I read the paper and I think that it is a good paper on the subject and for this reason should be published in a specialized international journal

Hi, I ve just read the paper, it is really very interesting and provides remarkable insights for both theories.

I believe that there is a potential problem with absolute advantage. If there is one country that does not have an absolute advantage in the production of any product, will there still be benefit to trade, and will trade even occur? The answer may be found in the extension of absolute advantage, the theory of comparative advantage.

I think that in Ricardo's comparative advantage theory there are several assumptions that limit the real-world application. The assumption that countries are driven only by the maximisation of production and consumption, and not by issues out of concern for workers or consumers is a mistake.

Hi Konstantinos,

Thank you for your kind words and interesting comments about my paper.

Regarding the question about absolute advantage and the benefits of trade, my short answer is yes. Even in the case when a country does not have an absolute advantage in the production of any product, it would still benefit from trade.

The explanation for this counterintuitive answer lies in the classical rule of specialization, which is the relevant rule for specialization. The classical rule of specialization makes an internal cost comparison (loosely speaking one can say that it is similar to a make-or-buy decision). It is therefore not dependent on any kind of external advantage.

With regards to the unrealistic assumptions associated with comparative advantage, I’m currently working on a paper that argues that the bulk of these assumptions were made by the so-called Ricardian trade model, which can be found in contemporary economic textbooks. This textbook trade model, however, has very little in common with Ricardo’s original demonstration of comparative advantage in the Principles. I have attached to this message a link to the first draft of the mentioned paper.

I agree with you that such a narrow view (maximization of production and consumption is the only thing that matters) would be a mistake. However, increasing production is crucial for reducing poverty and satisfying the growing needs of the population. And it is up to the will of the citizens in democratic societies to put the regulatory framework in place that has to be observed while pursuing the goal of increasing production.

Preprint Ricardo’s Numerical Example Versus Ricardian Trade Model: A ...

Hi Jorge, well said. Your paper on Ricardo' s comparative advantage vs. Ricardian model of international trade is very interesting. The principle of comparative advantage states that a country should specialise in producing and exporting those products in which is has a comparative, or relative cost advantage compared with other countries and should import those goods in which it has a comparative disadvantage . Out of such specialisation, it is argued, will accrue greater benefit for all.

Thanks, Konstantinos.

I am trying to draw the attention to another rule, the classical rule of specialisation. According to my interpretation of Smith and Ricardo, this rule was the only one which both considered as relevant for specialisation.

Just think of the following example: before someone decides to buy a product, let’s say bread, this person might think for a brief moment: Should I buy it or make it by myself? In order to make the correct choice, this person should compare the amount of labor time it needs to make the bread (plus the ingredients) with the amount of labor time it needs to earn enough money in order to buy the bread. If self-production requires more labor time, than this person should buy the bread. Otherwise, it should make the bread at home.

I grant that this kind of question is not very common nowadays. But this is only so because nowadays most products are either so affordable or complex that the possibility of self-production is evidently not efficient or even feasible. But this was quite different in Smith’s and Ricardo’s times.

Smith argued, and Ricardo agreed, that the division of labor was essential for increasing labor productivity and wealth.

Thanks for the hint, Hak Choi.

I read your paper. You are using here the old interpretation of Ricardo’s numerical example. Perhaps you would like to refer in your paper to the new interpretation. You can find it in the attached paper.

Preprint Comparative Advantage and the Labor Theory of Value

Choi, and you seem to be obsessed with proving Ricardo wrong. Perhaps you should dedicate more effort in trying to understand what he actually wrote.

Smith offers in the Wealth of Nations a good explanation for the persistency of trade barriers and protectionist trade policies: "To expect, indeed, that the freedom of trade should ever be entirely restored in Great Britain, is as absurd as to expect that an Oceana or Utopia should ever be established in it. Not only the prejudices of the publick, but what is much more unconquerable, the private interests of many individuals, irresistibly oppose it (WN, ii. 43)."

If you take the time to read the paper, you will find out why I consider Ricardo's insights regarding comparative advantage still perfectly relevant nowadays.

Dear colleagues,

The paper has been published now. You can find a copy of the publisher version in the attachment.

I would like to thank you all for your valuable comments.

Best regards,

Jorge

http://et.worldeconomicsassociation.org/papers/reconciling-ricardos-comparative-advantage-with-smiths-productivity-theory/

Congratulation Jorge for the publication of your interesting paper.

Note: This discussion is based on reading the final version of the paper that appeared in Economic Thought 3(2): 21-37, 2014. I have also argued on Morals Meoqui's paper on Comparative advantage and the labor theory of value that appered in History of Political Economy 43(4):743-763, 2011.

Morales Meoqui's paper Reconciling Ricardo and Smith gives a new insight on the theoretical relations between two masters of classical economics. They have much in common. To emphasize their differences has a risk to blur the fundamental opposition that lies between classical and neoclassical economics. On this reason, I agree with him on 2 of his 3 mains claims. They can be better summarized as follows:

(1) Smith and Ricardo both considered productivity growth important and it was one of their major concerns. 

(2) Ricardo used the classical rule of specialization when he cited this famous four numbers. Smith and Ricardo appealed to the same classical rule of specialization and in this regard they had much in common.

The third point that Morales Meoqui (MM afterwards) claims is questionable. It is too much influenced by the neoclassical trade theory, i.e. Heckscher-Ohlin-Samuelson theory of international trade.

The misfortune MM encountered was that he believed that the deformed  (or inaccurate) interpretation of Ricardo's four numbers (in opposition to the accurate interpretation) was derived by the constant-labour-cost assumption. Constant-labor-cost assumption has no relevance with accurate or inaccurate interpretation of Ricardo's four numbers.  

It is possible and more plausible to understand Ricardo's theory of international trade on the basis of constant returns than to reject it. He is obsessed by this unfortunate idea and repeats many times this idea. The expression "constant returns to scale" appears 2 times and "constant-labour-costs assumptions" 7 times in his paper. In all occasion, he repeats that "the whole notion about Ricardo's alternative logic [wrong and deformed interpretation after MM] appears to rest" on this notion (p.24). In reality, there is no reason that constant-returns-to-scale assumption forced people to a deformed interpretation.

