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The Unequal Exchange (A Summary)

The Unequal Exchange (A summary)

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(Conference on “New Approaches to Trade” at IDS, University of SussexJ 8.9.1975)

The Assumptions

Irrespective of any divergences between schools and theories, everybody will agree that ex post the price, P_a, of a commodity “a” is strictly equal to the price of the material inputs : c_a, plus the price of the immaterial inputs, the so-called value added.

This second part is the total of the remunerations of the factors (or of their owners), that is of those who “contributed” (between inverted commas) to the production under question, or (without inverted commas) of those who are bestowed with an established claim on a part of the value of this same production. It is sub-divided into the part accruing to wages v_a, and the part accruing to all other claims (profit, rent, interest etc.), and which, in a simplified model, we can aggregate under a single term, R.

In a system of k processes, we will then have: \begin{aligned} c_a + v_a & + R_a = p_a& \\ c_b + v_b &+ R_b = p_b& \\ \vdots \\ c_k + v_k &+ R_k = p_k &\\\end{aligned}

Now, this system, as every system, must ultimately be linked to some determination from outside the system. The exogenous element ensuring this is the independent variable of the system. Eventually, it is the choice of this independent variable which splits up the economists into two major camps, the subjectivists and the objectivists.

For the former, this ultimate determinant is to be found in the area of circulation; it is the needs and preferences of the consumers. These needs and preferences determine the prices of final goods and the prices of final goods, in their turn, determine upwards the prices of the ’’productive services’’, according to the proportion each one of them “contributes” to the production of final goods. These prices of productive services correspond to the various shares in the national income.

On the contrary, value theories situated on the cost-of-production side consider that the system provides itself at each time and prior to prices with a certain pattern of distribution of the national income. This is the independent variable, varying exogenously and actually reflecting the power relation of the moment between antagonist classes or groups. Then the prices of the factors determine downwards prices of the different commodities produced.

In a simplified Ricardian or Marxian model, where the national income is divided into two shares only, wages and profit, the former being fixed before the sale of the product and independently of its results and the latter being residual, it is obvious that the ultimate determinant, the independent variable of the system, can only be the wage. What is more, under these conditions, the wage can only be conceived in absolute terms, actually as a physical quantity of the numéraire-commodity k, representing the output of one particular process of the system. (Regime of convertible currencies).

This is the primary basic assumption underlying all theorems of the Unequal Exchange.

When this assumption is transposed onto the international plane, it has to be further qualified. In the international framework, capital is mobile enough to generate a tendency of equalization of the rates of profit on a world scale, while labour power is immobile enough to prevent national discrepancies in the rates of wages from being levelled off by foreign competition. There is no such thing as an international wage, whereas any national discrimination of profits constitutes a more or less short-run anomaly.

Naturally, besides the above, the model contains usual general simplifying assumptions, namely absolute free-trade conditions, no government interferences, absence of customs and of transport expenses.

The Theorems

There are three main theorems in the Unequal Exchange argument. They bear respectively on the international division of labour, the international values and the problems of development.

The International Division of Labour

If specialization is made according to comparative costs, yet not in terms of physical costs, or social costs (whatever this may mean), but in terms of market prices, determined by and equal to the amount of the prices of factors,

if prices of factors are fixed in an extra-economic way, so that the cheapest factor is not necessarily the most abundant,

if quantities of factors are not proportionate to each other, at least from branch to branch in each country,

it may follow

that trade results in the wrong specialization with, as a consequence, general reduction of real income in the whole system.

Since the thing to demonstrate is a mere possibility, a numerical example would do.

Suppose that Ricardian costs, 80, 90, 120, 100 are composite, each one of them made up of two different factors, F and G, entering in the proportion of 5 to 3 into wines and 1 to 8 of into clothes.

