Rybczynski Theorem Research Articles

Factor Demand and Substitution under Decreasing Returns to Scale. An Application to the Rybczynski Theorem

In the first part of this paper, the elasticity of substitution and factor demand are determined under decreasing returns to scale. By applying the properties of homogeneous functions, elasticities of marginal products with respect to factor uses are shown to be useful when determining the elasticity of factor substitution and factor demand elasticities. Second, the results are applied to the theorem developed by Rybczynski (1955), according to which an increase in the endowment of one factor, while the endowment of the other factor and commodity prices remain unchanged, will increase production of the good intensive in this factor, and will reduce production of the good intensive in the other factor. This theorem has been developed within the context of a two-good, two-factor model under constant returns to scale. In the more general case, under variable returns to scale, the conditions for the Rybczynski theorem have been derived by Jones (1968), Panagariya (1980) and Herberg, Kemp and Tawada (1982). The case of variable returns to scale includes both decreasing and increasing returns to scale. In this paper, however, we assume the simple model under decreasing returns to scale formulated by Hansson and Lundahl (1983). We interpret the necessary and sufficient conditions for the Rybczynski theorem using the elasticities of substitution and the factor demand elasticities and derive the condition under which expansion can occur in both sectors.

Endogenous Investment, Current Account and the Rybczynski Theorem

The purpose of this paper is to construct a simple intertemporal model of investment and international trade. The bulk of trade theory explores the behavior of an economy in a single period framework, and the traditional trade models assume that the agents in the economy save and invest nothing. The bulk of trade theory is also unable to analyze problems concerning the current account imbalance of an economy, since the traditional models assume that the economies never experience an imbalance in their current accounts. We remedy these shortcomings. We extend the standard, single-period two sector model of production to a two-period setting, while explicitly introducing endogenous saving, endogenous investment and international debt. In addition, we focus on some trade theorems traditionally derived from single period models. Bruno [1], Marion [4], and Marion and Svensson [5] have indeed employed two period models to study the effects of oil price changes on the current account of an open economy. The emphasis of their work, however, is quite different, and their models are not readily comparable with the standard two-sector general equilibrium model, largely because they assume perfect international mobility of capital. Dornbusch [2] and Svensson and Razin [7] have also utilized intertemporal models to examine the effects of terms of trade changes on the current accunt. Their emphasis also is quite different from that of the present paper. Further, Dornbusch, and Svensson and Razin focus more on the intertemporal consumption smoothing, and utilize a relatively simplified production structure of the economy. We simplify the consumption side of the economy by introducing proportional consumption (and hence, saving) functions, and develop a more elaborate intertemporal production structure.

The Rybczynski theorem in a model with nontraded goods and indecomposable interindustry flows: Revisited

In this paper we show that in a model with three goods (two traded goods and one nontraded good) and interindustry flows (1) Jones' magnification effects hold if and only if the marginal propensity to consume the nontraded good equals the average propensity, and (2) the condition implies that the factor movements bound the movement of the net output of the nontraded good, (3) which is equivalent to Jones' magnification effects. Furthermore, (4) the relation among various conditions is investigated, and (5) the results are extended to the many nontraded good case.

The Heckscher-Ohlin-Samuelson Model with Implicit Contracts

In a world with multiplicative production uncertainty and implicit labor contracts, we show that the Rybczynski theorem retains its validity; therefore the quantity version of the Heckscher-Ohlin theorem survives as well. We also show that the Stolper-Samuelson theorem may not hold. A small increase in the price of the capital-intensive good may benefit labor. We derive a strong version of the factor price equalization theorem that shows free trade tends to equalize sector-specific unemployment rates and sector-specific factor prices across countries. Finally, we relate trade patterns to international differences in the degree of risk aversion.