MM's another misconception is that he is firmly believing that constant returns and productivity growth are incompatible. MM misunderstands that if one accepts constant returns to scale one has to assume that production technique remains the same forever. Nobody claims such a non sense. MM is confused because he makes no distinction of time scales between constant to returns to scale and productivity growth. The law of constant returns to scale refers the stability of unit costs when the scale of production varies in a short lapse of time, when the knowledge on production process remains the same. Productivity growth refers to the results obtained from the improvements of the production process. It is a result of technical progress. The improvement is irreversible whereas returns-to-scale is reversible in the sense that the cost returns to the original level when the production volume returns. In other words, constant-returns-to-scale is atemporal whereas productivity growth is intertemporal concepts.

The notion of "increasing returns to scale" is always ambiguous because it may indicate tow possibilities: one is the reduction of average unit cost when the production volume increases (due to the existence of fixed costs) and another is the technical progress obtained by the lapse of time (due to the accumulation of experience and knowledge) and the possibility of greater division of labor due to the bigger volume. It is necessary to note that the latter requires a new division of labor and includes new arrangement or workplace and production methods. It requires time.

MM's idea on the incompatibility is motivated by his desire to refute Krugman's contention that "comparative advantage and increasing returns to scale are two separate and mutually exclusive explanations of the pattern of trade".(p.30) I understand MM's intention, but his claim is not well organized. Krugman showed a mechanism by which intra-industry trade occurs. His example is based on a extremely unrealistic assumption that all the competing firms have the same cost functions and specialization occurs purely incidentally. A firm specializes in a variety of products and gains the better cost position by the fact that it has a lesser unit cost because it produces more than others. He refers to technical progress due to the accumulation of experience but this is secondary to his logic of intra-industry trade. His starting model assumes the complete symmetry of all firms (the same cost function for all firms). He did not produce a theory by which to analyze what will happens when this asymmetry is destroyed.

MM's third point is not well formulated. Ricardo considered many factors that will influence patterns of trade, but it is probable that his logic is different from what MM thinks. Heckscher and Ohlin picked up the differences of factor endowments as a main cause that determines patterns of trade. In the HOS model, this is formulated based on the assumption that all countries have the same production techniques. It is the proportional differences of factor endowments that determine the pattern of trade.

Ricardo as well as Smith was aware that "soil, climate and locations" are related to the productivity. They knew that dexterity (or skills) of workers and introduction of machines influence greatly the productivity and thus the cost of production. There is no reason that they believed (like Heckscher and Ohlin or other neoclassicals) that proportional differences of factor endowments influenced directly the patterns of trade and specialization.

The biggest defect of MM's arguments is the lack of logic that determines pattern of trade. He only claims that Smith and Ricardo adopted multifactor approach in explaining the current pattern of international trade. There is a cumulative causation between specialization and productivity improvements. Smith and Ricardo, I believe, never denied this. This explains why the trade pattern shows certain stability but, this does not explain why some country comes to export products that were once what it has imported from abroad. MM has no logic to explains this.

What is usually called comparative advantage is the logic which explains which products is best suited for which country. This is a logic which is operative at a point of time. When time passes and technical competence changes, the pattern of trade changes. An aspect of this dynamic development was once analyzed by Kaname Akamatsu and this theory was usefully analyzed to explain the patterns of trade and specialization which immerged in East and South East Asia after 1980's. I have once explained why this catching up process frequently occurs in my paper (Section 5 Flying geese and fragmentations in The Economics of Great Unbundling).

MM lacks the logic of what determines pattern of trade. He only insists that it is determined by multifactor approach but he never make clear what is multifactor approach except that similar approach was adopted by neoclassical HOS theory. There is a good reason why he lacks this logic. MM believes that Ricardo presented his four number example to show that "the labour theory of value does not regulate the relative value of commodities in international trade"(pp.28-29). I agree with him that the theory of value that Ricardo constructed within a country does not apply to the international trade. I do not agree with him on this point. It seems that MM is thinking that we can go without any theory of international values (or a theory which determines exchange ratios between products which are exchanged internationally).

I believe that Ricardo tried to construct a new theory (a theory of international values) that is valid for international trade and is a generalization of the theory of domestic values. Labor theory value is irrelevant to this problem. Ricardo himself discarded this in the presence of material inputs of different proportions. The cost of production was what he believed to be the valid formula. It is the cost of production which ultimately regulate price (Ricardo, Principles, Note 9 to Chapter 2). He means by cost the cost of production including profits (Ricardo, Principles, Note 4 to Chapter 1). He could not arrive to formulate fully his theory of value even for exchanges inside a country and we have to wait until Sraffa finally formulate it in 1960.

Ricardo could not succeed in finding or construction a new theory of international values. The question of constructing a new theory of international values remained for along time unsolved, except that Mill and Marshall deformed the problem by their theory of reciprocal demand. Although it is difficult, it is possible to construct a new theory of international values and a new theory is already constructed for a wide range of situations: many country an many commodities, input trade and choice of techniques.

See some of my papers:

Final Resolution of the Ricardian Problem on International Values

(the core paper of my book : A Final Solution of the Ricardo Problem on International Values)

https://www.researchgate.net/publication/236154234_Final_Resolution_of_the_Ricardian_Problem_on_International_Values

The Revival of Classical Theory of Values (with presentation dataset)

https://www.researchgate.net/profile/Yoshinori_Shiozawa/contributions

The Economics of the Great Unbundling (with presentation dataset)

https://www.researchgate.net/publication/272943681_The_Economics_of_the_Great_Unbundling

On Ricardo's Two Rectification Problems (with presentation dataset)

https://www.researchgate.net/publication/266737921_On_Ricardo%27s_Two_Rectification_Problems

Conference Paper On Ricardo's Two Rectification Problems

Conference Paper The Economics of the Great Unbundling

Dear Prof. Shiozawa, 

Many thanks to you for taking the time to read and comment my paper. I am happy to read that we agree on two fundamental points. 

