Foreign Trade And Non-Uniform Rates Of Profits

This post raises a question. Supposedly, the classical concept of prices of production with non-uniform rates of profits can be recast as a theory of foreign trade. I do not see how wages can properly be treated in such recasting.

D'Agata (2018) and Zambelli (2018) are two recent papers that argue prices of production can be formulated with non-uniform rates of profits. They argue that this introduces a certain indeterminateness into prices, as in some of my examples of foreign trade. Both D'Agata and Zambelli cite Adam Smith and David Ricardo to justify their models as of classical inspiration. If somebody is to draw on this research for a theory of foreign trade, I hope they cite this passage from Adam Smith:

… every individual … endeavors as much as he can both to employ his capital in the support of domestic industry, and so to direct that its produce may be of the greatest value; every individual necessarily labours to render the of the society as great as he can. He generally, indeed, intends to promote the public interest, nor knows how much he is promoting it. By preferring the support of domestic to that of foreign industry, he only intends his own security; and by directing that industry in such a manner as its produce may be of the greatest value, he intends only his own gain, and he is in this, as in so many other cases, led by an invisible hand to promote an end which was no part of his intention.

I suspect many propertarians are not aware that Smith was arguing that a lack of foreign direct investment is desirable, that enough barriers exist against entrepreneurs investing in other countries that no need exist for certain protectionist laws to be passed by government.

D'Agata models non-uniform rates of profits as arising due to both "objective and idiosyncratic factors affecting producers' investment decisions". Objective factors are modeled by different groups of producers having access to different techniques of production for producing the same commodities. For example, firms in England and Portugal might have access to different techniques for producing corn and wine, as in Ricardo's Principles. I guess countries having different endowments of land and labor, thereby limiting the scale at which some processes can be operated, is also an objective factor important to the theory of foreign trade.

Idiosyncratic factors are formalized by different producers having different valuation functions, where a valuation function is a continuous, strictly increasing function of the rate of profits obtained in a given industry. In terms of the theory of foreign trade, one might model entrepreneurs in England all having identical valuation functions, while entrepreneurs in Portugal have another valuation function, common among the Portuguese. Each valuation function might be assumed not to vary among industries. For example, English entrepreneurs value the rate of profits made in making corn the same as the rate of profits made in making wine.

From these considerations, one can obtain a theory of foreign trade in which:

• Countries differ among themselves in the technology or endowments they have access to.
• In a full employment position with balanced trade, countries specialize in the production of different commodities.
• In such an equilibrium position, the rate of profits varies among countries.

(I do not claim such a theory is complete, since it does not consider Keynesian effective demand, paths with unbalanced trade, fluctuations in exchange rates, and so on.)

When I have tried to develop such a theory of foreign trade, I have created examples in which the wage also varies across countries. This is easy to justify based on an assumption of a lack of a free movement of people across national borders. But how is this idea formalized in D'Agata's approach?

References

• Antonio D'Agata, 2018. Freeing long-period prices from the uniform profit rate hypothesis: A general model of long-period positions. Metroeconomica 69: 847-861.
• Stefano Zambelli, 2018. Production of commodities by means of commodities and uniform rates of profits. Metroeconomica 69: 791-819.

Robert Visits An American Grave: Frederick Douglass

Frederick Douglass was an escaped slave, a great abolitionist orator, and generally a great American. Not too long ago, I read one of his autobiographies. Of his speeches, I am most likely to recognize bits from his 1952 observations on independence day. (Eldridge Cleaver quotes it in Soul on Ice.) This part is fierce:

What, to the American slave, is your 4th of July? I answer: a day that reveals to him, more than all other days in the year, the gross injustice and cruelty to which he is the constant victim. To him, your celebration is a sham; your boasted liberty, an unholy license; your national greatness, swelling vanity; your sounds of rejoicing are empty and heartless; your denunciations of tyrants, brass fronted impudence; your shouts of liberty and equality, hollow mockery; your prayers and hymns, your sermons and thanksgivings, with all your religious parade, and solemnity, are, to him, mere bombast, fraud, deception, impiety, and hypocrisy — a thin veil to cover up crimes which would disgrace a nation of savages. There is not a nation on the earth guilty of practices, more shocking and bloody, than are the people of these United States, at this very hour.

