An Assessment of Samuelson’s Ricardo-Sraffa Trade Model

Abstract

This article assesses Samuelson’s attempt to introduce Sraffa’s framework of “production of commodities by means of commodities” to the neoclassical-Ricardo trade model. We slightly modify Samuelson’s model to consider, on the one hand, more commodities than countries and, on the other hand, a positive rate of interest and full international (finance) capital mobility. In the first case, comparative advantage is unable to predict the direction of trade. In the second case, the principle does not warrant the existence of trade. In conclusion, a closer look at the neoclassical-Ricardian trade model through the lenses of Sraffa casts more doubts than certainties of the comparative advantage theory.

Keywords:

• Comparative advantage
• international trade
• Ricardo
• Samuelson
• Sraffa

JEL CLASSIFICATIONS:

• F11
• F60
• B24
• B51

Acknowledgements

We thank, without implication, the two anonymous referees for their helpful comments and suggestions.

Notes

1 See, among others, Feenstra (2004) for an undergraduate exposition of the neoclassical-Ricardian trade model.

2 Workers and firms usually bargain the money wage rate. Given the labor coefficients, the fall in the money wages ratio implies that Portugal’s real wage rate is also falling. Since England produces all commodities, all prices are proportional to its wage rate. Hence, Portugal’s money wage rate falls relative to all prices. When Portugal starts producing wine, a subsequent fall in its money wage rate causes the price of wine to fall, thereby leaving unchanged the real wage rate measured in wine. Nevertheless, the real wage rate will continue to decrease in terms of cloth. If Portugal ends up producing all commodities, the fall in its money wage rate leaves its real wage unaffected, but it raises England’s real wage rate. Therefore, variations in the relative money wage rate are equivalent to changes in both countries’ real wages. This close link between the relative money wage rate and real wage rates allows the specialized literature to consider variations in the former to examine the trade pattern determination.

3 As one anonymous referee correctly remarked, this is equivalent to assuming fixed exchange rates. However, this is a simplifying assumption, and the following argument does not hinge on it.

4 Condition 7 implies that:

$\frac{1}{a_{02}}>\frac{1}{a_{01}},\frac{a_{01}}{a_{02}}>1, \mathrm{and} \frac{1}{b_{01}}<\frac{1}{b_{02}},\frac{b_{02}}{b_{01}}<1$

By assembling these results, we get

$\frac{a_{01}}{a_{02}}>\frac{b_{02}}{b_{01}}.$

5 The unit cost of wine with the direct-labor-using process is:

$C_1^{\prime }=W{a\prime }_{01}$

The unit cost of wine with the capitalistic process is:

$C_1^{″}=W{a}_{01}^{″}+P_2{a}_{21}^{″}\mathrm{ }$

Since under autarky in Portugal there is only the direct-labor-using process to produce cloth, we have that $P_2=W{a}_{02}^{\prime },$ and so:

$C_1^{″}=W{a}_{01}^{″}+W{a}_{02}^{\prime }{a}_{21}^{″}.\mathrm{ }$

With Samuelson’s numerical example, we can state that:

${a\prime }_{01}<a_{01}^{″}+{a\prime }_{02}{a}_{21}^{″},$

Thus, under autarky, the unit cost of wine with the cloth-capital-using process is always higher than the direct-labor-using process. The same holds for England with the wine-capital-using process of cloth.