 On the third point – i.e. that Ricardo agreed with Smith’s multifactorial explanation of the pattern of trade, which includes increasing returns and economies of scale – you have touched several interesting subjects. That is why I would like to propose to you to discuss them one by one, perhaps in a series of shorter exchanges. 

 You wrote that my third point is too much influenced by the neoclassical trade theory. I’m surprised by this interpretation, because my purpose is in fact the complete opposite: to purge the contemporary interpretation of Ricardo’s numerical example from the last vestiges of the neoclassical theory of international trade. That is why I insist so much that the constant-labor-costs assumption has no place whatsoever in classical political economy in general, and in Ricardo’s theory in particular. This assumption belongs rather exclusively to the neoclassical school of economic thought.

 I do not believe that the inaccurate interpretation of Ricardo's four numbers was derived by the constant-labour-cost assumption. What I actually wrote is that the erroneous attribution of the constant-labor-cost assumption to Ricardo was the consequence of the misinterpretation of his numbers as unitary labor time costs. With the correct interpretation of the four numbers it is clear now that Ricardo did not use this assumption in the famous numerical example nor elsewhere in the Principles. 

As the paper has shown, the constant-labor-costs assumption is incompatible with important passages of the Principles, as well as with Ricardo’s proven adherence to Smith’s productivity theory. Notwithstanding,  you claim that it is possible and more plausible to understand Ricardo's theory of international trade on the basis of constant returns than to reject it. I would like to know which aspects of Ricardo’s international theory require this assumption.

Dear Jorge Morales Meoqui,

You prose to discuss several points one by one, perhaps in a series of shorter exchanges. Yes, it is necessary. So let us start from verifying the basic concepts.

When you say "labor cost," I suppose you are talking about total (labor) cost for producing something and for a certain amount of it. I start from this rather silly point, because when Ricardo used the expression "labour cost" two times in his Principles of Political Economy, he meant simply the wage rate of workers. (See I.37 (section 3) pp.26-27 in Sraffa's edition) When I say labor cost it means (wage rate)×(amount of labor necessary to produce a certain quantity of a commodity). 

We may have to distinguish two different concepts: constant-unit-cost assumption and constant-labor-cost assumption. The former means that the unit cost for a production remains constant when the scale (or speed) of producing the commodity varies at a certain time period and state of technology. Constant unit cost can change enormously when the production process changes by accumulation of experience and technology.  

I am not very sure what you mean by constant-unit-cost assumption. Normal understanding of this expression is that the labor cost remains constant when the scale of production changes at a certain lapse of time where the production process and knowledge concerning it remains the same. When time passes by, the labor cost per unit of product changes enormously. I suppose you are not demanding that this remains constant for many years.  Nobody asserts such a clearly false claim.       

Ricardo argued in many places that labor necessary to produce a product and assumed that this labor cost occupies the major part of the total unit cost. However, he admitted that the value is determined by cost, including (justifiable) profits. See the footnote at the end of Section VI of Chapter 1. Unit production cost includes all costs of inputs, labor and material.

My main contention is that the unit production cost for majority of industrial commodities remains constant when the scale of production is changed in a short time span and this is the very basis of classical theory of value, including Ricardo and Smith.

John Stuart Mill starts to discuss change of the unit cost when the scale of production was changed. This is one of reasons that Mill is said to open the way to neoclassical theory of values. Laws of various returns to scale came to be discussed at the time of Alfred Marshall and after.

At the time of Ricardo, there was no concept as constant returns to scale.  It is natural that Ricardo and Smith did not used the term "constant labour cost" assumption and others. When he used the word "returns" it usually meant the return from investment. Although Ricardo has no concept of constant returns to scale or constant labor cost (in the above sense), Ricardo's theory of value is based on the implicit assumption that unit production cost remains constant in a short run. 

Dear Prof. Shiozawa, 

Thank you for accepting my offer to discuss the issues one by one. 

I will try to clarify what I meant with labor costs. I refer to them in the paper when talking about the assumption of constant labor costs. In page 24 I define the constant-labor-costs assumption of the typical textbook trade model of comparative advantage as follows: it stipulates that the amount of labour needed for producing a single unit of a commodity or service does not vary with the amount of commodities or services produced. 

Thus, labor costs should be interpreted in this context as unit labor-time costs. The assumption that the unit labor-time costs remain constant was erroneously attributed to Ricardo because of the longstanding misinterpretation of the four numbers. 

According to the textbooks, a firm with a production function F (K, L) is said to have constant return to scale if (for any constant a greater than 0) F (aK, aL) = aF ( K, L), where K and L are the factors of production capital and labor, respectively. 

I’m of course aware that the so-called laws of return to scale – which in my opinion are no economic laws at all, but merely suppositions about how the rate of production of a firm varies relative to  the same rate of increase in inputs –  were formulated by neoclassical economists well after Smith and Ricardo.

We also seem to agree that Ricardo never used the terms constant returns to scale nor constant labor costs in the Principles, nor did he explicitly formulated something similar to the content of these concepts in the language of his time. 

What he explicitly wrote in the Principles is the following: 

"An alteration in the permanent rate of profits, to any great amount, is the effect of causes which do not operate but in the course of years; whereas alterations in the quantity of labour necessary to produce commodities, are of daily occurrence. Every improvement in machinery, in tools, in buildings, in raising the raw material, saves labour, and enables us to produce the commodity to which the improvement is applied with more facility, and consequently its value alters. In estimating, then, the causes of the variations in the value of commodities, although it would be wrong wholly to omit the consideration of the effect produced by a rise or fall of labour, it would be equally incorrect to attach much importance to it; and consequently, in the subsequent part of this work, though I shall occasionally refer to this cause of variation, I shall consider all the great variations, which take place in the relative value of commodities to be produced by the greater or less quantity of labour, which may be required from time to time to produce them" (Ricardo, Vol. 1, pp. 36-37, bold added). 

In order to better understand your position on his subject, I would very much appreciate if you could perhaps explain to me why you believe that Ricardo's theory of value is based on the implicit assumption that the unit production cost remains constant in a short run.