Frederick Douglass is buried in Mount Hope Cemetery in Rochester, NY. This is a family plot, with his widow at his left.

Variation Of Gains From Trade With International Prices

Figure 1: Intercepts of Production Possibilities Frontiers for England

1.0 Introduction

In this example, gains and losses from trade vary with international prices. Given rates of profits are compatible with an interval of relative international prices for linen and corn, when trade exists only in consumer goods. I explore whether, when trade exists in capital and consumer goods, more than one pattern of specialization among countries is possible, depending on relative international prices. I am beginning to think that specialization, in this model, in corn and linen is infeasible, except in knife-edge cases.

The theory of comparative advantage provides no valid justification for the abolition or the lowering of tariffs. Unregulated international trade is not about efficient use of an international allocation of resources. Many existing textbooks, including Krugman and Obstfeld's, should be ripped up, and the authors should start again.

2.0 Technology, Endowments, And The Rate Of Profits

I assume each of two countries (Tables 1 and 2) have a fixed-coefficients technology for producing three commodities. The technology varies between countries, although it has the same structure in both. Steel is the only capital good. Each commodity can be produced, in a year, from inputs of labor and steel. A coefficient of production shows the quantity of an input needed per unit output. For example, in England, one person-year and 1/30 tons of steel must be purchased per square meter of produced linen. Steel is totally used up in production, and constant returns to scale obtains.

Table 1: Coefficients of Production in England

Inputs	Industry
	Steel	Corn	Linen
Labor	a0, 1(E) = 1	a0, 2(E) = 8	a0, 3(E) = 12
Steel	a1, 1(E) = 1/5	a1, 2(E) = 1	a1, 3(E) = 1

Table 2: Coefficients of Production in Portugal

Inputs	Industry
	Steel	Corn	Linen
Labor	a0, 1(P) = 6/5	a0, 2(P) = 12	a0, 3(P) = 20
Steel	a1, 1(P) = 1/4	a1, 2(P) = 2	a1, 3(P) = 3/2

I take endowments of labor as given, as in the Ricardian model of foreign trade. Let England and Portugal both have available a labor force consisting of one person-year. So Production Possibilities Frontiers (PPFs) are found per person-year. By assumption, workers neither immigrate nor emigrate. In this model, full employment is assumed.

I also take the rate of profits as given, at 100 per cent in England and at 20 percent in Portugal. I assume that financial capital cannot flow between countries. So the rate of profits need not be the same across countries.

3.0 Summary

I apply my usual analysis to determine patterns of specialization, given technology, endowments, and rates of profits in each country. When foreign trade is possible in corn and linen, but not steel, the domestic price of steel and the wage in each country must be such that the going rate of profit is earned in producing steel. Likewise, firms in, say, England make neither extra profits nor incur extra costs in producing the consumer good in which England specializes. The firms would incur extra costs if they were to produce the other consumer good. The same principles extend to the case in which foreign trade is possible in all produced commodities.

In this analysis, which is an example of a small country model, prices for goods bought or sold in foreign trade are taken as given by firms in all countries. I find prices and specializations which are consistent with the given parameters. One can draw Production Possibility Frontiers (PPFs) for each country, given prices in foreign markets and specializations. A PPF shows possible baskets of consumer goods when labor is fully employed. In this model, each PPF is a decreasing function in the first sector of the two-dimensional space formed by quantities of corn and linen. Such a PPF is fully specified by the intercepts. The intercept with the corn axis is maximum amount of corn that can be consumer, per employed worker, given that no linen is consumed. Similarly, the intercept with the linen axis is the maximum amount of linen that can be consumed. Figure 1, above, and Figure 2, show the intercepts for the PPFs for England and Portugal, respectively.

