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~a@~djdj^~ld e[[[(w(wdX[[[w[[[[<2d<2The Infeasibility of Free Trade in Classical Theory: Ricardo's Comparative Advantage Parable has no Solution
Ron Baiman
Center for Tax and Budget Analysis
70 E. Lake St., Suite 1700
Chicago, IL 60601
Email: Baiman@ctbaonline.org
Abstract
In this paper formal models of Ricardos comparative advantage parable that include general forms of consumer price response behavior are constructed from a detailed textual exegesis of Ricardos story. Using these models the comparative advantage parable is shown to be mathematically overdetermined and therefore generally unsolvable. To reinforce this conclusion, a numerical solution is derived for a constant elasticity version of the model. A necessary condition for the existence of a solution to the constant elasticity model is that two price elasticities of demand must be functions of the other two price elasticities of demand. General formulas are derived expressing this dependency. When realistic elasticities for wine are set, the model can only be solved if Portuguese demand for English cloth is unrealistically elastic. This demonstrates that sustainable and mutually beneficial trade between England Portugal can only be realized through managed trade.
Key Words: Ricardo, International Trade, Free Trade, Comparative Advantage, Managed Trade.
1. Introduction
David Ricardos [1817, Ch. 7] perceived demonstration of a marketbased, mutually beneficial, comparative advantage trade equilibrium between countries with different domestic factorcost ratios has been part of the intellectual justification for free trade since its publication in 1817. Even economists critical of neoclassical trade theory contend that the insights of Ricardo and Hume are among the most important principles that need to be taught to undergraduates and to students who get formal training in economics (Krugman, 1996, pp. 117126). These doctrines that the benefits of trade are not limited to absolute advantages in production and that trade deficits selfcorrect are essential components of the argument for free trade. Ricardos parable encapsulates both ideas clearly, succinctly, and when the assumptions of the model are satisfied, irrefutably.
Wellknown critiques of Ricardos parable show that his assumptions do not hold in the real world. Some of these assumptions are fullemployment, current account based price adjustments between countries, quick and continuous withincountry substitutions of production, and widespread distribution of benefits from trade. These critiques note that when these assumptions are violated, free trade may cause rising unemployment, slower growth, and increasing inequality. Such negative consequences of free trade can more than offset any gains from comparative advantages (Prasch, 1996: Blecker, 1999: MacEwan, 1999; Eatwell & Taylor, 2000; Vernengo, 2000). However, the textbook stories endure and generally ignore these critiques.
This paper takes a different approach. It accepts the assumptions of the basic classical model, and shows that its free trade conclusion is logically inconsistent. This interpretation of Ricardos parable recognizes that while trade has the potential to be mutually beneficial, there is no theoretical basis for the claim that free market forces will lead to a sustainable realization of these benefits.1
Section 2 begins by constructing simple formal models of Ricardos parable that include the workings of Humes specie flow mechanism. This is an essential element of the story often left out of simple barter descriptions of comparative advantage.2 Using these models we show that the parable is mathematically overdetermined and therefore unsolvable. Ricardos free trade solution, which provides: (i) complete specialization, (ii) fullemployment, (iii) balanced trade, and (iv) balanced aggregate supply and demand (although not explicitly addressed by Ricardo, this condition is satisfied by his model) will generally not exist.3 I explore this point further by showing that, under plausible demand conditions, partial benefits of international trade based on comparative advantage in Ricardos model can only be realized if trade between countries is actively managed. Unmanaged free trade will generally result in unsustainable longterm deficits and surpluses between countries.
Thus, even when all the assumptions of Ricardos model are satisfied, there is no theoretical argument that free trade between countries will be mutually beneficial in the absence of policy intervention.
2. A Simple OwnPrice Formalization of Ricardos Comparative Advantage Parable
The comparative advantage parable is based on roughly twenty paragraphs (7.13 to 7.32) from Chapter 7 of On the Principles of Political Economy and Taxation [Ricardo, 1817].4 I will cite the first ten, and through detailed exegesis construct a formalization that I call Model S. As the later ten paragraphs illustrate the same points, their reproduction is not necessary. This formalization assumes no crossprice effects. The next section constructs a second formalization, Model G, which includes crossprice effects.
If Portugal had no commercial connexion with other countries, instead of employing a great part of her capital and industry in the production of wines, with which she purchases for her own use the cloth and hardware of other countries, she would be obliged to devote a part of that capital to the manufacture of those commodities, which she would thus obtain probably inferior in quality as well as quantity. 7.13
7.13 describes the fact that if Portugal was in a state of autarky and had no commercial connection with other countries she would be obliged to produce the cloth that she needed herself rather than trading wine for it.
The quantity of wine which she shall give in exchange for the cloth of England, is not determined by the respective quantities of labour devoted to the production of each, as it would be, if both commodities were manufactured in England, or both in Portugal. 7.14
In paragraph 7.14 Ricardo notes that if both countries are opened up to trade the exchange ratio between wine and cloth will not be determined by their relative labor requirements as it would under autarky. Under autarky Ricardo believed that relative prices, or exchange values, were primarily determined by direct labor costs of production.
