The positive profit with negative surplus-value paradox

New paper by Lucas (not that one) and Serrano. From the abstract:

This paper explains the “positive profits with negative surplus-value” example of Steedman (1975) and shows that while in joint production systems individual labour values can be negative, the claim that the total labour embodied in the surplus product of the economy (surplus-value) can also be negative is based on assumptions that have no economic meaning (such as negative activity levels). The paper also provides a way to measure the surplus-value of joint production systems which overcomes the problems of the traditional concept and restates the proposition that a positive amount of surplus labour is a necessary condition for positive profits.

Read full paper here. A preliminary version was briefly noted here in 2012. Academic publications are slow indeed.

Free trade and Portuguese decline

Last weekend, as a result of Brad DeLong's post on free trade, we had a brief Twitter exchange. He had suggested that the Heckscher-Ohlin (HO) model* implies gains from trade associated to comparative advantage. He went further and suggested, after I implied that the Methuen Treaty between England and Portugal had not been favorable to the latter, that Portugal had indeed benefited greatly from free trade.

It is important to note, before we get to Portugal, that the HO model, which is a direct application of marginalist theory of value to international trade, arguing that specialization depends on relative scarcity, with countries exporting the goods that use intensively the factor of production that is abundant, is open to the capital debates critique, as shown by Ian Steedman long ago. So the HO model results lack generality, and it is NOT possible to guarantee gains of trade, as suggested by Brad. Actually, there should be no surprise that one finds paradoxes and problems, like the famous Leontief Paradox.

That does not mean that comparative advantage is conceptually wrong. The old Ricardian model does not have the problems of the HO model (Brad would have been on more solid logical grounds using this model). It is open to critiques of its use of the labor theory of value (LTV), but those can be dealt by the Sraffian reinterpretation of the LTV (for that, although not related to trade, go here). Note, however, that Ricardo's model presumes fixed levels of employment (not full employment, but given or constant) and no capital mobility. Anthony Brewer showed (subscription required) that in the Ricardian model, with capital mobility, producers would move to the country with lower costs, basically lower wages (exogenously given by classical authors), and absolute advantage would dominate trade patterns.

So what about trade between England and Portugal, you may ask. In part, the reason why Ricardo, a descendant of Portuguese jews that emigrated to Italy, the Netherlands and then to England, used the cloth-wine/England-Portugal example in his Principles, is because of the Methuen Treaty of 1703, a sort of free trade agreement. If one looks at income per capita (Table below using the Maddison data), one finds that Portugal was, by the time that follows its control of the trade routes to Asia (after Vasco da Gama reached India in 1498), slightly ahead of England, but by 1700, on the eve of the Treaty, it was considerably behind. Yet, by 1750, it seems that Portugal caugth up a bit, only to fall inexorably behind after that. By 1820, the income per capita in Portugal is less than half of the English.

So is there any truth to Brad's view that Portugal benefited from the free trade agreement, you may ask again. The point is that, the Iberian Union (1580-1640), when Portugal was governed by Spanish kings, and the loss of the Asian Empire (but not Brazil) was behind the Portuguese long term decline, which started way before the Methuen Treaty. Guns (and sails, Carlo Cipolla would add), not comparative advantage, were behind the rise and fall of the Portuguese empire in Asia.  The Dutch and then the English would come to dominate those trade routes. And the improvement in income per capita in the 18th century in Portugal can be ascribed to the discovery of gold in Brazil (a little aside, it is the combination of Brazilian gold, the Methuen Treaty, and the infamous mistake in the pricing of silver by Sir Isaac Newton that, arguably, put England on a Gold Standard). Free trade did not explain that.