The part you have cited does not help you much to deny that Ricardo based his arguments on value  on the implicit assumption of constant returns to scale.

As I have explained in the first answer of mine (30th of all answers), the law of constant returns to scale refers the state for a short period of time where the production process and techniques do not change. If knowledge changes or some innovations are introduced, productivity changes enormously but law of constant returns say nothing about it.

You must be bewildered by the phrase  of Ricardo "are of daily occurrence."

In this place, Ricardo is talking of change of productivity, perhaps as a result of introducing a machine,  new tool, improving machinery or adoption of a new method of processing. Ricardo thinks this kind of innovation occurs everyday. However, this everyday does not mean that it occurs everyday for all industry. There are many products in an economy. Suppose there are more than one thousand commodities. An innovation occurs maybe everyday  for one of them. Then innovation occurs for a particular product once for every three years.

Constant returns to scale is concerned to the proportions of  inputs to outputs during the interval when there is no innovation for a product. If there is no change of productivity for two commodities during an interval of time, the relative value of the two commodities remains constant. It changes when the productivity of one product changes.     

With a change of productivity the labor necessary to produce a commodity changes and by consequence the value changes. At the top of the paragraph that you cited Ricardo explains what he wants to argue in this paragraph. It reads:

• Not so with other great cause of the variation in value of commodities, namely the increase or diminution in the quantity of labour to produce them.  (Ricardo, Vol. 1, pp. 36)

Ricardo is thinking the case when the value changes substantially (in opposition t the case when the profit rate changes). "Alternations in the quantity of labour necessary to produce commodities" in these circumstances do not violate the constant returns to scale. 

Now let us return to the most important point. What is the core principle of Ricardo's theory of value. It is explicitly written at the very top of his book.

• The value of a commodity, or the quantity of any other commodity for which it will exchange, depends on the relative quantity of labour which is necessary for its production, and not on the greater of less compensation which is paid for that labour.   (Ricardo, Vol. 1, p.11, the heading of section I) 

 We can find many other similar expressions. For example:

• The Principle that the quantity of labour bestowed on the production of commodities regulate their relative value,  considerably modified by the employment of machinery and other fixed and durable capital. (Ricardo, Vol. 1, p.30, the heading of section IV) 

Ricardo is here arguing that the principle should be modified to include indirect  labor among the concept of quantity of labor necessary to produce the product, but it is evident that he is thinking that the principle continues to be valid if the concept is changed to include indirect labor in addition to direct labor. 

I do not enter to the details of these modifications. The most important thing is the following. What does the expression "quantity of labour which is necessary" for the production of  a commodity mean?  Does it mean a unit of the commodity or any other predetermined quantity of it? There is no clear indication on it. However, it is clear that when Ricardo says that the value of a commodity "depends on relative quantity of labour which is necessary for its production," he is thinking of some units of commodities. If not, the word "relative" loses its meaning.

Suppose that x amount of commodity A will exchange against y amount of commodity B. The law of value that Ricardo proclaims at the very top of his book means that 

        　x : y   =  L(B) : L(A)                (1)

Here L(A) stands for the quantity of labor which is necessary for the production of a unit of commodity A and L(B) the quantity of labor necessary to produce a unit of commodity B.

There is no indication about the absolute value of x and y. One of them may be 1 whereas the other must be different from 1 when the quantities of labor necessary to produce a unit of commodities are different.

The question is whether the equation (1) can be applied to different  pairs of x and y. For example, let us assume that

     L(A) = 15  and L(B) = 10.

Then what does the equation (1) mean? Normal understanding is that exchanges are possible when

      x = 2, y = 3;   x = 10, y = 15;  x = 60, y = 90; x = 100, y = 150 etc.

If this interpretation is correct, it also implies that the quantity of labor necessary to produce is proportional to the quantity of production. If not, the exchange ratio must change. This is the meaning when I say that the assumption of constant returns to scale lies at the basis of classical theory of value.     

Dear Prof. Shiozawa,

Thank you for the fast reply and detailed explanation. Unfortunately, I do not see to what extent this explanation provides a viable proof for your main claim that the assumption of constant returns to scale lies at the basis of the classical theory of value.

According to Ricardo’s labor theory of value, if a certain amount of commodity A is exchanged for a certain amount of commodity B, and both commodities are produced in the same country (because the labor theory of value is not valid in international exchanges), then one can infer that the respective quantities of A and B embody the same amount of labor time.

For any quantity of A to be exchanged for any quantity of B, thus, the respective amounts of labor time required for their production would have to be same. Because two A and three B may have the same labor-time requirements, though, one cannot infer that a lot of 10 A has to have the same labor-time requirements as a lot of 15 B – or 60 and 90 etc. – unless one also assumes that the unit labor-time requirements for producing A and B remain constant, or at least change in the exact same proportion.  

Hence the importance of the quote of my previous post. It refutes the claim that Ricardo assumed constant labor-time costs, and without this assumption, one cannot suppose that the amount of output increases exactly in proportion to an increase in inputs (= constant returns to scale).

Ricardo attributes the frequent variations in the relative values of commodities mainly to the continuously changing labor-time requirements for producing them. Thus, non-constant labor-time costs should be considered as a cornerstone of Ricardo’s labor theory value. If your claim were accurate, then the classical theory of value could not explain the frequent changes in the relative value of the commodities that occur even in the short term.

Do you think when commodity A is exchanged to commodity B by an exchange rate 2 : 2, they will exchange  3 : 4 or 10 : 6 in other transactions? If so, what does an exchange value mean?

When Ricardo and and other classical economists say exchange value or simply value, they assumed it remains constant for a moment of time and valid for any transactions in that time. Of course, the real length of the moment may change and range from a day to a year or more depending on the circumstances.

If values change instantaneously from transaction to transaction, what meaning do they have? 

Ricardo admits that prices changes (even in a day). However, Ricardo make distinction between market price and natural price. Value is more related to natural price than market price. For example, in Chapter IV On Natural and Market Price, Ricardo writes as granted that  "natural price" is equal to "the quantity of labour necessary to their production" (p.90). Evidently the latter quoted expression is a substitute of the term value.