Portugese wine 50 F & 30 G
Portugese cloth 10 F & 80 G 60 110
English wine 75 F & 45 G
English cloth 11\frac{1}{9} F & 88\frac{8}{9} G 86\frac{1}{9} 133\frac{8}{9}
146\frac{1}{9} 243\frac{8}{9}

If both factors have the same unit-price everywhere (e.g., one monetary unit), monetary costs will be the same (or stand in the same proportions) as Ricardian physical costs:

Portugese wine: (50 \cdot 1) + (30 \cdot 1) = 80
Portugese cloth: (10 \cdot 1) + (80 \cdot 1) = 90
English wine: (75 \cdot 1) + (45 \cdot 1) = 120
English cloth: (11\frac{1}{9} \cdot 1) + (88\frac{8}{9} \cdot 1) = 100

By either macro- or micrometrical standards, Portugal will specialize in wine and England in cloth. In that case,

Portugal produces 2 “wine” with 100 F & 60 G
England produces 2 “cloth” with 22\frac{1}{9} F & 177\frac{7}{9} G 122\frac{1}{9} 237\frac{7}{9}
and the whole system, for the same
aggregated production, spares 23\frac{8}{9} 6\frac{1}{9}

Suppose now that the price of factor F doubles in Portugal, all other things remaining unchanged. Monetary costs will work out as follows:

Portugese wine: (50 \cdot 2) + (30 \cdot 1) = 130
Portugese cloth: (10 \cdot 2) + (80 \cdot 1) = 100
English wine: (75 \cdot 1) + (45 \cdot 1) = 120
English cloth: (11\frac{1}{9} \cdot 1) + (88\frac{8}{9} \cdot 1) = 100

As 130/100 > 120/100, England specializes in wine and Portugal in cloth. As a consequence,

Portugal produces 2 “cloth” with 20 F & 160 G
England produces 2 “wine” with 150 F & 90 G
170 F & 250 G

and the whole system, for the same aggregate production, wastes (as compared with the pre-trade situation) 23 8/9 F and 6 1/9 G.

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The above point has been disputed by David Evans on the ground that total quantities of factors employed after specialization do not square, country by country, with those employed before. For figures in excess, Evans argues that either the additional quantities of factors existed already and were formerly unemployed or they did not. If they did exist, maximization of their employment is welcome; if they did not exist, specialization could not have created them.

My answer is that (a) the goal is not the maximization of employment irrespective of the output, but the maximization of the output for a given employment, (b) as immobile as they may be from country to country, factors are not inelastic within the boundaries of one country as Heckcher-Ohlin have assumed. Specialization does create factors. Most of them are convertible into one another (produced out of one another). If they were not and if we abode by the usual oversimplified models where all products are exportable, not only my refutation of the comparative costs theorem but the theorem itself would collapse. For wrong specialization causes the imbalance pointed out by Evans not qua wrong but just qua specialization. In the first case above, specialization of Portugal in wine and of England in cloth, although quite right, would nevertheless make the former spend 100 F and 60 G instead of the previous 60 F and 110 G and England, 20 F and 180 G instead of the previous 86 1/9 F and 133 8/9 G. As soon as the plurality of factors and the variety df their proportions is introduced into the model, to find out figures satisfying Evans objection is as difficult with endogenous as with exogenous determination of factor prices. There is indeed no reason to suppose that the proportion of factors required for either branch is exactly the same to that of the existing quantities of factors in the country at the precise moment of the opening of trade.

To get over it, one has to make some supplementary assumptions: existence of unexportable and interchangeable commodities, of second-best techniques (especially in these home orientated branches) and, above all, the fact that all factors, even “primary” ones, except perhaps the roughest uncultivated land and the rudest illiterate labourer, are themselves, in the long run, being produced out of one another. (Germany does not specialize in chemicals because she got an abundance of chemists but she produces chemists abundantly because she is specialized in chemicals).

On the other hand, if the exogenous (institutional) forces determining income distribution are strong enough, factors which are immobile in the economic sense, may very well be as mobile physically as is necessary to palliate technical distortions of the sort pointed out by Evans. Reciprocally, when the market for a factor is free enough, a small physical mobility may in some circumstances be sufficient to implement what we call ’’mobility” in the economic sense. The massive immigration of South-European and North-African labourers of recent years had no effect at all on the wage rate gap between home and recipient countries, whereas marginal capital movements, absolutely insufficient in physical terms to promote quick development of the Third World, proved nonetheless quite sufficient to bring about a tendency of equalization of the rate of profit.

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Now, if we reason in terms of maximization of the output instead of minimization of the inputs, we can use the following numerical example bringing into play the two traditional factors, labour and capital, and two goods, j and k, making up all inputs and outputs of the system.

