Ricardo’s numerical example versus Ricardian trade model: A comparison of two distinct notions of comparative advantage

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The so-called Ricardian trade model of contemporary economic textbooks is not a rational reconstruction of Ricardo’s famous numerical example in chapter seven of the Principles. It differs from the latter in terms of definition of the four numbers, relevant cost comparison, rule of specialisation, assumptions and theoretical implications. Thus, the widespread critique regarding the unrealistic assumptions of the textbook trade model does not apply to Ricardo’s original proof of comparative advantage.

Posted for comments on 5 Jul 2016, 1:51 pm.

Comments (5)

  • Tiago Camarinha Lopes says:

    The paper presents an accurate description of how current models of trade presented in textbooks differ from the original example of David Ricardo’s chapter 7 of Principles of Economics. It argues that it is not possible to defend that these two models are the same, an argument which is recovered from Parrinelo (1988), who previously pointed out to the differences between Ricado and the ricardian trade model. So the paper strongly suggests researchers to read the original source without prejudgment. I fully agree with this claim, which helps bringing attention of researchers back to the primary example of England and Portugal trading wine and cloth.

    The author explains that the theory of comparative advantages, which is one of the milestones of the political effort to open barriers for international trade, has many critics. Many of these criticism are directed to the unrealistic assumptions, so that, in their view, reality is much more complex and the model could not conclude decisively in favour of free trade between nations. The problem is that those assumptions do not exist in the original Ricardo’s example, so it is not correct to consider that this type of critique affects him.

    The author then presents the reader with a detailed description of the modifications that took place in the process of popularizing Ricardo’s example in the textbooks, so that one can actually see that many assumptions were inserted in the model as it became more and more complex. This speaks decisively in favour of the paper, because the comparative advantage is a very important concept taught in economics, but few recall the very first example presented by Ricardo in 1817.

    The paper correctly differ characteristics that do not belong to the original example from those that do belong to Ricardo’s original model. It shows that, although modern trade models are not exactly the same, they indeed maintain some of the original ideias. So, in the end, which model is best suited to defend the thesis that concentration of efforts according to relative capabilities of production preceding trade is the best policy for labor division among countries? The author tries to convince the reader that Ricardos original system is better than the textbooks trade models. Here, I would suggest a more precise pattern for comparison. If we were to choose between these two models in order to use them at some empirical test, the more sophisticated scheme of trade models would be better off. We need then to check for what reason are we comparing them. I believe that the author’s assertion is fully correct if the purpose is to teach the principle of comparative advantage. For educational proposals, Ricardo’s original example is indeed more simple, direct and elegant than the complex models. From my own experience as economics lecturer, I can say that the original source certainly help the students not only to understand more easily the main idea of comparative advantage, but also to grasp the historical context in which the idea was developed. When the original source is used as a guide to teach the theory of free international trade, then talking about the geopolitical context that originated british liberalism becomes also a necessity. So, the original model is not superior in any case: but precisely when we need to recover the history of this model, going back to Ricardo’s Principle and the debates of Classical Political Economy.

    In that sense, it would be very interesting to have further considerations on the geopolitical side of the story behind the pledge for free trade that stems from the comparative advantage argument. It would be then necessary to separate the technical discussion from the political one, and it would be clearer to the reader that the theoretical model is serving the specific purposes of the strongest nation ahead of the mercantile-industrial raceway. I believe this separation is important because comparative advantage derives from the optimal solution of resource allocation, as described by linear programming methods of solving maximization problems. It is impossible to undermine it from a technical point of view, which does not consider the relations of property above relations of concrete production. The gains from this maximization is another story: it is the story of the structure of property behind the nations in conflict to take the most of the increases originated by labor division across the globe. This other side of the story is crucial to understand not only the British Empire but today’s advocates of free trade in those areas where they have the greatest chances to capture the value increases derived from the division of labor. That would take us to the topic of imperialism, which could then close the paper.

    So, in my view, there are only two things that would still increase the paper’s quality: to indicate that the superiority of Ricardo’s model is undoubtful not in every aspect, but only when the purpose is to teach the principles of comparative advantage and the historical context in which it emerged.