The Rybczynski Theorem: Short-Run Adjustment

The modern, open economy must constantly re-allocate factors of production during the process of adjusting to external shocks. Few issues present us with greater economic and political problems due to the ensuing re-distribution of the national income and power. Terms of trade variations constitute a very important source of change, and the literature provides us with a number of recent contributions dealing with the issue of mobility after an exogenous shift in relative prices.' Less attention has been devoted to changes in the factor endowments.2 This is understandable since significant, one-time shifts in factor supplies are not as common as price shocks. Yet they do occur. Regime changes which lead to alterations in immigration policy or foreign investment policy may provoke sudden increases in labor or capital endowments. Foreign assistance may increase discontinuously, or technical change may occur rapidly, increasing the stock of effective capital in a onetime manner. Moreover, these endowment shocks may immediately affect one industry more heavily than the other. We know how the open economy must eventually adjust to such changes. The answer is given by the Rybczynski Theorem [15] in the event that both factors of production are completely mobile in the long run. One industry will expand and the other will contract. The industry which experiences growth will be the one that uses intensively the factor which has become more plentiful. In the new equilibrium, factor prices and factor ratios are unchanged from their original values, and the growing industry has received some of both factors from the other sector in addition to all of the initial inflow.

Transport costs, factor intensities and the Rybczynski theorem

Abstract We discuss whether the Rybczynski theorem (with and without magnification effects) holds or not under the assumption that there is a resource-using shipping industry. The implication of factor intensities in such a model is also examined.

The Rybczynski theorem in the three-factor, two-good model

This paper proves that if each factor is normal in the three-factor, two-good model, the expansion of a factor endowment always increases, at constant commodity prices, the output of the commodity which uses the expending factor most intensively.

Some theorems of trade with joint production

This paper establishes the following principal results: In the general model with many industries, many factors and many commodities, and with joint production, the concepts of ‘sectoral’ and ‘commodity’ factor intensities will be clarified. Necessary and sufficient conditions for the Rybczynski theorem to be valid will be presented. Necessary and sufficient conditions for the Stolper-Samuelson theorem to be valid will be presented. The two conditions are not the same. This is characteristic of the joint production case.

The Rybczynski Theorem under Decreasing Returns to Scale

One of the most celebrated theorems of international trade is the Rybczynski theorem. This theorem was originally developed by Rybczynski (1955) within the context of a two-good, two-factor model. The theorem states that when the supply of a factor grows, output of the good which uses the growing factor intensively will increase at constant commodity prices, while the output of the other good will fall. The Rybczynski theorem was originally derived for the case of production functions which were assumed to be linearly homogeneous so that no advantages or disadvantages of scale existed in either industry. The case of variable returns to scale has, however, been treated by Jones (1968), Kemp (1969, pp. 154-67) and Panagariya (1980), who have used various methods to derive necessary and sufficient conditions for the theorem to carry over to this case as well. But these contributions are problematical because the conditions derived are such that simple economic interpretation of the results may be difficult. The difficulties are mainly due to the high level of generality of the exposition, where both increasing and decreasing returns to scale-defined in a wide sense-are included.' In this paper, we are concerned with deriving simple necessary and sufficient conditions under which the Rybczynski theorem carries over to a more restricted case: that of decreasing returns to scale in one or both industries, defined as a degree of homogeneity less than one in the sectoral production function.

Rybczynski's Theorem in a Context of Exhaustible Resources: The Case of Time-Contingent Prices

Rybczynski's Theorem in a Context of Exhaustible Resources: The Case of Time-Contingent Prices

On Perfect Aggregation in the National Output Deflator and Generalized Rybczynski Theorems