 At the end of the chapter, Ricardo is more explicit:

• In speaking then of the exchangeable value of commodities, or the power of purchasing possessed by any one commodity, I mean always that power which it would possess, if not disturbed by any temporary or accidental cause, and which is its natural price. (Ricardo, 195, p.92, Italics added by me) 

With the change of demand and supply, market prices may change but Ricardo often assumes that natural price remains constant. What does this mean for you?

The purpose behind the distinction between market price and natural price is to separate the causes which may occasion a variation in the exchange value of a commodity. Both the market and natural price can change in the short-term, but these changes are the result of different causes. Temporary factors like fluctuations in the demand and supply can affect the market price of a commodity while leaving its natural price unaltered. The latter is affected by variations in the quantity of labor required for the production of the commodity.

Ricardo wrote at the beginning of chapter IV titled On Natural and Market Price: “In making labour the foundation of the value of commodities, and the comparative quantity of labour which is necessary to their production, the rule which determines the respective quantities of goods which shall be given in exchange for each other, we must not be supposed to deny the accidental and temporary deviations of the actual or market price of commodities from this, their primary and natural price" (Vol. 1, p. 88). 

Ricardo acknowledges thus that many temporary and accidental factors can affect the proportion in which two commodities are exchanged in the market place, but he wants to leave them out in his analysis of exchangeable value. Therefore he wrote at the end of the same chapter: 

 “Having fully acknowledged the temporary effects which, in particular employments of capital, may be produced on the prices of commodities, as well as on the wages of labour, and the profits of stock, by accidental causes, without influencing the general price of commodities, wages, or profits, since these effects are equally operative in all stages of society, we will leave them entirely out of our consideration, whilst we are treating of the laws which regulate natural prices, natural wages and natural profits, effects totally independent of these accidental causes. In speaking then of the exchangeable value of commodities, or the power of purchasing possessed by any one commodity, I mean always that power which it would possess, if not disturbed by any temporary or accidental cause, and which is its natural price (Vol. 1, pp. 91-92).”

If the alterations in the quantity of labour necessary to produce commodities are of daily occurrence, as Ricardo wrote, then how can he assume that the natural price is constant? 

You admit that

• Temporary factors like fluctuations in the demand and supply can affect the market price of a commodity while leaving its natural price unaltered. The latter is affected by variations in the quantity of labor required for the production of the commodity. (A part of the first paragraph of your last post, Emphasis is mine.)

You also admit that Ricardo wanted to leave all those temporary and accidental factors and wanted to concentrate in the examination of exchange value .

Then, do you admit that, when Ricardo talks of natural price, he is talking of the value of commodities? In other words, do you admit that exchange value is the proportion of commodities at a state of the market where the commodities are exchanged at the natural prices?

How do you explain, then, that the natural price or exchange value remain unaltered, independent of any temporary and incidental causes?

It seem for me that Ricardo is thinking that the natural price remains unaltered because the quantity of labor required for the production of the commodity remains constant. Do you have any other interpretation?

The exchange value or value in exchange of a commodity is the power of purchasing other goods which the possession of that commodity conveys. See, for example, Smith (I.iv.13, p. 44). 

While Ricardo is treating of the laws which regulate natural prices, natural wages and natural profits, he wants to leave the temporary effects on the prices of commodities produced by accidental causes out of consideration. Thus, when he talks about exchange value in this context, he means the power of purchasing which the commodity would possess, if it were not disturbed by any temporary or accidental causes. The commodity would be exchanged then according to its natural price. 

Temporary effects on the exchange value of commodities are excluded for analytical reasons. That does not mean, though, that Ricardo believed that accidental causes had no effect on the exchange value on a commodity.  

You have no explanation on why natural prices remain unaltered. The power of purchasing which a commodity possesses is not a characteristic of a commodity such as use-value but the quantity of labor necessary to produce it. This is what Ricardo meant when he cited labor as the foundation of the value of commodities (Ricardo, vol.1, p.20, and p.88)

 Now, let us see how Ricardo explains. I cite a whole paragraph from Ricardo.

•  Let us suppose that all commodities are at their natural price, and consequently that the profits of capital in all employments are exactly at the same rate, or differ only so much as, in the estimation of the parties, is equivalent to any real or fancied advantage which they possess or forego. Suppose now that a change of fashion should increase the demand for silks, and lessen that for woollens; their natural price, the quantity of labour necessary to their production, would continue unaltered, but the market price of silks would rise, and that of woollens would fall; and consequently the profits of the silk manufacturer would be above, whilst those of the woollen manufacturer would be below, the general and adjusted rate of profits. Not only the profits, but the wages of the workmen, would be affected in these employments. This increased demand for silks would however soon be supplied, by the transference of capital and labour from the woollen to the silk manufacture; when the market prices of silks and woollens would again approach their natural prices, and then the usual profits would be obtained by the respective manufacturers of those commodities. (Ricardo 1954, vol.1, pp.90-91, IV.4.8)

Here, Ricardo sets an ideal situation, where all commodities are at their natural price, and hence they are exchanged in proportion to the labor necessary to produce them. He then assumes that the demand for silks increases and demand for woolens decrease. He reminds us that their natural price, i.e. the quantity of labor necessary to their production remains unaltered. 

As an effect of this change of demands, there will be a brief change of market prices but this disturbance does not continue for a long time. The increased demand for silks will be responded by the increase of the silk production and the woolen production will be decreased. The market price of silks and woolens would again approach their natural prices. Why? Because the quantity of labor necessary to produce them remains constant. 

To summarize the situation, we have two propositions: 

(1) The quantity necessary to produce silk remains constant when its production is increased. 

(2) The quantity necessary to produce woolens remains constant when its production of silk is increased. 

Here, Ricardo clearly assumes that the quantity necessary to produce commodities (silks or woolens) remains constant. Ricardo is assuming constant returns to scale (implicitly in general case and explicitly here). This is what I meant when I have written that Ricardo's theory of value is based on the implicit assumption that unit production cost remains constant in a short run. 