  • Jorge Morales Meoqui says:

    I would like to express my gratitude to Tiago Camarinha Lopes for his interesting and encouraging review of my paper. I am very pleased that he agrees with its central statements. In particular, he mentions in the review that the paper accurately highlights the significant differences between Ricardo’s famous numerical example and the textbook trade model. Because of these differences, researchers should not interpret the original numerical example in the Principles through the lenses of the textbook trade model. Instead, they should read it without prejudgment.

    Tiago further supports the claim that Ricardo should be absolved from the widespread critique regarding the unrealistic assumptions of the so-called “Ricardian” trade model, because his original numerical example does not rely on any of the criticised assumptions.

    He also acknowledges the fact that the increased complexity of the textbook trade model was not the unavoidable side effect of trying to make Ricardo’s numerical example more realistic, but rather the result of crucial misinterpretations of it.

    Finally, Tiago agrees with me that Ricardo’s numerical example is better suited for teaching the comparative-advantage insight.

    Notwithstanding these significant areas of agreement, there is a single point in which our respective views seem to differ. While Tiago apparently thinks that the superiority of Ricardo’s numerical example is limited to the teaching of comparative advantage, I consider it to be superior to the textbook trade model in other aspects as well. They are explained in the paper with some detail in section 6 titled “Main advantages of Ricardo’s numerical example over the textbook trade model”. Besides the already mentioned advantage with regard to the assumptions, I also point out there that the numerical example in the Principles offers a simpler way of calculating the gains from trade, and that its main propositions are easier to test empirically. Unlike the textbook trade model, Ricardo’s proof of comparative advantage is compatible with Smith’s productivity theory and explanation of international trade patterns.

    In fact, I cannot think of any relevant aspect in which the textbook trade model might excel the numerical example in the Principles. Perhaps Tiago can help me out here by further elaborating on the alleged advantages of the textbook trade model over Ricardo’s proof of comparative advantage.
    With regard to the recommendation of including an analysis of the historical context and geopolitical considerations surrounding the formulation of comparative advantage and its role in the debate on free trade in Britain, these are indeed interesting topics. As I have already indicated in a previous article (Morales Meoqui, 2014, p. 30), Ricardo stated his unequivocal support for free trade in the Principles along the lines of Smith’s productivity theory and prior to the enunciation of the comparative-advantage proposition. He did not use comparative advantage as a decisive argument in favour of free trade.

    I am doubtful though that the addition of a comprehensive analysis of these topics would increase the quality of the paper. Its most certain effect would be an increase in the length of the paper. In order to accommodate this analysis within the given space limit, it would be necessary to shorten significantly the argumentation in support of the main claims of the paper. I am sure that Tiago agrees with me that this would not be a prudent choice, given the fact that these claims are hotly contested in the economic literature. Therefore, it seems to me that an analysis of the historical and geopolitical context surrounding the formulation of comparative advantage would be better suited for a separate paper.

    Finally, I would like to thank Tiago for his valuable comments. They will be very helpful in the revision of the paper.

    Morales Meoqui, J., 2014. Reconciling Ricardo’s Comparative Advantage with Smith’s Productivity Theory. Economic Thought, 3(2), pp.21–37. Available at: http://et.worldeconomicsassociation.org/files/WEA-ET-3-2-MoralesMeoqui.pdf

  • Tiago Camarinha Lopes says:

    I would like to share my thoughts on Jorge Morales Meoqui’s response to my review. First, I feel that he has seriously engaged with all the points I have mentioned and has correctly understood my perspective on the issue. I agree with almost everything in the paper, as he adequately described. The only matter where there is divergence regards the extension of superiority of Ricardo’s model over textbook international trade models. In my view, text book models could help empirical studies better than Ricardo’s. So Ricardo’s model would be better suited for teaching the principles of comparative advantage, and text book models (with all necessary adjustments made by the researcher) would be more adequate to investigate the concrete situation of production division between different economic unities. So, I am looking to find a possible continuity between Ricardo and those models, which Meoqui tries to delete. Anyway, there is a very positive effect in his effort to detach Ricardo from the neoclassical textbook framework, which I fully support.

    Moreover, I contend that his arguments are very strong to defend his perspective. Also, I am not capable at the moment to show with numerical examples the superiority of text book models over Ricardo’s model. I must say that in this respect, I would have to study the matter with greater caution to check if my position is more closer to the truth than Meoqui’s position, as I think it is.