England may be so circumstanced, that to produce the cloth may require the labour of 100 men for one year; and if she attempted to make the wine, it might require the labour of 120 men for the same time. England would therefore find it her interest to import wine, and to purchase it by the exportation of cloth. 7.15
Paragraph 7.15 states the basic assumptions of the parable for England. She would need the labor of 100 men for a year to produce the cloth or to satisfy Englands domestic (autarkic) total domestic demand for cloth, and 120 men for the same time (a year) to make the wine or to satisfy Englands domestic (autarkic) demand for wine. We can therefore assign relative labor value prices of 100 for cloth and 120 for wine for Englands autarkic total domestic demand for cloth and wine respectively. As described below, the international exchange ratio between these two goods will not be based on relative labor requirements, as it will be influenced by specie flow between the countries.
The paragraph goes on the state that England will want to export cloth and import wine since shes a more efficient producer of cloth. As explained below, this assumes that Portuguese wine is less costly in (international) gold prices in England than English wine. This is an easy assumption to make, as wine made in Portugal requires less labor than wine made in England.
Although Ricardo does not say that England will completely specialize in producing cloth, this can be inferred from his statement in the next paragraph (7.16) that Portugal should completely specialize in wine and import all of its cloth from England even though cloth made in England requires more labor than cloth made in Portugal. This can also be inferred from a later example regarding the consequences of the discovery of a more productive wine making process in England, where Ricardo notes that in this case: it might become profitable for the two countries to exchange employments; for England to make all the wine, and Portugal all the cloth consumed by them. (7.21, emphasis added) 5
Note that Ricardo does not specify units of measurement for Englands total domestic wine and cloth demands in this paragraph. The only references Ricardo makes to units of measurement in the parable are in paragraph 7.22, where (in the context of another example) he assumes a price of wine in England of 50 per pipe and a price of 45 for a certain quantity of cloth. Lets assume that Englands total domestic demand for wine is A pipes, and that a certain quantity is square yards; so Englands total domestic demand for cloth is B square yards of cloth. Ricardo is then assuming that in England the price of B square yards of cloth and A pipes of wine is 100 and 120 respectively.
To produce the wine in Portugal, might require only the labour of 80 men for one year, and to produce the cloth in the same country, might require the labour of 90 men for the same time. It would therefore be advantageous for her to export wine in exchange for cloth. This exchange might even take place, notwithstanding that the commodity imported by Portugal could be produced there with less labour than in England. Though she could make the cloth with the labour of 90 men, she would import it from a country where it required the labour of 100 men to produce it, because it would be advantageous to her rather to employ her capital in the production of wine, for which she would obtain more cloth from England, than she could produce by diverting a portion of her capital from the cultivation of vines to the manufacture of cloth. 7.16
Paragraph 7.16 states the basic assumptions of the parable for Portugal. In Portugal it requires the labor of 80 men for one year to produce Portugals (autarkic) total domestic demand for wine and 90 men for one year to produce her total autarkic domestic demand for cloth. Again, Ricardo does not specify quantities, or units of measurement.
Ricardo then goes on to state that, just as with England for wine in 7.15, it would be advantageous for Portugal to import her domestic demand for cloth that she makes with 90 men from a country where it required the labor of 100 men to produce it because it would be advantageous to her rather to employ her capital in the production of wine, for which she could obtain more cloth from England, than she could by diverting a portion of her capital from the cultivation of vines to the manufacture of cloth. (7.16)
This makes clear that Portugals autarkic total domestic demand for cloth that can be produced in Portugal with 90 men is equal to Englands autarkic domestic demand that requires 100 men for its production in England or, based on our assumption from paragraph 7.15, B square yards. In addition, Ricardo claims that it would be advantageous for Portugal to completely specialize in wine production, as she could obtain more cloth this way than by diverting [even] a portion of her capital from the cultivation of vines to the manufacture of cloth (emphasis added).
Since 100 men in England can produce B square yards of cloth, if England employed all of the 100+120=220 men that were engaged in cloth and wine production under autarky just in cloth production, she would be able to produce 220/100=2.2B square yards of cloth. As Portugals autarkic domestic demand for cloth was also B, in order for England to be able to fully employ these 220 men after complete specialization, free trade must increase Portuguese demand for cloth by 0.2B so that:EMBED Equation.3 or, cancelling the Bs:
EMBED Equation.3 (1)
must hold, where EMBED Equation.3 is the proportional increase over B of free trade induced Portuguese demand for English cloth that is greater than the initial autarkic Portuguese and English demand for cloth of 2B.
Thus England would give the produce of the labour of 100 men, for the produce of the labour of 80. Such an exchange could not take place between the individuals of the same country. The labour of 100 Englishmen cannot be given for that of 80 Englishmen, but the produce of the labour of 100 Englishmen may be given for the produce of the labour of 80 Portuguese, 60 Russians, or 120 East Indians. The difference in this respect, between a single country and many, is easily accounted for, by considering the difficulty with which capital moves from one country to another, to seek a more profitable employment, and the activity with which it invariably passes from one province to another in the same country. 7.17
Similarly, paragraph 7.17 states: Thus England would give the produce of the labour of 100 men [English cloth makers] for the produce of the labour of 80 [Portuguese wine makers]. From paragraph 7.15 we can assume that England will fully specialize in cloth production and import from Portugal all of the wine that she previously consumed under autarky. The produce of 100 English men working in cloth production, B square yards, is thus going to be exchanged for the produce of 80 Portuguese men working in wine production, and these wine imports from Portugal will fully satisfy English demand for wine (assumed to be A pipes). This implies that autarkic Portuguese production and demand for wine is also A pipes.