6 Since the capital-using process of wine in Portugal requires only cloth as capital, we have: $\begin{array}{c}{P}_1=W{a}_{01}+P_1\left({\overline{P}}_2/{\overline{P}}_1\right)a_{21}\\ & =W{a}_{01}+P_1\pi a_{21}\\ & =\frac{W{a}_{01}}{1-\pi a_{21}}\\ p_1=P_1/W=\frac{a_{01}}{1-\pi a_{21}}\end{array}$

7 Since the capital-using process of cloth in England requires only wine as capital, we have: $\begin{array}{c}{P}_2=W{b}_{02}+P_2\left({\overline{P}}_1/{\overline{P}}_2\right)b_{12}\\ & =W{b}_{02}+P_2{\pi }^{-1}{b}_{12}\\ & =\frac{W{b}_{02}}{1-{\pi }^{-1}{b}_{12}}\\ p_2=P_2/W=\frac{b_{02}}{1-{\pi }^{-1}{b}_{12}}\end{array}$

8 Jones (1980) attempts to reveal the impossibility of defining comparative advantage before trade in a model with intermediate inputs and different input-output coefficients among countries. The author considers a case with two finished products and one intermediate input. The latter is given in quantity and is free to move across countries to get paid the higher rental. Only one of the final goods uses the intermediate input for its production. He then supposes that one country is more efficient in using the input but less efficient in using labor. In this case, the trade pattern may differ or reverse for different terms of trade (the final goods’ relative price). Note that Jones’s assumptions are tantamount to admitting international capital mobility. We leave the discussion about the implications of this phenomenon to Section On the Possibility of Unilateral Exclusion from Trade.

9 See Dvoskin and Ianni (2021) for a general criticism of comparative advantage.

10 Our example resembles that from Jones (1980, sec. III). However, the author employs this setting for alternative purposes. He assumes a given trade pattern and discusses how this Ricardian case becomes a model with Heckscher-Ohlin properties. Then he proceeds to study the distributional effects of a change in the terms of trade.

11 One could also justify this procedure by arguing that, in the current context of globalization, it is no longer relevant to compare countries’ aptitude to produce the finished good integrally, but how good they are at different production stages.

12 See Crespo, Dvoskin, and Ianni (2021) for a critical assessment of the claim about the impossibility of exclusion under flexible wages.

13 Joan Robinson (1973, 16) claimed that the assertion that a nation “cannot be undersold all around” derives from the “postulate of universal full employment.” Nevertheless, in neoclassical theory, full employment is not a postulate but a result of the working of free competition. Indeed, in the pure-labor neoclassical Ricardian model that we have been discussing so far, the fall in the wage rate eventually allows a country to compete in at least one sector. Once the country begins to produce, if there are still unemployed workers, the fall in the wage rate lowers the commodity’s price, increasing its demand. The equilibrium international commodity-price ratio ensures a demand composition such that full employment prevails in both countries.

14 See Woods (1990) for an elegant exposition of Sraffa’s model based on a two-commodity case.

15 The maximum interest rate of each country depends on its input-output matrix. Specifically, the maximum eigenvalue of the solution to the eigenproblem associated with the domestic input-output matrix also gives the solution to the maximum interest rate. Admittedly, the higher the maximum eigenvalue, the lower the maximum interest rate. One of the theorems of Perron-Frobenius states that the maximum eigenvalue of the input-output matrix is an increasing function of the elements of the latter (Pasinetti 1977, 272). Since, by assumption, $A^{\text{Eng}}<A^{\text{Port}},$ the maximum eigenvalue of England’s input-output matrix is lower than the maximum eigenvalue of Portugal’s input-output matrix. This result, in turn, means that England has a maximum interest rate higher than Portugal—and therefore, can also pay a higher normal interest rate.

16 We could also represent the inferior trade pattern that we previously ignored, but it would be unobservable since it always lays below the canvas plotted in Figure 6.

Additional information

Notes on contributors

Gabriel Brondino

Gabriel Brondino is a postdoctoral fellow at the Instituto de Humanidades y Ciencias Sociales del Litoral, an institute of double-dependency of the Universidad Nacional del Litoral (UNL) and the National Scientific and Technical Research Council of Argentina (CONICET).

Ariel Dvoskin

Ariel Dvoskin is Senior Manager of Economic Studies at the Central Bank of the Argentine Republic and a researcher at CONICET and the Escuela Interdisciplinaria de Altos Estudios Sociales (IDAES) of the Universidad Nacional de San Martín (UNSAM).