    So, despite this particular divergence, I am fully in favour of publishing Meoqui’s paper as it is. I agree that the suggestions on the geopolitical context of the model go beyond the purposes of this work. The further development of this debate could occur as a formal reaction to the published paper.

  • Andrea Maneschi says:

    Morales Meoqui’s paper addresses an important topic in trade theory and policy, and clarifies significant differences between Ricardo’s own trade model and the way it has been presented and at times misinterpreted in textbooks. I agree with the main thrust of the paper, and believe it will attract the attention of trade theorists and historians of economic thought. My suggestions to further enhance its quality are the following:

    1) What the author refers to as “the classical rule for specialization” (pp. 8, 11, 12) is also known (thanks to Jacob Viner in the 1937 book that the author cites) as the eighteenth-century rule. It would be good for the author to point this out in order to avoid any confusion on the reader’s part.

    2) The author compares what he calls “the textbook rule” of specialization (that proposed by most trade textbooks) with “the classical rule for specialization” to verify if they select the same commodities for specialization and trade. By changing 120 to 95 for the men needed to produce the wine in England, he makes what he calls a “slight variation” in one of the four numbers (80, 90, 100, 120) chosen by Ricardo for the men needed to produce the bundles of cloth and wine traded by England and Portugal. He finds that the two rules for specialization then lead to different conclusions.
    In my opinion, this is not a “slight” or marginal change in this set of four numbers, but a substantial one. More importantly, the new set of four numbers no longer give England and Portugal the incentive to trade with each other. For both countries, the labor embodied in the export of wine is smaller than that embodied in the import of cloth, so both countries wish to export wine, but no country wishes to import it in exchange for cloth. In terms of the symbols that appear in Table 1 of the paper and are defined on p. 7, for England (Portugal) to be willing to export cloth (wine) and import the other commodity, the numbers chosen for Ce, We, Cp and Wp must be such that Ce < We and Wp < Cp, as the author himself points out on p. 8. Since the modified four numbers are Ce = 100, We = 120, Cp = 90 and Wp = 95, they satisfy the inequality Ce < We, but not the inequality Wp < Cp, so that trade cannot take place. Hence these numbers cannot be used to test whether the classical rule and the textbook rule lead to the same conclusions regarding the pattern of trade and comparative advantage.

    3) The author states on p. 16 (and repeats on p. 24) that “The textbook trade model implies of course complete specialization by each trading partner according to its comparative advantage.” This is not necessarily the case. In the chapter devoted to the two-commodity Ricardian trade model in most international trade textbooks, two possibilities are envisaged: first, that the two countries specialize completely in their export commodity (the only case analyzed by Morales Meoqui), and second, that the “small” country specializes in its export commodity, while the “large” country produces both goods (because the small country cannot satisfy the larger country’s total demand for the importable commodity). Hence, complete specialization is not a forgone conclusion.

    4) On p. 16 the author notes correctly that Ricardo, in his lengthy footnote on p.136 of the Principles, discusses the possibility that a country may not specialize completely in its export commodity. It is worth pointing out that this eventuality is also mentioned in the text of the Principles on pp. 134 and 137, so that it is not an adventitious and unlikely event, but a realistic possibility in Ricardo’s trade model. When his model is extended to more than two traded commodities (a case analyzed by Viner among others), complete specialization by both countries in a single commodity becomes of course impossible. Ricardo himself mentioned the need for his trade model to extend to more than two commodities.

    5) On p. 19, the author states that “Ricardo did not bother to explicitly mention the cost of carriage.” But Ricardo in fact did allow for transportation costs, as the author himself admits in footnote 36 (p. 22 of his paper), quoting Ricardo’s Principles.

    6) In my opinion, Gottfried Haberler’s trade model is unfairly disparaged on pp. 26-7. In the trade literature Haberler is usually given credit, together with Heckscher and Ohlin, for generalizing the CULC (constant unit labor cost) Ricardian model by introducing other factors of production besides labor in the context of neoclassical production functions. In the two-commodity case, these lead to concave (rather than linear) transformation curves, which increase the likelihood that countries become incompletely (rather than completely) specialized in their export commodities. Haberler should be given credit for generalizing the Ricardian trade model which was based on linear transformation curves. The Ricardian trade model had led countries (in most cases) to specialize fully in their export commodities. Haberler’s model is not a one-factor, 2-2-1 model, but a multi-factor (and possibly multi-commodity) neoclassical (and hence non-Ricardian) model that became in the 1930s (together with Heckscher and Ohlin’s) the mainstream trade model.