Thus, if Portugal specializes in wine production and imports all of her cloth (B square yards of cloth produced by 100 English cloth workers), Portugal will produce (80+90)/80 =2.125A pipes of wine. This implies that for full employment to be maintained under free trade, or for all of the Portuguese cloth workers to be redirected to wine production, Portugal must produce and sell: EMBED Equation.3 pipes of wine, so that after cancelling the As, the condition:
EMBED Equation.3 (2)
must hold, where EMBED Equation.3 is additional free trade induced English demand for wine that is greater than existing English and Portuguese autarkic demand for wine of 2A.
It would undoubtedly be advantageous to the capitalists of England, and to the consumers in both countries, that under such circumstances, the wine and the cloth should both be made in Portugal, and therefore that the capital and labour of England employed in making cloth, should be removed to Portugal for that purpose. In that case, the relative value of these commodities would be regulated by the same principle, as if one were the produce of Yorkshire, and the other of London: and in every other case, if capital freely flowed towards those countries where it could be most profitably employed, there could be no difference in the rate of profit, and no other difference in the real or labour price of commodities, than the additional quantity of labour required to convey them to the various markets where they were to be sold. 7.18 Experience, however, shews, that the fancied or real insecurity of capital, when not under the immediate control of its owner, together with the natural disinclination which every man has to quit the country of his birth and connexions, and intrust himself with all his habits fixed, to a strange government and new laws, check the emigration of capital. These feelings, which I should be sorry to see weakened, induce most men of property to be satisfied with a low rate of profits in their own country, rather than seek a more advantageous employment for their wealth in foreign nations. 7.19
In 7.18 and 7.19 Ricardo explains why the parable assumes that there will be no capital flow or investment between countries, so commercial arbitrage of productivity and cost differences between countries will take the form of international trade rather than reallocation of investment as it would in one country as between Yorkshire and London in England.
Gold and silver having been chosen for the general medium of circulation, they are, by the competition of commerce, distributed in such proportions amongst the different countries of the world, as to accommodate themselves to the natural traffic which would take place if no such metals existed, and the trade between countries were purely a trade of barter. 7.20
In 7.20 Ricardo asserts that, although trade between England and Portugal will be conducted through a medium of circulation such as gold and silver, the end result will be the same as if it had been conducted through barter. Portugal will specialize in wine production and import all of the cloth that she consumes from England; England will do the opposite.
Thus, cloth cannot be imported into Portugal, unless it sell there for more gold than it cost in the country from which it was imported; and wine cannot be imported into England, unless it will sell for more there than it cost in Portugal. If the trade were purely a trade of barter, it could only continue whilst England could make cloth so cheap as to obtain a greater quantity of wine with a given quantity of labour, by manufacturing cloth than by growing vines; and also whilst the industry of Portugal were attended by the reverse effects. Now suppose England to discover a process for making wine, so that it should become her interest rather to grow it than import it; she would naturally divert a portion of her capital from the foreign trade to the home trade; she would cease to manufacture cloth for exportation, and would grow wine for herself. The money price of these commodities would be regulated accordingly; wine would fall here while cloth continued at its former price, and in Portugal no alteration would take place in the price of either commodity. Cloth would continue for some time to be exported from this country, because its price would continue to be higher in Portugal than here; but money instead of wine would be given in exchange for it, till the accumulation of money here, and its diminution abroad, should so operate on the relative value of cloth in the two countries, that it would cease to be profitable to export it. If the improvement in making wine were of a very important description, it might become profitable for the two countries to exchange employments; for England to make all the wine, and Portugal all the cloth consumed by them; but this could be effected only by a new distribution of the precious metals, which should raise the price of cloth in England, and lower it in Portugal. The relative price of wine would fall in England in consequence of the real advantage from the improvement of its manufacture; that is to say, its natural price would fall; the relative price of cloth would rise there from the accumulation of money. 7.21
In 7.21, Ricardo further explains that cloth cannot be imported into Portugal, unless it sells there for more gold then it cost in the country from which it was imported, and similarly for wine. Thus, Ricardo makes clear that comparative advantage operates through gold, and that international gold prices for English cloth in Portugal and Portuguese wine in England have to be lower than their respective domestic gold prices for there to be trade.
Trade will thus be conducted through market mechanisms based on gold (or international currency) prices. Any increases or declines in demand for cloth or wine from their initial autarkic equilibrium demands of A pipes of wine or B square yards of cloth will be a function of gold price reductions.
7.20 and 7.21 also make clear that for purposes of international trade the operative price is not the laborvalue price but the international exchange or gold price that will, following Humes specie flow mechanism, rise or fall depending on the inflow or outflow of gold into the domestic economy. This inflow or outflow, in turn, is based on the existence of trade surpluses or deficits, respectively.