Let us write p_j, p_k for price of j, k
r_{Aa}, r_{Ba}, r_{At}, r_{Bt} for rate of profit in country A, B resp. in autarchy and rade situation.
p_k = 1.
All wage rates are equal to 1k.

The proportions of factors (techniques) are the same from country to country but not from branch to branch. In branch j, this proportion is a fixed capital of 80j and 8Ok for 10 units of labour, while in branch k, it is 10j qnd 10k for 10 units of labour. Country A produces 10j and 100 k; country B produces resp. 12 and 80. If monetary wages are the same everywhere in terms of an international standard, viz., one k for one unit of labour, and if constant circulating capital (intermediate consumption) is abstracted, we will have the following equations:

Country Br. Wages Profit Output Solutions J K
A J (10 \cdot 1) + (80p_j + 80)r_{Aa} = 10p_j p_j = 73 10
K (10 \cdot 1) + (10p_j + 10)r_{Aa} = 100 r_{Aa} = 0,1216 100
B J (10 \cdot 1) + (80p_j + 80)r_{Ba} = 12p_j p_j = 47,5 12
K (10 \cdot 1) + (10p_j + 10)r_{Ba} = 80 r_{Ba} = 0,144 80
Total autarchy production 22 180
A specializes in K and produces 200
B specializes in K and produces 24
Aggregate inputs being the same, overall gain is 2 20

Suppose now that wages in A are multiplied by 6, all other things remaining constant Equations in A will turn out:

A J (10 \cdot 6) + (80p_j + 80)r_{Aa} = 10p_j p_j = 38
K (10 \cdot 6) + (10p_j + 10)r_{Aa} = 100 r_{Aa} = \frac{4}{39}

As 38 < 47,4, A specializes in j and B in k.

Obviously, this is the wrong specialization, since with the same aggregate inputs our system will produce 20j and 160k, instead of 22j and 180k in the autarchy situation or 24j and 200k in the inverse specialization.1

To be sure, if we have been able to say which one is the wrong specialization and somehow to measure the loss, this is only due to the oversimplification of our examples and to prearranged figures allowing both inputs in the first example and both outputs in the second to vary in the same direction, thuş making it possible to compare heterogeneous physical magnitudes independently of the prices. But when inputs and outputs become more numerous, such combinations are practically impossible. But the very fact that certain variations in the distribution of income, that is mere transfers of value from one economic agent to the other, without any change in the material conditions of the production, entail a reswitching of specializations is sufficient in itself to prove that free trade does not necessarily lead to the optimal division of labour, even it it does not enable us to say which one is sub-optimal and by how much.

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Let us now revert to the specialization with equal initial wages. After-trade equations will run as follows:

A K (20 \cdot 1) + (20p_j +20)r_{At} = 200
B J (20 \cdot 1) + (160p_j + 160)r_{Bt} = 24p_j

If r_{At} \neq r_{Bt} (Ricardian condition), we shall have in the system one more degree of liberty and we must take as given exogeneously one of the three unknowns, r_{At}, r_{Bt}, p_j. Rates of profit being residual, the only variable which, under the circummstances, can be exogenous is p_j and here we are with the neoclassical story of demand elasticities fixing freely the ratio p_j/p_k between the limits of comparative costs. In the above example, these limits are 73, 47,5.

At p_j = 47,5 workers in country A gain to the extent that they buy j and workers in country B neither gain nor lose anything. At p_j = 73, workers in country A neither gain nor lose, while workers in country B lose to the extent that they buy j. At a medium price, p_j = 60 1/4 k, gains and losses are equal for every unit of j bought by the workers of either country. Below the medium price, workers of A gain more than what workers of B lose and above that price the effect is contrary. Workers gain or lose to the extent that they consume the imported or the exported article, being given that with the opening of the trade the former becomes cheaper and the latter dearer.

As regards rates of profit, at p_j = 47,5, there is of course, no variation in country B, but the rate of profit in country A rises from 0,1216 to 0,1856; at p_j = 73, the rate of profit in country A remains unchanged, but that of country B rises from 0,144 to 0,146. In all intermediate prices, both rates rise. This means that even in cases where the aggregate working classes of both countries is better off – 47,5 < p_j < 73 – both capitalist classes get a higher rate of profit too.