Fisher and Shell [1972] attempted to place the theory of output deflation on a production-theoretic foundation in the same way as the theory of the cost-ofliving index is based on a consumer-theoretic foundation. It developed a production-theoretic output deflator to which actually computed indices, such as the GNP deflator, serve (sometimes) as bounding approximations. The present paper continues that work. In it, I inquire as to the possibility of building up the production-theoretic deflator from subindices each of which is a deflator for a particular sector or industry. In what sense, if any, is it possible, for example, to talk of the steel industry's contribution to inflation? Clearly, such a statement would be well defined if the full output deflator could be expressed in terms of specific industry deflators; the question is whether this is possible. Obviously, such questions are trivial when considering the Paasche approximation to national output deflation, the GNP deflator. Paasche or Laspeyres indices can be expressed in terms of subindices in a simple, arithmetic way. Yet to be content with this answer is, in effect, to ignore the question. The steel industry deflator in the Paasche approximation is a bound on the productiontheoretic deflator for the steel industry. The full Paasche approximation is a similar bound on the production-theoretic deflator for the economy as a whole. Yet if the economy-wide, production-theoretic deflator is not simply a function of production-theoretic deflators for separate industries, it is not at all plain that much interest should attach to the percent of Paasche-approximated deflation accounted for arithmetically by the Paasche deflator for the steel industry. More generally, someone attempting to construct deflators for a particular sector or industry will do so without regard for prices outside that sector. If this is done for every sector of the economy, can the results then be used directly to construct the national output deflator? If not, then what can one say concerning the errors that are likely to be committed in proceeding on a sector-by-sector basis? What approximation theorems can be proved? The present paper is only the beginning of research into such questions. It

A Graphical Analysis of Factor Accumulation in a Three-Sector, Three-Factor Model of International Trade

In the 2 X 2 international trade model, the effect of factor accumulation on output levels is summarised in the Rybczynski Theorem, which states that a rise in the supply of a factor, at constant commodity prices, results in an increase (decrease) in the output of the good that utilises the expanding factor more (less) intensively. This can be easily established graphically. However, when it is extended to higher dimensions, complicated mathematical manipulation is usually required.' This paper attempts to extend the Rybczynski Theorem beyond the two-factor, two-good case by means of a graphical method. In particular, some new graphical techniques are presented to analyse the effect of factor accumulation on output levels in a three-good, three-factor modei with constant commodity prices, in which one of the factors is specific to the production of one or two goods. It is hoped that the graphical analysis will bring out the logical deductions in a more intuitive way and appeal to a wider range of economic audiences. These techniques may also be useful in the exposition of similar models of higher dimensions. Section I analyses the case where one of the factors is specific to the production of one of the goods. Section II extends the analysis to the case where the specific factor is employed in two sectors. Although the model in section I is a special case of that in section II, they are presented separately because different graphical techniques are employed.

A generalization of the Samuelson reciprocity relation, the Stolper-Samuelson theorem and the Rybczynski theorem under variable returns to scale

Assuming the Marshallian externalities, a generalization of the Samuelson reciprocity relation, the Stolper–Samuelson theorem and its dual Rybczynski theorem is demonstrated with n commodities and n inputs. Further it is shown that the ‘weak’ Stolper–Samuelson property does not coincide with the ‘strong’ property even when n=2. Then the effect of an own or other commodity price change on a commodity output is examined.

Variable returns to scale in general equilibrium theory once again

This paper relaxes some assumptions made by Jones (1968) and reconsiders the implications of variable returns to scale (VRS) for the Stolper-Samuelson and Rybczynski theorems. It also analyses for the first time the relationship between factor-returns and factor-supplies at constant commodity-prices. It is shown that the validity of the Rybczynski and/or Stolper-Samuelson theorem is neither necessary nor sufficient for the production possibilities frontier to be locally strictly concave to the origin. Several other new results are derived and an attempt is made to give an intuitive explanation of the most important findings.

The Rybczynski Theorem in a Model with Non-Traded Goods and Indecomposable Inter-Industry Flows

According to the Rybczynski [1955] theorem, applied to the standard twocountry, two-good, two-factor model, an increase in one factor will result in aln absolute rise in the output of the commodity which is relatively intensive in the increased factor, and to an absolute fall ill the output of the other commodity. The generalization of the theorem by Jones [1965] states that if factor endowments expand at different rates, the commodity intensive in the use of the fastest growing factor expands at a greater rate than either factor, and the other commodity grows (if at all) at a slower rate than either factor. The application of Jones' version of the theorem to a model with three goods, one of which is nontraded, two factors and indecomposable inter-industry flows is studied here. The introduction of inter-industry flows makes necessary a distinction between net and gross Rybczynski output effects and also between direct and total factor intensities of commodities. It is found that a sufficient condition for the generalized Rybczynski theorem, defined in terms of total factor intensities, to hold for both net and gross outputs, net output changes being proportionately greater than gross changes, is that the net output change of the non-traded good is bounded by the factor changes. This result is compared with earlier findings and the meaning of the sufficient condition is discussed in terms of basic demand parameters.