Ricardo notes that if England were to discover a winemaking process that would make it cheaper for her to produce wine domestically than to import it from Portugal, she would cease to trade cloth for wine and would export cloth to Portugal for money. In this case: Cloth would continue for some time to be exported from this country [England], because its price would be continue to be higher in Portugal than here [in England]; but money instead of wine would be given in exchange for it, till the accumulation of money here [in England], and its diminution abroad [in Portugal], should so operate on the relative value of cloth in the two countries, that it would cease to be profitable to export it [when the gold price of cloth in England again becomes higher than the gold price of cloth in Portugal]. So: If the improvement in making wine were of a very important description, it might become profitable for the two countries to exchange employments; for England to make all the wine, and Portugal all the cloth consumed by them; but this could be effected only by a new distribution of the precious metals, which should raise the price of cloth in England, and lower it in Portugal.
This example explains Ricardos pricing principles: (i) relative domestic prices reflect labor productivity, but (ii) the overall domestic price level will be tied to the level of the accumulation of money and (iii) this accumulation or withdrawal of gold will determined by international trade surpluses or deficits.
We can therefore assume that in Ricardos initial configuration of the comparative advantage parable, before trade, the gold price values of the domestic currencies reflect labor values, as he writes in 7.18 that in this initial situation: The wine and cloth shall both be made in Portugal indicating that the Portuguese labor value prices of 80 and 90 person years for B square yards of cloth and A pipes of wine are less expensive in terms of gold than the English labor value prices of 100 and 90 person years for the same quantities of wine and cloth. We can also assume that Portugals initial trade surplus will result in an accumulation of gold in Portugal that will drive up Portuguese gold prices until specialization and trade based on comparative advantage becomes feasible. Ricardos parable relates to this equilibrium position, described in 7.20, whereby gold will be distributed in such proportionsso as to accommodate itself to the natural traffic that would take placeand the trade between countries were purely a matter of barter.
For cloth to be made in England, its gold price has to be relatively lower than the gold price of Portuguese cloth and, conversely, the gold price of Portuguese wine has to be lower than the gold price of wine produced in England. Therefore, if E>1 represents the increase in overall gold prices in Portugal relative to gold prices in England that results from the initial accumulation of gold in Portugal and withdrawal of gold from England, at the equilibrium comparative advantage trading solution described above the gold price of Portuguese cloth must be greater than that of cloth produced in England (E90> 100) and the gold price of Portuguese wine must be lower than that of wine produced in England (E80 < 120).
The pricebased increase in English demand for wine over autarkic demand for A pipes will therefore be a function of the reduction in the gold price, E80, of Portuguese wine relative to the gold price of wine in England of 100 so that:
EMBED Equation.3 (3)
where EMBED Equation.3 is a general demand function that gives the relative increase in English demand for wine as a function of the gold price of Portuguese wine relative to its English price of 100, andEMBED Equation.3 is a ratio increase over A pipes. A value of EMBED Equation.3 would mean that English consumers are buying 0.2A more wine at this reduced Portuguese import price.
Similarly, the pricebased increase in Portuguese demand for imported English cloth will be a function of the reduction in the gold price in Portugal for imported English cloth, 100/E, relative to the gold price of cloth in Portugal of 90 (recall that 90 > 100/E). Note that gold prices in Portugal have all risen by E times their original value relative to gold prices in England, so that relative to the new aftertrade gold prices in Portugal the English gold price of 100 becomes 100/E. 100/E thus becomes the relative and operative price that induces increased demand for English cloth in Portugal.
EMBED Equation.3 (4)
Conditions (2) and (4) presume that all of Portugals additional wine production of EMBED Equation.3 pipes, beyond that needed for domestic consumption A, is exported and consumed in England. Likewise, from (1) and (3) above, all of Englands additional cloth production of EMBED Equation.3square yards, is exported and consumed in Portugal. These rather restrictive conditions on the gains from specialization can be relaxed if crossprice effects are included (see below).
Ricardo assumed that under these conditions market forces will generate a solution for the equations above.
Finally, for Ricardos model to work trade must be balanced. A trade imbalance would cause gold to accumulate in one country and be withdrawn from the other, leading to gold price increases in the first and gold price reduction in the second. Unbalanced trade would eventually make specialization and comparative advantage based trade unprofitable, and not economically viable. So Ricardos parable must also include a (goldprice denominated) balanced trade condition:
EMBED Equation.3 (5)
Here EMBED Equation.3 is the value of Portuguese wine exports to England in terms of labor value price per unit ofEMBED Equation.3in Portuguese gold, and EMBED Equation.3 is the value of English cloth imports to Portugal in English gold prices.
Assuming that all revenue from sales is spent on wine and cloth, these last three equations also ensure that aggregate demand equals aggregate supply in each country as by multiplying (1) byEMBED Equation.3, (2) by EMBED Equation.3 and using (5) we get:
EMBED Equation.3 (6)
This shows that the additional income received by workers and/or capitalists in Portugal matches their additional expenditure on less expensive English cloth, and:
EMBED Equation.3 (7)
which shows that the same is true for English workers and capitalists.6
This gives us a simple system (which we call Model S) that does not take into account crossprice effects. Model S has five independent equations, (1) to (5), and three unknowns: EMBED Equation.3EMBED Equation.3andEMBED Equation.3. They set out conditions for: a) complete specialization, b) fullemployment, c) balanced trade, and d) balanced aggregate supply and demand, for each country. Ricardo claims that market forces will generate a solution to this system. However, this is clearly not the case, as the system is missing two degrees of freedom and is thus overdetermined and not generally solvable.