Figure 2: Intercepts of PPFs for Portugal

In the example:

• When foreign markets exist only for corn and linen:
• England specializes in the production of linen (and steel), while Portugal specializes in corn (and steel).
• England suffers a loss from trade, except when the international relative price of linen is at its highest feasible level.
• Portugal obtains a gain from trade.
• England’s loss and Portugal’s gain is smaller for larger relative prices of linen on international markets.
• When foreign markets exist for steel, corn, and linen:
• For a relatively small ratio of the international price of linen to the international price of corn, England specializes in corn and linen, and Portugal specializes in steel.
• In this range, prices compatible with England specializing in linen and Portugal specializing in steel and corn provide England with extra profits in producing corn.
• This case is infeasible. England only obtains steel by trading corn for it. England is unwilling to trade linen for steel, and Portugal is unable to acquire linen by selling steel.
• For a relatively large ratio of the international price of linen to the international price of corn, England specializes in linen, and Portugal specializes in steel and corn.
• In this range, prices compatible with England specializing in corn and linen and Portugal specializing in steel provide Portugal with extra profits in producing corn.
• England obtains a gain from trade, as compared to when foreign trade is only possible in consumer goods
• For a low price of linen in this range and a consumer basket heavily weighted to corn, England suffers a loss from trade, as compared to autarky.
• Otherwise, England obtains a gain from trade, as compared to autarky.
• Portugal’s PPF is identical to what it would be if foreign trade were possible only in consumer goods.
• Accordingly, Portugal obtains a gain from trade, as compared to autarky.

Gain or Loss from Trade with Multiple Equilibria

Figure 1: Production Possibility Frontiers

1.0 Introduction

Suppose foreign trade is possible in consumption goods, but not in capital goods. In this example, whether or not England achieves gains from trade depends on relative international prices. If foreign trade were possible in both consumption and capital goods, both England and Portugal would obtain gains from trade. The numeric example in this post is a modification of one in a previous post.

As I understand it, most students of economics are taught this numeric example cannot exist. And it raises questions on, for example, tariffs and the distribution of income that you will be hard-pressed to find discussed.

2.0 Technology, Endowments, And The Rate Of Profits

I assume each of two countries (Tables 1 and 2) have a fixed-coefficients technology for producing three commodities. The technology varies between countries, although it has the same structure in both. Steel is the only capital good. Each commodity can be produced, in a year, from inputs of labor and steel. A coefficient of production shows the quantity of an input needed per unit output. For example, in England, one person-year and 1/30 tons of steel must be purchased per square meter of produced linen. Steel is totally used up in production, and constant returns to scale obtains.

Table 1: Coefficients of Production in England

Inputs	Industry
	Steel	Corn	Linen
Labor	a0, 1(E) = 2	a0, 2(E) = 3	a0, 3(E) = 1
Steel	a1, 1(E) = 1/20	a1, 2(E) = 1	a1, 3(E) = 1/30

Table 2: Coefficients of Production in Portugal

Inputs	Industry
	Steel	Corn	Linen
Labor	a0, 1(P) = 2	a0, 2(P) = 7	a0, 3(P) = 2
Steel	a1, 1(P) = 1/40	a1, 2(P) = 1	a1, 3(P) = 1/100

I take endowments of labor as given, as in the Ricardian model of foreign trade. Let England and Portugal both have available a labor force consisting of one person-year. So Production Possibilities Frontiers (PPFs) are found per person-year. By assumption, workers neither immigrate nor emigrate. In this model, full employment is assumed.

I also take the rate of profits as given, at 25 per cent, in both countries. I originally intended to assume that financial capital cannot flow between countries. So the rate of profits need not be the same across countries.