To understand Ricardo's theory in a dynamical way, it is necessary to distinguish short-run constant returns assumption (a state of productivity) and the change of this productivity which takes place suddenly or gradually in time. 

When Ricardo is thinking that a value is determined by the quantity of labor (or more exactly by the cost of production), he is thinking that a proportion between inputs and output remains constant. This maybe expressed by constant coefficients. For example, if y is the quantity of output in the production of a commodity i and x0, x1, x2, ... , xN are the inputs of the production, then we have the stable relations: 

        x0 = ai0 y, x1 = ai1y, x2 = ai2y, ... , xN = aiN y. 

These describe a state of productivity. If we put 

        a0 = (a10, a20, ... , aN0)t

 and  

        A = (　aij　)  i= 1, ... ,N and j = 1, ... , N,

then a price vector p = (p1, p2, ..., pN)t is given by the equation: 

       (1+r) {w a0 + A p } = p, 

where r is the standard rate of profit and w is the wage rate.

If the matrix A is productive and r is sufficiently small, we get an explicit formula 

      p = (1+r) w {I - (1+r) A}-1a0. 

This formula has two meanings:

(1) Values remain constant even when demand changes.

(2) If a production technique changes, the values will change accordingly.

 Assuming constant returns to scale does not impede us to interpret Ricardo dynamically. On the contrary, Ricardo's theory of value is totally based on the state of production techniques. If the production techniques change, the values change and produce various effects through the change of values.

Of course there is an explanation for why the natural price of a commodity might remain unaltered despite a hike in the demand: because the natural price of a commodity can only be altered per definition by changes in the quantify of labor necessary for its production. 

In the paragraph you quoted above Ricardo wants to emphasise the point that variations in the demand of a commodity can affect its market price and thus alter the proportion in which it is exchanged for other commodities at any given moment in time. Such a variation in the exchange value, though, would only be temporary, and soon the market price of the commodity would again approach its original natural price, as long as the quantity of labor necessary for its production remains unaltered.  

In chapter XXX of the Principles titled “On the Influence of Demand and Supply on Prices", Ricardo states:  “It is the cost of production which must ultimately regulate the price of commodities, and not, as has been often said, the proportion between the supply and demand: the proportion between supply and demand may, indeed, for a time, affect the market value of a commodity, until it is supplied in greater or less abundance, according as the demand may have increased or diminished; but this effect will be only of temporary duration. Diminish the cost of production of hats, and their price will ultimately fall to their new natural price, although the demand should be doubled, trebled, or quadrupled. Diminish the cost of subsistence of men, by diminishing the natural price of the food and clothing, by which life is sustained, and wages will ultimately fall, notwithstanding that the demand for labourers may very greatly increase (Vol. 1, p. 383).”  

In order to separate the temporary effects on the exchange value of a commodity caused by demand and supply from variations in the exchange value caused by alterations in the cost of production, Ricardo has to refer to the case in which the later remains unchanged. But one cannot infer from it that he assumed constant returns to scale, nor that his labor theory of value is based on the implicit assumption that the unit production cost remains constant in the short run. As much as you would like to belittle the importance of the paragraph in pp. 36-37, you cannot deny that Ricardo unmistakably affirmed there that the alterations in the quantity of labour necessary to produce commodities are of daily occurrence, and consequently their value alters on a daily basis too. 

This is in fact the opposite of constant returns to scale, constant labor-time costs and constant unit cost of production even in the short run, unless you consider “short run” to last merely a few minutes or hours. 

The text you have cited (chapter XXX, p.383) supports my contention.

It is the cost of production which ultimately regulates the price of commodities. The cost of production remains constant provided that the law of constant returns to scale holds and prices of inputs are kept the same. In other assumptions, the cost of production changes except for a special case where different changes offset their effects.

The latter half of the citation only tells the case when the cost of production changes and by consequence the case when the value changes.

The first part tells that the exchange value or natural price remains constant as far as the cost of production remains the same. When there is a sudden change of demands, it takes time to adjust the production and the supply. During that time, the market price may be different from the natural price and the value. As demand and supply approaches to an equality, (Ricardo talks of "proportion" but it will be better to think that he is talking about the balance of supply and demand), the market price returns to the natural price. Rciardo(s expression "this effect will be only of temporary duration" means this. The cost of production remains constant despite the fact that the scale of production is changed.

I have asked you why the natural price or the cost of production remains constant despite the fact that the volume of production is changed. You could not answer this question.

If Ricardo is supposing a variable law of returns, the (average) cost of production must change. If you assume increasing returns to scale, the cost of production decreases when the production is increased, and increases when the production is decreased. Ricardo thinks that the cost of production remains constant for certain duration of time. Even during this time, he thinks that it is possible to change the production scale. A definition of constant returns to scale is this constancy of the cost of production when the production volume changes.

Ricardo's paragraph which includes the phrase "alterations in the quantity of labour necessary to produce commodities, are of daily occurrence" (p.36) only shows that your framework of interpretation does not lead you to a reasonable system of Ricardo's theories which includes the theory of value as its essential part.

Let me start with a direct quote of your reply: 

 “If you assume increasing returns to scale, the cost of production decreases when the production is increased, and increases when the production is decreased.” 

 “A definition of constant returns to scale is this constancy of the cost of production when the production volume changes.”

 You seem to confound assumptions regarding returns to scale – which by definition do not consider the costs of inputs – with economies of scale. It is only the later which considers how the cost of production may change with the quantity of output produced.

Your statements are only accurate when procuring more labor and capital does not affect their prices. If procuring a greater amount of factors of production drives the respective prices up or down, than the inverse relationships between returns to scale and economies of scale could be observed. If the prices of the inputs increases, than increasing returns to scale could result in diseconomies of scale; if input prices decreases (volume discounts), than decreasing or constant returns to scale could result in economies of scale. 

To answer your question: the cost of production may remain constant even in the presence of increasing return to scale if the price of the factors of production increases. One does not have to assume constant returns to scale for that. 

Can you answer the following question: If an increase in the scale of production does not change the cost of production, then why does the market price of the commodity varies with respect to the natural price in the short run?