Moreover as noted in footnote 2, from 7.16 and 7.17 it is clear that though Ricardo based his parable on complete specialization, partial specialization would also result in an overdetermined and unsolvable mathematical outcome as it would remove one of the full employment constraints (1) or (2) above but still be missing one degree of freedom.
3. CrossPrice and NCountry Formalizations are also OverDetermined
To see if the overdetermination problem results from not taking crossprice effects into account, or if it is an artifact of the twocountry model, we construct an ownprice and crossprice interpretation of Ricardos parable (Appendix B expands this to an ncountry model).
We start by including crossprice effects. Classical political economists generally focused on the costbased determinates of equilibrium natural prices (see 7.21 above) and thought of market prices as relatively uninteresting transitory prices that were not fruitful objects of analysis. They also understood that demand was affected by real price changes relative to other prices, as opposed to nominal overall price changes that do not change relative prices or incomes [Ricardo, 1817, Ch. 7]. They therefore realized that a nominal price change in one good would affect the real prices of the other goods. This effect would be particularly strong in a twogood model and this might have led them to consider crossprice as well as ownprice effects.
To allow for this possibility, Model G includes crossprice effects. This implies the following system of four demand equations:
EMBED Equation.3 (8)
EMBED Equation.3 EMBED Equation.3 (9)
EMBED Equation.3 (10)
EMBED Equation.3 (11)
where EMBED Equation.3 andEMBED Equation.3are the proportional changes, from autarkic demand of unity, in English demand for wine, Portuguese demand for wine, Portuguese demand for cloth, and English demand for cloth, and EMBED Equation.3andEMBED Equation.3 are their respective demand functions, as in Model S.
To these equations we must add, as in Model S, two fullemployment equations that assume complete specialization:
EMBED Equation.3 (12)
EMBED Equation.3 (13)
and one balanced trade condition:
EMBED Equation.3 (14)
W assume normal responses to price changes and normal specie flow international exchange rate effects so thatEMBED Equation.3and EMBED Equation.3, all other variables are greater or equal to zero, and EMBED Equation.3 and EMBED Equation.3 These inequality conditions assume that some Portuguese wine consumers, and some English cloth consumers, substitute consumption of cloth for wine, and wine for cloth, in response to lower relative prices of each, and that the equilibrium exchange rateEMBED Equation.3sets terms of trade between the relative price ratios of the two countries (as in Model S).
Finally, as with Model S, posttrade aggregate income and expenditure for both countries will be balanced in this system, as from (12) we have:
EMBED Equation.3
and from (13) we have:
EMBED Equation.3
But from (14) these imply that:
EMBED Equation.3 (15)
demonstrating that Portuguese consumers spend all the extra export income that they make by specializing in wine production on (relatively inexpensive) English cloth imports and (relatively more expensive) domestically produced wine, and:
EMBED Equation.3 (16)
which gives a similar result for English consumers.
We now have a more general formalization of Ricardos parable. It again provides for: a) complete specialization, b) fullemployment, c) balanced trade, and d) balanced aggregate supply and demand, for each country. However, this more complete model has five unknowns:EMBED Equation.3EMBED Equation.3EMBED Equation.3EMBED Equation.3and EMBED Equation.3, and seven equations; it is again missing two degrees of freedom and is thus overdetermined and not solvable. Again, partial rather than complete specialization will result in deficit of one degree of freedom, and the model will still be overdetermined.
Appendix B generalizes the constant elasticity version of this model (see section 4) to ncountries and shows that this general model is also overdetermined and not solvable. As this degrees of freedom calculation is independent of the precise specification of the model (with constant elasticities), this demonstration shows that the general ncountry, ngood, Ricardian model with crossprice effects is overdetermined.
We conclude that regardless of whether Ricardos story is interpreted more restrictively (as in Model S) or more generously (as in Model G), and regardless of the number of trading partners to which it is applied (see Appendix B), it is fundamentally overdetermined and not generally solvable.
4. A Fully Specified Constant Elasticity Model of Ricardos Parable
It is instructive to work out the policy implications of the overdetermination problem by specifying and solving a constant elasticity version of Model G that we call Model E. In Model E behavioral demand decisions are assumed to be captured by fixed consumer elasticities of demand for wine and cloth in England and Portugal respectively.
Let EMBED Equation.3 be the English price elasticity of demand for wine, EMBED Equation.3 the Portuguese price elasticity of demand for wine, EMBED Equation.3 the Portuguese price elasticity of demand for cloth, and EMBED Equation.3 the English price elasticity of demand for cloth. All other notation will follow that of Model G.
Note that these crossprice models take into account the fact that when the price of an imported good is lower than the domestic price of the same good, the relative price of the other (nonimported) good rises. Thus, for example, if cloth can be bought in England at a price (in Portuguese currency) that is lower than the price of Portuguese cloth, Portuguese wine becomes relatively more expensive than cloth for Portuguese consumers. This implies that the Portuguese will purchase less wine and more cloth than they used to, in response to an appreciation of (the international value) of Portuguese prices and a reduction in English prices.