If we pass now to the second case of specialization, with unequal initial wages, we have the following after-trade equations;

A J (20 \cdot 6) + (160p_j +160)r_{At} = 20p_j
B K (20 \cdot 1) + (20p_j + 20)r_{Bt} = 160

Abiding by the same assumption, r_{At} \neq r_{Bt} we see that according to the elasticities of international demand p_j will vary from 38k to 47,5k and that workers throughout the system will be better or worse off to the extent that they consume the imported or the exported article exactly as in the previous case of “right” specialization.

But those are gains or losses in use values. In terms of abstract value, that is, in terms of the homogenizing element (units of k), wage rates have been assumed to be rigid. Consequently, if specialization – either right or wrong – does not cause a variation in the level of the employment – as in the above example – the mass of the wages, in monetary terms, will also remain unchanged. It is then the mass of profits which will be reduced to keep in line with the reduction of value added subsequent to the wrong specialization.

But the decline of the mass of profits may very well be consistent with a rise of their rates, if the wrong specialization involves either the dropping of some capital out of business, or – as in the above example – the transfer of a certain amount of capital into the pre-trade low rate country. Contrary to a previous assertion of mine – last March in Sussex – I think now that neither rate of profit can decline as a result of a wrong specialization.

To put it concretely: some factor being under or overvalued in England or in Portugal, English wine and Portugese cloth acquire a monetary comparative advantage, notwithstanding their physical disadvantage and begin to arrive resp. at Portugese and English ports underselling local productions. Portugese vineyards and English textile mills will be destroyed and this will be a pity for the aggregate performance of both countries. But, cloth rising in Portugal in terms of wine and wine rising in England in terms of cloth while neither cost of production has risen, there is no reason for pre-trade rates of profit in the surviving branches resp. Portugese cloth and English wine, to fall.

In this respect, I must refer to a misunderstanding created by some poor passages of the second chapter of my book and of my tables in pages 62 and 63. The decline of the rate of profit of country B which is only implicit in these tables is linked with the passage from non-mobility to mobility of capital and not with the one from pre-trade to after-trade.

The unequal rates which can be deduced from my model as previous rates of profit, for resp. country A and country B, are not the rates of profit in the autarchic situation but rates of profit after trade and specialization, though before financial circulation and equalization of profits.

In the passage from pre-trade to after-trade situation, rates of profit rise generally: in the passage from non-equalization to equalization, general rate of profit will necessarily lie between, the previous national ones.

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The International Values

We pass now to the second stage. It is characterized by free financial circulation added to the free commodity circulation already attained at the previous stage and entailing a tendency towards the formation of a general rate of profit.

As soon as we assume that r_{At} = r_{Bt}, the degree of liberty (indetermination zone), which we found above on the basis of the contrary assumption (r_{At} \neq r_{Bt}), vanishes, p_j becomes an unknown endogenously determined (along with the common rate of profit), and there is a single solution, which in the above numerical example is p_j = 60 5/6 k, r = 0,1455.

In other words, as long as the capital was immobile, the terms of trade were freely floating – according to the whims of reciprocal demands – within the limits of the Ricardian limbo. The only relevant question then was how the entire limbo moved about when the distribution of income was changing (in the above example from the range (73 – 47,5) to that of (47,5 – 38). But when mobility of capital starts up, the terms of trade become predetermined by the absolute differentials of monetary costs, consequently by the discriminating (immobile) element in those costs and there are no more limbos.2

In the real world, the most important discriminating factor is the wage and this is why the main theorem of the Unequal Exchange is formulated in terms of wage variations. Theoretically, however, it could equally be formulated in terms of any factor varying exogeneously along national lines, for instance, rent.

Since all demonstrations I am capable of have already been presented in my previous (long) paper, I shall here confine myself to give a mere enunciation of the theorem:

In a system of two or k countries (already trading and specialized in two or k articles),

if all w’s (wages) are given exogeneously, prior to anything, in terms of units of one among the k goods,

if the rate of factor r is equalized throughout the system but fixed simultaneously and in mutual interdependence with prices of goods, a unique set of prices being consistent with this equalization,


any autonomous variation of some w_i will entail q variation of the same sign of respective p_i (price of i) and a reverse variation of (general) r, viz., \delta w_i \cdot \delta p_i > 0 and \delta w_i \cdot \delta r < 0,

and, as a consequence,

it will entail a variation of the real revenue of people receiving all other w’s, variation of the opposite sign to that of the variation of