On the Structure of Comparative Advantage in a Multifactor Trade Model

The theoretical structure of a two-country, two-factor, two commodity Heckscher-Ohlin trade model is widely known. Factor-price equalization, the Stolper-Samuelson theorem, and the Rybczynski theorem may be deduced as its major corollaries. Jones, in his seminal contribution [1956-1957], summarized this structure and extended the model to include additional commodities. In his two-factor, n-commodity model, Jones proposed that (1) the ranking of commodities according to their capital-labor ratios is precisely their ranking by order of comparative advantage, and (2) demand conditions merely divide this chain into exportable goods on one side and importable goods on the other.2 A basic theoretical question, however, has remained unanswered thus far: Under what circumstances in a two-country, many commodity model, in which there are three or more factors of production, and in which factor prices are not equalized internationally (due to, say, transport costs), is a chain of comparative advantage unambiguously determinate on the basis of factor proportions employed in production? For the purpose of exploring this question, we employ the usual assumptions of the Heckscher-Ohlin trade model. In particular, they include (i) each good is produced according to a linearly homogeneous production function common to both countries; (ii) production functions are characterized by strong factor intensity; (iii) inputs are of homogeneous quality across countries; (iv) inputs

Monopoly, intermediate goods and the pure theory of international trade

In a model with two traded good sectors between which intersectoral flows of intermediate goods are allowed and with a monopolized non-traded good sector, the wage rate in terms of two traded goods increases and the rental of capital in terms of two traded goods decreases when the price of relatively more labor intensive traded good sector increases, though nothing definite can be said about the direction of change in the wage rate and rental in terms of the non-traded good. When prices of traded goods are kept constant and labor and/or capital increase(s), output of the non-traded good sector increases provided that the non-traded good is not inferior, having income elasticity of demand less than unity. The factor intensity condition for the traded goods is in general not sufficient for the validity of the Rybczynski theorem to hold with respect to net outputs of the traded goods. We have derived sufficient conditions for the magnification effect to be observed with respect to net outputs of the traded good sectors. Specifically, we have shown that the factor intensity condition (23) is sufficient for the magnification effect to prevail when only labor increases.

Some remarks on the Stolper-Samuelson and Rybczynski theorems

First, this paper provides a necessary and sufficient condition for a weak form of the Stolper-Samuelson criterion in the n× n case. It will be shown that it is a sufficient condition in the uneven case where the number of primary factors is larger than the number of products. Secondly, this paper offers two conditions. Conditions (II) and (III), that are equivalent to Chipman's and Uekawa's weak form of the Stolper-Samuelson criteria, respectively. Our economic interpretations of these conditions are given in the final section by applying a notion of Hicks's imperfect stability.

On Rybczynski's theorem in a setting of growth

This note re-examines earlier work by Petith on a two-sector economy in steady state growth facing constant world prices. It is shown that a steady state with higher saving propensities out of wages or profits has a higher output of the capital good per head, and greater exports of it compared to the no-trade equilibrium, if and only if the capital good is more capital-intensive. Petith's example yielding counterintuitive results is shown to be in error.

The Relevance of the Two-Sector Production Model in Trade Theory

This paper examines how well the basic properties of the traditional 2 × 2 model of a competitive economy, commonly used in much of the pure theory of international trade, generalize when more goods and factors are considered. The notion of factor intensity and the Hekscher-Ohlin, Stolper-Samuelson, and Rybczynski theorems are discussed. The role played by the no-joint-production assumption as opposed to small dimensionality in the latter two results is stressed. The mathematical appendix provides a compact and formal statement of the properties discussed in the text.