Equations (17) and (19) model the increased demand for imports resulting from the reduced own prices of imported goods, while equations (18) and (20) model the induced decline in demand for domestically produced goods resulting from their relative (domestic) price appreciation. These equations explicitly substitute ownprice for crossprice elasticities a procedure that will only work in the twogood case. (See Appendix A for the derivations of these equations, and Appendix B for ngood and ncountry models with standard crosselasticity formulations, which also demonstrate that the results below are not an artifact of the twogood model.)
In Model E we can fully specify 1b through 4b as the following four price elasticity of demand equations:
EMBED Equation.3 (17)
EMBED Equation.3 (18)
EMBED Equation.3 (19)
EMBED Equation.3 (20)
To these we can add the fullemployment equations assuming complete specialization:
EMBED Equation.3 (21)
EMBED Equation.3 (22)
and the balanced trade condition:
EMBED Equation.3 (23)
Where as with the general model, for feasibility and specialization: EMBED Equation.3and EMBED Equation.3 and all other variables are greater or equal to zero; and EMBED Equation.3and EMBED Equation.3 Finally, as the posttrade aggregate income and expenditure balances for both countries derived in Model G depend only on (21), (22), and (23), versions of aggregate demand balance equations (13) and (14) will hold in Model E.
Because consumer demand behavior in Model E is presumed to be captured by fixed price elasticities of demand, the general overdetermination problem of Model G becomes a condition on possible elasticities of demand. Since Model E has nine variables (the four changes in quantity demanded, the four elasticities, and the exchange rate) and seven equations, only two of the elasticities can be freely specified. Overdetermination implies that in order for there to be a solution to Ricardos parable (or feasible natural prices, an exchange rate, and quantities demanded, that satisfy all of Ricardos conditions), two of the demand elasticities must be precise functions of the other two.
For example, if we set EMBED Equation.3 , EMBED Equation.3 , and solve for EMBED Equation.3 and EMBED Equation.3 , we get the following general solution with two degrees of freedom to Ricardos parable (after excluding degenerative one degree of freedom solutions with negative elasticities):
EMBED Equation.3
Similarly we can solve for EMBED Equation.3EMBED Equation.3EMBED Equation.3EMBED Equation.3, andEMBED Equation.3 based on these elasticity solutions.7
For example, if we assume that wine is a price elastic luxury good in both countries and set EMBED Equation.3 and EMBED Equation.3, we get the following unique elasticity solution to Ricardos example:
EMBED Equation.3 (24)
EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3
EMBED Equation.3= 1.2234
It can be verified through substitution that these values solve equations (1) to (5) above. Thus these values are consistent with complete specialization, fullemployment, balanced trade, and a feasible exchange rate that induces Portugal to specialize in wine and England in cloth. In addition, assuming that workers and capitalists receive and spend all of the revenue from production and that the lower prices on imported products are completely passed through to consumers, aggregate income and expenditure will be equal in both countries.8
Although theoretically consistent, this is an extremely unlikely solution as it requires that the Portuguese price elasticity of demand for cloth be inordinately high: EMBED Equation.3 , especially for a good that is usually considered a necessity. Reasonable demand behavior in Model E thus appears to be generally inconsistent with the notion that free trade (or automatic market mechanisms) can generate sustainable specialization and comparative advantage. Rather, in order to partially realize sustainable benefits from comparative advantage, it appears that England will have to restrict imports of Portuguese wine in order to maintain balanced trade.
More specifically, an English tariff or quota on Portuguese wine imports would have to restrict English imports of Portuguese wine to a level consistent with Portuguese demand for English cloth based on EPC< 2.7177. This reduction in wine exports would reduce the gold inflow, and lower the goldprice increase in Portugal, so that E < 1.2234. However, because of the tariff or quota on Portuguese wine, English demand for less expensive Portuguese wine would still be reduced: EMBED Equation.3 to a level consistent with Portugals demand for cheap English cloth:EMBED Equation.3. This implies that if full employment were to be maintained in both countries, neither Portugal nor England could fully specialize so that only partial gains from trade could be realized.
A (nonspecie flow based) increase in E could also reduce the trade imbalance. However, any such a single variable adjustment, without additional trade or demand management policy measures, would similarly most likely not produce balanced trade and full employment in both countries, as the model requires two extra degrees of freedom for a general solution.
5. Conclusion
We have found that, with a plausible consumer price response, Ricardos story is mathematically overdetermined. Therefore, a sustainable and mutually beneficial free trade equilibrium point will generally not exist in Ricardos model. Even when all of its assumptions are satisfied, Ricardos parable does not demonstrate mutually beneficial free trade. Rather, the parable should be interpreted as demonstrating the potential for mutually beneficial and sustainable gains from trade based on comparative advantage when this trade is properly managed and not exclusively governed by market forces.9
Put another way, under plausible demand assumptions, sustainable and mutually beneficial comparative advantage based trade between England and Portugal can only be realized if England reduces imports of Portuguese wine to a level commensurate with Portuguese demand for English cloth through a public policy mechanism. Even if all of the standard assumptions are satisfied, mutual comparative advantage based gains from free trade will generally not be forthcoming as purely marketbased trading will generally produce unsustainable unbalanced trade and unemployment.