3.0 One of Two Equilibria

One can analyze each country under autarky, that is, under the assumption that foreign trade is not possible. One can find, given the rate of profits in each country, relative prices of corn and linen in each country. Suppose foreign trade is possible in corn and linen, but not in steel. And suppose the ratio of the international price of linen to the international price of corn is between the corresponding ratio of autarkic prices in England and Portugal. (I have chosen the rates of profits so this ratio is lower in England than in Portugal under autarky.) Then the English specialize in producing linen, and the Portuguese specialize in producing corn. I consider international prices at the two extreme ends of this range. This section presents the first extreme.

3.1 Trade in Corn and Linen

Table 3 present prices and costs when trade is only possible in corn and linen. I follow the notation in a previous post. The rows show the international price of corn, the international price of linen, wages in each country, the domestic price of steel, the cost of producing corn, and the cost of producing linen. If anybody wants to work it out, wages and the price of steel are such that the given rate of profits is made in producing steel in each country.

Table 3: Trade in Consumer Goods

Variable	England	Portugal
P2	$15 per Bushel
P3	$49/17 per Sq. Meter
w(n)	$45/17 Person-Yr.	$155/99 per Person-Yr.
p1(n)	$96/17 per Ton	$320/99 per Ton
p1(n)a1,2(n)(1 + r(n)) + a0, 2(n) w(n)	$15 per Bushel	$15 per Bushel
p1(n)a1,3(n)(1 + r(n)) + a0, 3(n) w(n)	$49/17 per Sq. Meter	$314/99 per Sq. Meter

Firms in a country will only produce a commodity if its cost of production does not exceed its price. With the prices in the above table, the English are willing to produce both corn and linen, while the Portuguese produce only corn. I want to ignore that the English might want to produce corn. If the price of linen on international markets was just an infinitesimal higher, the English would not be willing to produce corn.

The upper half of the figure at the top of this post illustrates this case. When, at these prices, England specializes in linen, they obtain a loss from trade. Portugal obtains gains from trade throughout.

3.2 Trade in Steel, Corn, and Linen

I now consider this case with foreign trade in steel also. Table 4 shows prices and costs. The first row is for the price of steel on international markets. I also introduce a row for the cost of producing steel. With the same logic as above, I ignore that England can produce steel, as well as corn and linen, with these prices. I take the international prices of corn and linen as unchanged from the previous subsection.

Table 4: Trade in Capital and Consumer Goods

Variable	England	Portugal
P1	$96/17 per Bushel
P2	$15 per Bushel
P3	$49/17 per Sq. Meter
w(n)	$45/17 per Person-Yr.	$93/34 per Person-Yr.
P1 a1,1(n)(1 + r(n)) + a0, 1(n) w(n)	$96/17 per Ton	$96/17 per Ton
P1a1,2(n)(1 + r(n)) + a0, 2(n) w(n)	$15 per Bushel	$891/34 per Bushel
P1a1,3(n)(1 + r(n)) + a0, 3(n) w(n)	$49/17 per Sq. Meter	$471/85 per Sq. Meter

In this case, both England and Portugal gain from trade. England specializes in corn and linen, and Portugal specializes in steel. The possible consumption baskets for both England and Portugal, under trade in all commodities, is also shown in the upper half of the figure at the top of this page. Even if you click through, it is hard to see that the maximum amount of linen that can be consumed in England is strictly greater than autarky in this case. Samuelson calls the additional gains from trade obtained through foreign trade in capital goods as the "Sraffian bonus". I have previously shown that the Sraffian bonus can be negative.

4.0 A Second Equilibrium

Now suppose the international price of linen is at the opposite extreme, with the same specializations. Again, this is the endpoint of what should be an open interval.

4.1 Trade in Corn and Linen

Table 5 shows prices and costs when foreign trade is possible only in consumer goods. English firms make the going rate of profits in producing steel and linen, but would incur extra costs if they produced corn domestically. Portuguese firms make the going rate of profits in producing any of steel, corn, and linen. But I treat them here as specializing in producing corn for foreign trade and obtaining linen only through foreign trade.