Can you explain and define 

(1) constant returns to scale

(2) increasing returns  to scale

(3) decreasing returns to scale

when you have

(a) only one input

(b) more than two kinds of inputs?

If you assume (a), which is a very special case and maybe a typical case that Ricardo and Smith considered,  it is rather easy to define (1), (2), (3). In case of (b) it is quite difficult to define (2) and (3) without  any reference to input prices.  How can you separate or distinguish constant returns to scale and  economies of scale?  

Constant returns to scale can be defined even in case of (b). It is the case when all inputs increase or decrease proportionally. (I have explained this case in one of my previous posts.)

Your answer to my question is no answer. Let us assume a very simple case, i.e. (a). You can think that the unique input  is labor. Suppose we have an function which connects input x  to output y:

                     x = f ( y ).

Function f can take various forms:

     (1)           f ( y ) = a y    (this is the constant returns case);

     (2)           f ( y ) =  a yα　(α>1)  (this is the decreasing returns case);　

     (3)           f ( y ) = a  yα　(a

What seems completely improbable to me is that Ricardo would have based even the most insignificant detail of his value theory on such unrealistic assumptions as constant returns to scale or constant labor-time costs, and there is in fact no basis in his writings to make a viable claim that he did. These assumption are completely alien to his economic theory. What Ricardo explicitly assumed was variable labor time costs.   

Evidently, we won’t agree on this subject, so I would like to propose to move on to another point. 

I am surprised by your affirmation that my paper fails to explain the logic behind the pattern of trade. I believe that this explanation can be found in pp. 30-33. It starts with the interest of a country in a particular exchange (classical rule of specialisation). For a trade to be mutually beneficial, one has to assume that the countries have different relative facilities in producing certain commodities. The ability of a country to produce certain commodities with less labor-time costs than another country can be explained by both natural and artificial factors. 

Have you given up discussing Ricardo's theory of values? Without it , you cannot understand his theory of international trade.The question I raised is not " insignificant detail " as you think. If you think so, it means that you have never considered Ricardo's theory of values. 

Your claim that constant returns to scale is realistic is only your presumption.  You are too much influenced either by low qualified neoclassical economists or by some fundamentalist Sraffians. (I am a Sraffian but not a fundamentalist.)

Even neoclassical economics often assumes constant returns to scale.   For example, Cobb-Douglas production function or many other production functions are homogeneous of degree 1. Do you know this is another expression of constant  returns to scale? 

Homogeneity of degree 1 is also the very basis of neoclassical theory of distribution. Suppose you have two factors, labor and capital. Then a production function in neoclassical style take the form like this:

                  Y = f (L, K).                                                                          (1)

It is usually supposed that f is homogeneous of degree 1. This means

                  f (s L , s K) = s f ( L, K )   ∀s > 0.

If f is continuously differentiable, then you have by Leibniz law of composite functions

               Y =  w L + r K ,

where 

             w = ∂ f / ∂L   and  r  =  ∂ f / ∂K

taken at the point of production. If the production function is homogeneous of a degree different from 1, you cannot get this result. So any reasonable neoclassical economists admit that production function is homogeneous of degree 1.

☆ Remind that I do not admit this reasoning. I only show how the neoclassical theory is build.☆

Neoclassical economics emphasize input substitution. This is totally different thing than homogeneity of degree 1 or constant returns to scale.   

In the case of production function (1), neoclassical theory argues the effects of factor prices. If for example,

             w ≠ ∂ f / ∂L   or  r  ≠  ∂ f / ∂K ,

there is a better combination of inputs and the input proportions of L and K will be changed. This is the substitution problem. In the neoclassical framework, this is important, because this substitution assures the existence of an equilibrium.

Substitution obeys a kind of "law of decreasing returns."  So the there are many neoclassical economists who claim that constant returns denies this substitution effects. They are completely wrong, because they are confusing constant returns to scale and no substitution.

Substitution is not important for classical economics, because we have  non-substitution theorem (after P. Samuelson's naming) or by a better denomination minimal price theorem. If you have many production techniques which produces the same product, you face a similar situation like neoclassical economists face. You should choose a production technique that cost you least at given prices. This situation happens in every products. What will happen? 

Standard neoclassical theory claims that prices change  when the demand composition changes. When a minimal price theorem holds, there is no necessity to change from one production technique to another  even when demand  proportions change. This is the very basis of classical theory of value. In the time of Ricardo, economists did not know this theorem, but they correctly observed that the value or natural prices does not change even if demand proportions change. 

You may also influence too much by some Sraffians. It is true that Piero Sraffa has written in the preface to his book (Sraffa, 1960) that he is not assuming constant returns (to scale).  This contention may be right as far as self-replacing  state is concerned. However, when he starts to talk about standard commodity, it is necessary to consider a state of production which is different from the original self-replacing state.  Sraffa continues to assume the same coefficients when the scales of production change. How is this kind of things permissible? Sraffa implicitly assumes  constant returns to scale. If not, coefficients must change every time  the volume of production changes.

I can discuss the patterns of trade of specialization, but I do not think that you are prepared to discuss the problem in a reasonable way. Can you explain what will happen if the labor inputs (counted in million workers for a year) are given by the following table?  Please explain what kind of specialization takes place in this case.  

                                   Country A    Country B    Country C  

Corn                                10                 10                 10

Linen                                 5                   7                   3 

Cloth                                  4                   3                   2

The problem is that so far we have merely discussed a rather basic aspect of Ricardo’s value theory which is, quite frankly, not so difficult to understand.

I will make a final attempt. Let’s assume there is an increase in the demand of a commodity and its market price goes up. The increase in profits attracts new capitalists to the industry. Let’s further assume that the production facilities of the new firms are very similar to the already existing ones. Consequently, the cost of production of the commodity does not change, so its natural price remains the same. With the past of time the increased demand is satisfied by the output of the new firms and the market price of the commodity returns again to the original natural price. The output of the whole industry has been increased in order to satisfy the increased demand for the commodity, but the scale of production of the individual firms has remained more or less the same. Therefore, not every increase in the output of an industry is the result of an increase in the scale of production at the firm level. And as you perfectly know, the assumption of constant returns to scale was originally made for the production function of an individual firm.