The realization of gains from comparative advantage based trade is thus, like the realization of profit in Marxian economic modeling, or of fullemployment in a Keynesian or Keleckian macroeconomy, dependent on demand management, as marketgenerated demand will often be inadequate or disproportionate to production depending on demand behavior and price response. Neoclassical theory circumvents this problem by assuming highly responsive (and unrealistic) elasticities of substitution in production.10 In Ricardos classical comparative advantage model this general realization or effective demand problem produces a mathematical inconsistency due to overdetermination.
Appendix A
Equations (18) and (20) are derived as follows. By definition:
EMBED Equation.3
which after cancelling the EMBED Equation.3 terms in the denominator and a bit more manipulation becomes (18). Equation (20) is derived in a similar fashion.
Appendix B
It is instructive to outline a threegood, threecountry model, and then extend it to the ngood, ncountry case. Assume that we have three countries England, France and Portugal that produce three goods Cloth, Beef, and Wine, respectively. Assume that each country initially consumes and produces one unit of each good at the following labor productivity levels. In Portugal 70 units of labor can produce a unit of wine, 80 units of labor can produce a unit of Beef, and 90 units of labor can produce a unit of cloth. In France the corresponding ratios are: 95, 85, and 105. In England: 120, 110, and 100. With these relative productivity levels, England will specialize in the production of cloth, France in beef, and Portugal in wine.
Looking at England, given two exchange rates,EMBED Equation.3, which gives the price of Portuguese currency in English currency, andEMBED Equation.3, which does the same for French currency, and using the notation of Section 3, we have the following set of three equations for English demand for the three goods:
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
Where EMBED Equation.3 and EMBED Equation.3 are ownprice elasticities for English demand for wine and beef from Portugal and France, respectively. The other four elasticities are crossprice elasticities reflecting the affects of relative changes in French beef prices (EMBED Equation.3) on English demand for Portuguese wine, and Portuguese wine prices (EMBED Equation.3) on English demand for French beef; and of Portuguese wine prices (EMBED Equation.3) and French beef prices
(EMBED Equation.3) on domestically produced and consumed English cloth. Note that crossprice elasticities cannot be converted to ownprice elasticities in this case as they can in the twocountry case.
Since England has a comparative advantage in cloth it will specialize in this good. In order to maintain fullemployment England must produce 3.3 units of cloth which it will consume at home and export to France and Portugal. This results in the following fullemployment condition for England:
EMBED Equation.3
Finally, if England is to have balanced trade with France and Portugal the following balanced trade condition must be satisfied:
EMBED Equation.3
France or Portugal will have to satisfy a similar set of five equations. The remaining third country will only have to satisfy four independent equations as the third trade balance equation will be dependent on the other two trade balance equations. We will thus get a total of 14 equations and 29 variables (18 elasticities, 9 changes in quantity demanded, and 2 exchange rates) for the three countries. This sums to 15 degrees of freedom for 18 exogenous elasticities, leaving three missing degrees of freedom for a general solution.
For n>2, similar ncountry, ngood, model will require EMBED Equation.3elasticities, EMBED Equation.3 commodities, and EMBED Equation.3 exchange rates for a total of EMBED Equation.3 variables. On the other hand the model will require EMBED Equation.3 demand equations, n full employment equations, and n1 trade balance equations (because world trade must net to zero, any single countrys trade balances can be inferred from those of the other n1 countries), implying that it will have EMBED Equation.3  EMBED Equation.3 = EMBED Equation.3 degrees of freedom. But as it needsEMBED Equation.3, it will be missing EMBED Equation.3 degrees of freedom.
Acknowledgments
The author wishes to thank the many colleagues whose support was critical to sustaining the effort to getting this paper published despite numerous rejections over many years from multiple mainstream and heterodox journals: Mel Rothenberg, Joe Persky, Bill Barclay, Sidney Hollander, and Elce Redmond, as well as Mehrene Larudee and Haydar Kurban, of the Chicago Political Economy Group; students of the Neoliberalism and Globalization Big Problems 20002007 senior seminar cotaught with Mel Rothenberg at the University of Chicago where the paper was conceived; William Greider and Ian Fletcher whose supportive feedback came at particularly despairing moments; and last but not least, the anonymous referees of the Review of Political Economy who took the submission seriously and helped improve it. May dogmatic barriers in political economy someday come tumbling down!
References
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Colander, D. (1998) Macroeconomics 3rd Edition (New York: Irwin/McGraw Hill).
Dornbusch, R., Fischer, S. & Samuelson, P. (1977) Comparative advantage, trade, and payments in a Ricardian model with a continuum of goods, American Economic Review, 67(5), pp. 823839.
Eatwell, J. & Taylor, L. (2000) Global Finance at Risk (New York: New Press).
Krugman, P. (1996) Pop Internationalism (Cambridge, MA: MIT Press).
Leontief, W. (1933) The use of indifference curves in the analysis of foreign trade, Quarterly Journal of Economics, 27, pp. 493501.