So the Methuen Treaty by itself did not cause the ruin of Portugal. But it added to the problems associated to the loss of the Asian empire, and created patterns of specialization that did not lead to further technical change and economic development. Trade matters, because what one country produces and exports matters. Complex products with higher value added are more likely to lead to the incremental innovations that are behind the wealth of nations. You may call that increasing returns or cumulative causation. Trade agreements that ossify the production structure in sectors with low levels of technological dynamism lead to lower growth, and, as in any process with path dependency, failure breeds failure. Portugal, like England, needed managed trade, not 'free' trade.

* The model is often referred to as Heckscher-Ohlin-Samuelson (HOS), since Paul Samuelson was instrumental in formalizing the HO theorem and extending some of its results. Also, less frequently the model is referred to as Heckscher-Ohlin-Vanek (HOV), as done by Brad, since Jaroslav Vanek noted that trade of goods is indirect trade of factors of production, providing further extensions to the model.

More on Sraffa and the theory of value and distribution

Two posts by Alejandro Fiorito, at the Revista Circus blog, and Robert Vienneau follow up my previous post on Sraffa and the Labor Theory of Value (LTV). The former is on the debate between Garegnani and Samuelson, just published in a book edited by Heinz Kurz. Garegnani, who debated with Samuelson since the latter's seminal paper on the production function as a parable back in the early 1960s, basically argued against the notion that Sraffa's system can be seen as a special case of Walrasian General Equilibrium, which was ultimately Samuelson's position.

Vienneau discusses several issues. One that I think it's particularly relevant is Steedman's view that one might have a positive profit rate and negative aggregate surplus value. Serrano and Lucas (not that Lucas!) have written a paper on the subject which suggests that Steedman's counterintuitive results are basically irrelevant. At any rate, as noted by Robert, "Marxist political economy should remain a live and exciting field of scholarly research," and this is to a great extent possible because of Sraffa's legacy.

More on "free" trade

In a recent post I promised to develop the critique of the dominant trade model, the so-called Heckscher-Ohlin-Samuelson (HOS) theory. While the Ricardian concept of comparative advantage is based on the labor theory of value (and is compatible with modern versions of that theory, as developed by Sraffa), and its results hold if the assumptions are realistic (limited capital mobility, and a fixed level of employment, the latter could result from domestic demand policies), the HOS is an application of the marginalist theory of value and distribution and it suffers from that theory's inconsistencies.

The HOS theory says that a country exports the goods that are intensive in the use of the factor of production that is abundant in the country. A country with lots of workers, and according to theory cheap labor, would produce goods that are labor intensive and export them, while importing capital intensive goods. The graph below illustrates the argument.

If there are two goods (a and b), and one (a) is always more capital intensive (bigger capital-labor ratio) than the other (b), and in both goods we have that as capital intensity increases (larger K/L ratio) the rate of interest falls, then as the rate of interest falls the relative price of the capital intensive good with respect to the labor intensive one falls too. In other words, in a capital abundant country, capital intensive goods would be cheap, and specialization would be guided by the relative prices.

The capital controversy showed that there is no reason, in a world with multiple capital goods, to have a monotonic decreasing relation between capital intensity and the remuneration of capital. One way in which that effect could be represented would be with a capital intensity reversal in the production of goods a and b, as shown below.

In that case, as the intensity of capital increases (K/L goes up) at first, as before, a is the capital intensive good, but now there is a switch and b becomes the capital intensive good at lower rates of interest. The consequence is that for a part of the process as the capital-labor ratio increases the price of a with respect to b increases, but after the switch, the other part of the process, it decreases. The relative abundance of capital and labor is not a guide for relative prices anymore, and as a result, neither can it determine patterns of specialization.

 

As a result, it is not generally true that trade depends on comparative advantage based on relative scarcities of factors of production. This suggests (as the critique of the Ricardian version of the model) that absolute advantage, lower costs, might be more important than conventional wisdom suggests. Also, it implies that history and institutions are central to understand patterns of trade specialization.

The seminal work in this area was done by Ian Steedman, extending the ideas of Sraffa to foreign trade. The classic papers have been collected in Steedman's edited book Fundamental Issues in Trade Theory.