Table 5: Trade in Consumer Goods

Variable	England	Portugal
P2	$15 per Bushel
P3	$314/99 per Sq. Meter
w(n)	$4710/1617 Person-Yr.	$155/99 per Person-Yr.
p1(n)	$10048/1617 per Ton	$320/99 per Ton
p1(n)a1,2(n)(1 + r(n)) + a0, 2(n) w(n)	$26690/1617 per Bushel	$15 per Bushel
p1(n)a1,3(n)(1 + r(n)) + a0, 3(n) w(n)	$314/99 per Sq. Meter	$314/99 per Sq. Meter

The bottom half of the figure above shows Production Possibility Frontiers for this case. Both England and Portugal obtain gains from trade. (The PPF for England, under trade in consumption goods, is not easy to visually distinguish from the PPF under autarky.) A given technology and given rates of profits is compatible with a country both obtaining gains and suffering losses from foreign trade in consumption goods, depending on international prices.

4.2 Trade in Steel, Corn, and Linen

International prices of corn and linen are the same in Table 6 below and Table 5 above. Table 6 is drawn up for the possibility of foreign trade in steel, corn, and linen. England specializes in corn and linen, and Portugal specializes in steel. As seen in the bottom half of the figure at the top of this post, both England and Portugal have gains in trade, as compared to autarky and to foreign trade in consumer goods, when trade is possible in all produced commodities.

Table 6: Trade in Capital and Consumer Goods

Variable	England	Portugal
P1	$1448/297 per Bushel
P2	$15 per Bushel
P3	$314/99 per Sq. Meter
w(n)	$2645/891 per Person-Yr.	$5611/2376 per Person-Yr.
P1 a1,1(n)(1 + r(n)) + a0, 1(n) w(n)	$11123/1782 per Ton	$1448/297 per Ton
P1a1,2(n)(1 + r(n)) + a0, 2(n) w(n)	$15 per Bushel	$181/8 per Bushel
P1a1,3(n)(1 + r(n)) + a0, 3(n) w(n)	$314/99 per Sq. Meter	$28417/5940 per Sq. Meter

5.0 Conclusion

In this example, only one process is known in each country for producing each commodity domestically. The possibility of foreign trade creates a choice of technique. I wonder if more processes existed for each country's technology, would the range of international prices for consumer goods consistent with certain national specializations be narrowed? Would the introduction of consumer demand in the model remove the indeterminism? I suppose, for exploring the last question, I should see what has been done with J. S. Mill's approach to analyzing foreign trade.

Elsewhere

• Matthew Klein writes, in Barron's, about "Tarrifs and the Minimum Wage Are More Alike Than You Think". I disagree with some of the stuff in the middle about efficiency and reject the dualistic notion that government intervention is a meaningful concept. But this article otherwise parallels some of my arguments here.
• Josh Mason has made available his piece in Jacobin about the state of economics after the global financial catastrophe.
• The Review of Political Economy has made available Pierangelo Garegnani's posthumous On the Labour Theory of Value in Marx and in the Marxist Tradition. I have yet to read Fabio Petri's introduction. Some points from Garegnani's article:
• Chapter 1 of volume 1 of Capital is not meant to be a proof of the Labor Theory of Value (LTV).
• The LTV fills an instrumental role in providing a calculation of the rate of profits prior to the system of prices of production.
• Much of volume 1 remains valid, even after correcting the mathematical theory. For a given technology, there is a trade-off between wages and the rate of profits. Capitalists try to increase relative and absolute surplus value.
• Marx's account of profits as the result of the exploitation of workers is descriptive, not a moral or ethical judgement.
• Rudolf Hilferding did not have the mathematical machinery (e.g., theorems on the principal Eigenvalue of a matrix) to counter Eugen Böhm von Bawerk's criticism of Marx. Consequently, his attempt is misdirected.