Lerner, A. P. (1934) The diagrammatic representation of cost conditions in international trade, Economica, 12(1), pp. 319334.
MacEwan, A. (1999) NeoLiberalism or Democracy? (New York: Zed Books).
Marglin, S. (1984) Growth, Distribution, and Prices (Cambridge, MA: Harvard University Press).
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Meade, J. E. (1952) A Geometry of International Trade (London: George Allen & Unwin).
Mill, J. S. [1848] (2004) Principles of Political Economy (Amherst, NY: Prometheus Books).
Prasch, R. (1996) Reassessing the theory of comparative advantage, Review of Political Economy, 8(1), pp. 3956.
Ricardo, D. [1817] (1973) The Principles of Political Economy and Taxation (New York: Dutton).
Salvatore, D. (2005) Introduction to International Economics (New York: John Wiley).
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Taylor, L. (1990) Socially Relevant Policy Analysis (Cambridge, MA: MIT Press).
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Footnotes
1. I hope that this endogenous theoretical critique contributes to more realistic and beneficial international trade policies. To avoid any misunderstanding regarding the policy implications of this analysis, let me state at the outset that the issue here is not whether trade or globalization is beneficial (I generally favor increased world trade), but rather whether free, or marketled, trade is viable. As many of the empirical critiques point out, during the 19501973 Bretton Woods managed trade regime, world trade grew faster (according to WTO statistics at almost double the rate) than during the Neoliberal 19732005 period (WTO, 2006, Chart II.1).
2. Many introductory texts use the simple barter story to demonstrate the advantages of specialization and trade, and jump from this to support free trade by assuming that the international price in gold for Portuguese wine is 100 and Portuguese cloth 112.5; i.e., they assume a 25% inflation of Portuguese prices, or in modern terms, a 25% appreciation of Portugals currency relative to Englands. The better texts explain that either price inflation (with fixed exchange rates via a specieflow mechanism) or exchange rate devaluation is necessary for Ricardos comparative advantage story to work. After covering absolute advantage, Colander (1998, p. 134) notes: "The point of the argument is that both developed and developing countries have comparative advantages in different goods. How do I know? Because trade is a twoway street. If one country could produce all the goods at a lower cost, all production would flow to that country, and its exchange rate  the rate at which one countrys currency exchanges for another countrys currency  would rise. Then the comparative cost structure would change." Some international economics texts go into more detail (see Salvatore, 2005, Ch. 2).
3. My model also applies to cases of partial specialization and unemployment in one of the trading partners. The major difference, as can be deduced from dropping one of the complete specialization full employment conditions below, is that one rather than two degrees of freedom will be missing.
4. From the third edition published in London in 1821 by John Murray. See HYPERLINK "http://www.econlib.org/LIBRARY/Ricardo/ricP.html" http://www.econlib.org/LIBRARY/Ricardo/ricP.html for the entire book.
5. Although the argument in this paper does not depend on complete specialization in both countries see footnote 3.
6. As Ricardo, like other classical political economists, believed that real wages were socially determined, most of the benefits of trade in his model will accrue to capitalists see footnote 9 below.
7. All calculations have been done with Scientific Workplace, Version 2.5 software, a product of TCI Software Research.
8. It can also be demonstrated that these solution satisfy the MarshallLerner conditions, indicating that devaluation will improve the trade balance in either country.
9. One might question whether this outcome is a function of the limitations of the Ricardian, laborvalued pricing, fixedcoefficient model, which does not allow for partial specialization and does not take consumer demand behavior into account. In fact, Ricardos neglect of demand was recognized by Mill [1848]. Based on work by Marshall (1890), Leontief (1933), and Lerner (1934), Meade (1952) perfected a geometric demonstration of a free trade equilibrium that allowed for partial specialization and included demandside price response behavior. It is widely believed that Meades more flexible variablecoefficient story, which explicitly assumes that prices are determined by supply and demand, and that changes in relative prices will affect production techniques, shows that unhindered international market forces will induce beneficial and sustainable trade based on comparative advantage (Chacholiades, 1990, Ch. 4). However, Meades proof depends on highly unrealistic substitution parameters and fullemployment assumptions, particularly for northsouth trade between countries with highly unequal factor costs. This might be better modeled as unequal exchange (Baiman, 2007).
10. In a wellknown paper, Dormbusch et al. (1977) substitute a continuum of goods (each produced with fixed labor productivity as in the original Ricardian parable) for the twogood model, and then hypothesize movement along the continuum as countries specialize in their comparative advantage goods. This allows for continuous labor cost or productivitybased substitution in production, as in the neoclassical model, while assuming fixed labor productivity for each individual good. Trade is then balanced through real wage adjustments that are inconsistent with Ricardos belief in socially determined real wages that do not adjust to balance trade.
Using a truly neoclassical trade model, Meade constructed a proof of the existence of a free trade equilibrium. His proof, which underlies neoclassical trade theory, assumes variable coefficient production with highly varying diminishing marginal product substitution. Although standard neoclassical macro models require variable coefficients and highly unrealistic elasticities of substitution in production to work, this is not the case for variable coefficient (with more modest and realistic factor price substitution) neoMarxian and neoKeynesian macro models (Marglin, 1984; Taylor, 1990, 2004).
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