Ricardo is completely right when he states that changes in the proportion of demand and supply are merely responsible for temporary or accidental variations in the exchange value of a commodity, whereas enduring changes are the result of variations in the amount of labor time that is required for its production. And as it is shown above, neither Ricardo nor anybody else need to rely on the assumption of constant return to scale in order to explain this.

Can we move on to the next topic now?

You finally admitted that Ricardo assumed constant returns to scale. 

Constant returns to scale have tow versions, if you like: micro and macro versions. The first is concerned with a firm or independent producer (including independent worker). The second is related to total production in an economy (regional or national, or others). In this version, constant returns to scale are obtained when all firms or producers are very similar and have the same (or similar) input-output relations. If operating firms have the same size of production and if the number of firms changes, inputs and outputs change proportionally to the number of producers. 

In the time of Ricardo, most firms were small if we compare with the present large enterprises. Certainly, Ricardo assumed this version. 

With the arrival of greater firms, mainly after 1890's, the first version came to contain two realities. In some industries like agriculture, producers remained family business and (if there were some differences of scales) the productivity remained similar. In this case, classical logic applied. Other industries experienced a major change. Some firms became very big and others had ruined or been absorbed. If an industry counts only a few number of firms which produces the same products, each firm was obliged to adjust themselves to the variation of demands. In this case, if all firms have similar input-output relations, then the total input and the total output keep the same linear relations. The constant returns to scale holds in the economy level too. If we do not assume a monopolist, any case contains a transition from micro to macro. So the story is the same for all cases. 

It seems you want to claim that the classical story is not the constant returns to scale. You wrote: 

• [T]he assumption of constant returns to scale was originally made for the production function of an individual firm. 

This is the question of the history of economic theory. It is clear that in the time of Ricardo, there was no explicit notion such as constant returns to scale. As I have written in the previous post, examination on returns (constant, increasing, and decreasing) started at the time of Marshall. Many points are ambiguous, but Marshall observed two cases: returns in an individual firm and returns in industry. This is the very point why Marshal had to introduce a concept of external economy. He thought that a firm would soon grow to a monopolist firm if it enjoys internal increasing returns. So, he admitted only external economy and claimed that individual firms obey constant or decreasing returns to scale. 

My objection to your paper is only on the third point of your three major claims. I agree to the first two. So there is no more point to discuss with you. Moreover, I am highly appreciating you proposal to use the term “classical rule” instead of a bit pejorative "18th-century rule" coined by Jacob Viner. I have recently written a paper (or we have as it is coauthored and not published yet) that adopted the term "classical rule."  

Let me add that what you describe as new discovery of Ruffin and Maneschi is not new, at least for Japanese readers. A senior colleague of mine, late Kenzo Yukizawa have written a paper in 1974: Genuine Interpretation and Deformed Interpretation of Ricardo's "Theoy of Comparative Costs". (In Japanese: リカード「比較生産費説」の原型理解と変形理解) It clarified the difference between common interpretation (what Yujizawa called deformed interpretation) and the true or genuine interpretation. It was based on a detailed study of Ricardo's text. I have referred to this in a note to our paper: Inter and Intra Company Competition in the Age of Global Competition: A Micro and Macro Interpretation of Ricardian Trade Theory, p.23, note 23. (you can read this paper in my RG contribution page.) 

As I have written there, the point is that Ricardo assumed the quantities of cloth and wine so that they are exchanged at the international trade. Ruffin and you are right to emphasize that the four numbers are not the usual coefficients of labor input necessary to produce "a single unit of commodity or service" (your paper, p.6). 

You are half right when you claim that  (1) "the four numbers [should be] interpreted accurately as the amounts of men working for a year required to produce some unspecified amounts of cloth and wine traded between England and Portugal" (your paper, p.7). However, when you claim that  (2) "since the amounts of cloth and wine were not specified, it is not even possible to calculate the unitary labor costs in Ricardo’s original numerical example" (ibid.), you are completely wrong. (Expression (1) is admissible, but expression (2) is pure non-sense.)

The amounts of cloth and wine are specified, not in the text but in thought. At least, these quantities are determined. 

100 workers in England and 90 workers in Portugal produce some specified quantity of cloth. 120 English workers and 80 Portugal workers produce some specified quantity of wine. Ricardo did not specify this quantity in his text, because it was not necessary to mention it. 

However, there is another important question. Do you believe that England and Portugal at that time exchanged only the products of only 100 workers at maximum? Ricardo has chosen four numbers only to keep them at the scale that a common people can easily imagine.

If an exchange of 100 English workers' product of cloth and 80 Portuguese workers' product of wine is profitable, why is the same exchange not undertaken with the same exchange rate? If this is repeated 3 times, then England exports 300 workers' product of cloth to Portugal and Portugal exports 240 workers' product of wine to England. 

Do you think this is unrealistic? If you think this is unrealistic, Ricardo’s text is really unrealistic.

Sorry for the late reply, but I have been quite busy in the last weeks.

We can agree to disagree on the subject of constant returns to scale. 

I don’t understand what you mean when you write: “The amounts of cloth and wine are specified, not in the text but in thought. At least, these quantities are determined.” 

Later on you recognise that Ricardo did not specify the quantities of cloth and wine traded because it was not necessary. I cannot see here any point of disagreement between us, just a self-contradiction from your part. 

I don’t think it is unrealistic. Ricardo’s numerical example is perfectly suited for the specific purpose for which it was originally formulated. However, it is not a swiss army knife for every conceivable problem in the field of international trade theory. 

You can find my interpretation of its original purpose here. 

I'll look the paper over, and tell you. Is this for acceptance by your journal?

Regards,

M McGuire

Dear Prof. Mcguire, 

Thank you very much for your kind offer. The paper which is mentioned in the group's question has been already published. I have added a link to the published version. 

I would very much appreciated if you could comment on the working paper "Ricardo's numerical example versus Ricardian trade model: A comparison of two distinct notions of comparative advantage "

Best regards, 

Jorge

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