    • Jorge Morales Meoqui says:

      I’m thankful for the thorough review of my paper by Prof. Maneschi. He is a well-known expert on the topic of comparative advantage, who has played a major role in spreading the correct interpretation of the four numbers in Ricardo’s famous numerical example in recent years, so it is very encouraging for me to read that he agrees with the main thrust of the paper.

      I certainly appreciate all his suggestions, which will be indeed very helpful in enhancing the quality of the paper. Notwithstanding, I would like to comment specifically on the suggestions 2) and 6), where there seems to be a difference of opinion.

      Let us start with the second suggestion. The purpose behind the two numerical examples on page 13 is to demonstrate that the current rule for determining comparative advantage suggested by economic textbooks is not logically equivalent to the rule used by Ricardo, since they do not always yield the same results from identical inputs.

      The numerical proof for this is provided with the least possible alteration to Ricardo’s numerical example, since only one of the original four numbers was modified. In the first example on page 13, the quantity of men working for a year required to produce wine in England was reduced by approximately 20 %, from 120 men to 95. Following Ricardo and the classical rule for specialisation, this change would have a substantial effect on England. The import of wine from Portugal would cease to be beneficial for her under the new conditions, because she could save the labour of 5 men by starting to produce the wine internally, as indicated in the paper.

      Maneschi suggests that the new set of numbers cannot be used to test whether the classical rule and the textbook rule lead to the same conclusions regarding the pattern of trade and comparative advantage, because no trade would take place under these conditions due to a lack of interest by one of the trading partners (England). But how does one prove that this exchange is not in England’s interest? Maneschi refers in the review to pages 7 and 8 of the paper, where I have only applied the classical rule for specialisation. What does the assessment of this exchange with the textbook rule for specialisation on page 13 indicate, though?

      According to the textbook method for determining comparative advantage and the pattern of trade, the exchange might still be in England’s interest, because the proposed change in her wine-making process does not alter the result provided by the comparison of cost ratios (80/95 < 90/100) and its corresponding rule for specialisation; England would still export the good (cloth) in which she has the smallest absolute disadvantage, and Portugal would export the good (wine) in which she has the largest absolute advantage.

      A second contradictory assessment by the textbook rule and the classical rule for specialisation is highlighted in the last paragraph of page 13. This time the number of men working for a year required to produce the wine traded in Portugal increased to 95 men. As indicated in the paper, the textbook rule for specialisation suggests that the exchange under the new set of numbers is in Portugal’s interest, whereas the classical rule for specialisation clearly shows that the import of English cloth would cease to be beneficial for her.

      Therefore, I believe that both numerical examples on page 13 are perfectly suitable for demonstrating that the textbook rule for determining comparative advantage is not logically equivalent to the classical rule used by Ricardo.

      Regarding suggestion number 6, I don’t think that Gottfried Haberler’s trade model is unfairly disparaged in the conclusions. I merely recommend there to rename the textbook trade model of comparative advantage after Haberler instead of Ricardo, since the former had the greatest influence on its current formulation, as has been recognised in the literature. Therefore, the critical assessment of Haberler’s work is limited to his alleged accomplishment in reformulating Ricardo’s numerical example in terms of opportunity costs in 1930. Based on several reasons indicated in the paper, Haberler’s alleged accomplishment in this respect seems utterly questionable. It has been shown, for example, that his reformulation was based on a significant misinterpretation of the relationship between comparative advantage and the labour theory of value. Moreover, Haberler’s reformulation also introduced such unrealistic assumptions as perfect internal mobility and full employment of the factors of production into the mainstream demonstration of comparative advantage. These assumptions, among others, are responsible for the current perception that the trade model of comparative advantage is unrealistic.

      It is still a pending task for scholars to revaluate Haberler’s general contributions to international trade theory in the light of the significant reinterpretation of Ricardo’s numerical example that has been taking place in the last two decades. Such a complete reassessment of his work, though, is beyond the scope of the present paper.

      With respect to suggestions number 1), 3), 4) and 5), I fully agree with them. The suggested references and corrections will be added to the corresponding passages in the paper.