Gains And Losses From Foreign Trade: A Numeric Example

Figure 1: Production Possibility Frontiers

1.0 Introduction

This post presents a numeric example of foreign trade in a model of the production of commodities by means of commodities. This is a modification of the model here, which considers a flow-input, point output technology. As usual, I show neoclassical economics is mistaken. Frictions, increasing returns, information asymmetries, principal agent problems, and so on do not need to be introduced to explain why the outcomes of free markets are not always ideal. Even under ideal conditions, problems can arise.

2.0 Technology, Endowments, And The Rate Of Profits

I assume each of two countries (Tables 1 and 2) have a fixed-coefficients technology for producing three commodities. The technology varies between countries, although it has the same structure in both. Steel is the only capital good. Each commodity can be produced, in a year, from inputs of labor and steel. A coefficient of production shows the quantity of an input needed per unit output. For example, in England, one person-year and 1/30 tons of steel must be purchased per square meter of produced linen. Steel is totally used up in production, and constant returns to scale obtains.

Table 1: Coefficients of Production in England

Inputs	Industry
	Steel	Corn	Linen
Labor	a0, 1(E) = 2	a0, 2(E) = 3	a0, 3(E) = 1
Steel	a1, 1(E) = 1/20	a1, 2(E) = 1	a1, 3(E) = 1/30

Table 2: Coefficients of Production in Portugal

Inputs	Industry
	Steel	Corn	Linen
Labor	a0, 1(P) = 2	a0, 2(P) = 7	a0, 3(P) = 2
Steel	a1, 1(P) = 1/40	a1, 2(P) = 1	a1, 3(P) = 1/100

I take endowments of labor as given, as in the Ricardian model of foreign trade. Let England and Portugal both have available a labor force consisting of one person-year. So Production Possibilities Frontiers (PPFs) are found per person-year. By assumption, workers neither immigrate nor emigrate. In this model, full employment is assumed.

I also take the rate of profits as given, at 300 per cent, in both countries. I originally intended to assume that financial capital cannot flow between countries. So the rate of profits need not be the same across countries. (If you find the rate of profits unacceptably high, read "year" as "decade" throughout this post.)

3.0 Aspects of Autarky

Suppose all three commodities are each produced in each country. Foreign trade is not possible. The technology allows one to calculate the labor embodied in each commodity. For steel, the number of person-years embodied in each ton of steel is:

v₁(n) = a_{0, 1}(n)/(1 - a_{1, 1}(n))

The labor embodied in corn and linen is:

v_j(n) = a_{0, 1}(n) a_{1, j}(n)/(1 - a_{1, 1}(n)) + a_{0, j}(n), j = 2, 3.

Labor values are useful in drawing the PPF for each country, under autarky. Consumers in England can consume 1/v₂(E) bushels of corn per person-year of labor hired, if they consume no linen. Or they can consume 1/v₃(E) square meters per person-year, with no corn. Any linear combination of these two consumption baskets, with positive quantities of both corn and linen, can also be consumed.

Each PPF embodies a rate of transformation between corn and linen, in a comparison of stationary states. For example, in England 61 bushels of corn can be traded off, in some sense, for 291 square meters of line. England has a comparative advantage in linen, as compared to corn, at a rate of profits of zero.

v₃(E)/v₂(E) < v₃(P)/v₂(P)

Portugal has a comparative advantage in steel, as compared to both corn and linen, at a rate of profits of zero.

4.0 Trade in Corn and Linen

In this section, I assume that foreign trade is possible in the consumer commodities, corn and linen. But international markets do not exist in the capital good, steel. The introducition of the possibility of foreign trade creates a choice of technique.

