. This data is sufficient to calculate the wage in each country. The wage is such that supernormal profits are not earned in the commodity produced domestically, but the cost (including profits) does not exceed revenues for produced commodities. With these wages, the costs of producing a commodity in which a country does not specialize will exceed the price. It is cheaper in each country to acquire such commodities on international markets.

Table 2: International Prices and Rates of Profits
Price
of Wine
Price
of Linen
Rate of Profits
EnglandPortugalGermany
I3/42/30%0%0%
II0.830.750%0%20%
III0.8833/420%60%0%
IV1.061.360%50%90%
V1.15/440%150%70%
VI4/50.7540%20%20%

The prices shown in Table 2 are not unique. For the given set of rates of profits, international prices must fall within a certain range to obtain a long period position consistent with the pattern of specialization. And rates of profits may vary in certain ranges too. I have not figured out a good way of visualizing how the spaces of prices and rates of profits is divided up by the patterns of specialization. Maybe a region for a given pattern of specialization if, contrary to this example, restitching was possible under autarky.

The numeric example illustrates that:

  • The pattern of specialization in foreign trade can be driven by technology and the distribution of income.
  • Only some distributions are compatible with all countries being able to specialize in a consistent way.
  • The results of such specialization may not provide a country with overall gains from trade, nevermind individual groups defined by the functional distribution of income.

I have assumed constant returns to scale, but which commodity a country specializes in producing may be of importance because of considerations of learning-by-doing. Technological progress may be easier to obtain in some commodities (e.g., manufactured industrial products) than others (e.g., products of agriculture). I suspect these observations generalize to a more comprehensive Neo-Ricardian theory of trade, such as that of Yoshinori Shiozawa.

These theoretical observations, I guess, are enough to blow up much mainstream teaching on trade. I might have even made some progress on the work of Mainwaring, Metcalfe, and Steedman. Nevertheless, this model puts much aside. I am thinking of, especially, Keynesian issues of exports, imports, and effective demand; foreign exchange rates and monetary policy; and international finance.