In the small country model, firms take prices, including on international markets, as given. I introduce the following notation:

• P₂: The price of a bushel corn on international markets.
• P₃: The price of a square meter of linen on international markets.
• w(n), n = E, P: The wage.
• r(n), n = E, P: The rate of profits.
• p₁(n), n = E, P: The domestic price of steel.
• p₁(n)a_1,2(n)(1 + r(n)) + a_{0, 2}(n) w(n), n = E, P: The cost of producing a bushel corn domestically.
• p₁(n)a_1,3(n)(1 + r(n)) + a_{0, 3}(n) w(n), n = E, P: The cost of producing a square meter of linen domestically.

Table 3 shows the value of each of these variables. Firms will not produce commodities when their cost of producing it exceeds what it can be purchased for on international markets. Accordingly, England specializes in producing linen and the necessary steel at these prices. Portugal produces corn and linen. The domestic price of steel and wages are such that firms cannot make extra profits in steel, corn, or iron production.

Table 3: Trade in Consumer Goods

Variable	England	Portugal
P2	$6 per Bushel
P3	$2/3 per Sq. Meter
w(n)	$19/32 Person-Yr.	$117/286 per Person-Yr.
p1(n)	$35/64 per Ton	$69/88 per Ton
p1(n)a1,2(n)(1 + r(n)) + a0, 2(n) w(n)	$127/32 per Bushel	$6 per Bushel
p1(n)a1,3(n)(1 + r(n)) + a0, 3(n) w(n)	$2/3 per Sq. Meter	$1869/2200 per Sq. Meter

The ratio of the prices of linen and corn are a key variable here. Countries specialize in the consumer commodity in which relative international prices exceeds the domestic relative price, as calculated under autarky. Since the rate of profits is positive, relative domestic prices differ from the slope of the autarkic PPF. That is, the relative autarky price is what determines comparative advantage, in some sense. But the slope of the autarkic PPF is important in analyzing whether gains from trade are positive or negative.

The possibility of foreign trade in consumer goods has made consumers in England worse off, in a comparison of stationary states. The English PPF is rotated inwards, when firms specialize as induced by these prices. Consumers in Portugal, on the other hand, are better off. Their PPF is rotated outwards.

4.0 Trade in Steel, Corn, and Linen

I now assume trade is possible in all goods, including the capital good. Let P₁ be the price of steel on international markets. Cost of domestic production are modified in the obvious way in Table 4.

Table 4: Trade in Capital and Consumer Goods

Variable	England	Portugal
P1	$10/9 per Bushel
P2	$6 per Bushel
P3	$2/3 per Sq. Meter
w(n)	$14/27 Person-Yr.	$1/2 per Person-Yr.
P1 a1,1(n)(1 + r(n)) + a0, 1(n) w(n)	$34/27 per Ton	$10/9 per Ton
P1a1,2(n)(1 + r(n)) + a0, 2(n) w(n)	$6 per Bushel	$143/18 per Bushel
P1a1,3(n)(1 + r(n)) + a0, 3(n) w(n)	$2/3 per Sq. Meter	$47/45 per Sq. Meter

England specializes in the production of corn and linen, and Portugal specializes in the production of steel. Firms in England obtain the steel they need to continue production by trading corn and linen in foreign trade. Likewise, consumers in Portugal obtain corn and linen from firms selling the surplus steel product in foreign trade. No firm incurs extra costs or obtains extra profits in any process which they operate. And operated process would incur extra costs.

The opening up of foreign markets in steel has made England better off, both in comparison to autarky and in comparison with foreign trade only being possible in consumer goods. (Although it is difficult to see in Figure 1, the intercept of the PPF, for trade in all commodities, with the ordinate strictly exceeds the intercept for the other PPFs). The opening up of foreign trade in steel has made Portugal worse off, as compared to trade only in consumer goods. Whether the Portuguese are better off as compared to autarky is ambiguous. It depends on the consumption basket.

5.0 Conclusion

Why, oh why, do mainstream economists teach untruths about the theory of trade?