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THE POSITIVE THEORY OF INTERNATIONAL TRADE RONALD W. JONES University of Rochester and J.PETER NEARY* University College Dublin Contents 1. Introduction 2. Models of trade 2.1 The exchange model 2.2 The Ricardian model 2.3 The Heckscher-Ohlin model 2.4 The specific-factors model 2.5 Extensions 3. Multi-level trade 3.1 Trade in intermediates and natural resources 3.2 Trade in factors 3.3 Trade in technology 3.4 Trade in securities 4. Multi-behavioral trade 4.1 Market distortions 4.2 Increasing returns 4.3 Imperfect competition 5. Concluding remarks References *This paper was begun while the authors were visitors at the International Institute for Applied Systems Analysis, Laxenburg, Austria. We are grateful to this Institute and to the national Science Foundation under grant no. SES-7806159 for support and to J.N. Bhagwati, A.V. Deardorff, A.K. Dixit, W.Ethier, M.C.Kemp. P.B.Kenen, F.P.Ruane, and L.P.F.Smith for helpful comments. Handboook of International Economics, vol.1, edited by R.W.Jones and P.B.Kenen Elsevier Science Publishers B.V., 1984 1. Introduction The theory of international trade is one of the oldest subfields of economics and its central concerns remain those of Ricardo. Nevertheless, in recent years the field has not stood still, but has exhibited an expansion of the range 'of topics studied and of the analytical tools brought to bear on them. In this chapter we attempt to present an overview of the present state of positive trade theory, concentrating on developments since the surveys of Mundell (1960), Bhagwati (1964) and Chipman (1965-66) while at the same time drawing attention to the continuity in the development of the subject. We begin in this section by outlining the scope of the field as we see it and the criteria which have guided our selection of topics to be covered. As the title of our chapter indicates, we confine our attention to the positive theory of international trade, leaving normative questions for Chapter 2. Although the distinction is somewhat arbitrary, a reasonably clear line of demarcation can be drawn. As a rough guideline, questions concerning the effect of exogenous or policy changes on the level of aggregate real income or dealing with the ranking of alternative policy instruments will be considered the province of normative trade theory. By contrast, questions concerning the effect of exogenous or policy changes on the composition of outputs, relative prices, trade flows, or on the domestic distribution of real income will be considered within the realm of positive trade theory. While trade theory makes extensive use of general-equilibrium theory, with its concern for interactions among markets, the key feature which distinguishes it is its recognition that not all commodities and factors are equally mobile. This phenomenon of differential mobility can take many forms. From Ricardo onwards, much of trade theory has been conducted in terms of the Classical mobility assumptions: all final goods are tradeable between countries whereas primary inputs are non-tradeable, though fully mobile between different sectors of the domestic economy. However, a great deal of recent work has been concerned with examining the consequences of departures from these assumptions. Another feature which characterizes international trade theory is its focus on applied questions, making it natural to conduct analysis in the context of relatively small-scale models. This is not to say that trade theory is wedded to any particular model. For example, despite its dominance in the 1960s, the Heckscher-Ohlin model has not supplanted the Ricardian model, nor has it in its turn been eclipsed by the recent revival of interest in the specific-factors model. Rather, positive trade theory uses a variety of models, each one s0ited to a limited but still important range of questions. While this eclectic approach is sometimes criticized, since it is easy to show that the propositions derived from any one model are not necessarily robust with respect to relaxations of that model’s assumptions, it seems to be a more satisfactory way of yielding useful insights and suggesting hypotheses for empirical testing than the attempt to construct general model which encompasses all others as special cases. This viewpoint is not shared by all trade theorists. For example, Pearce (1970, p. 17) states "There is but one world and only one model is needed to describe it." Among the issues with which positive trade theory deals is the question of the determinants of the pattern of trade, to which the proximate answer usually given is still that of Ricardo: namely, the principle of comparative advantage, with its focus on a comparison among autarkic relative prices in different countries. In the case of two commodities and two countries the principle is both easy to formulate and incontrovertibly true: Nevertheless, the principle, with its denial that absolute superiority in productive power determines the pattern of trade, remains suspiciously counterintuitive to most non-economists. Samuelson (1969) recalls the time he was challenged by the mathematician Stanislaw Ulam to “name me one proposition in all of the social sciences which is both true and non-trivial.” Samuelson remarks that years later he thought of the appropriate answer: the Ricardian theory of comparative advantage. "That it is logically true need not be argued before a mathematician; that it is not trivial is attested by the thousands of important and intelligent men who have never been able to grasp the doctrine for themselves or to believe it after it was explained to them." each country will tend to export under free trade that commodity which has the lower relative price in autarky. However, with more than two commoities the appropriate way to generalize the principle is not immediately apparent. It is tempting, for example, to argue that if commodities are ranked by their relative price ratios in autarky in the two countries, demand conditions will determine a critical ratio such that, when trade is opened up, the home country will export all commodities whose autarky relative price is below this ratio and import all other commodities. This assertion is correct in the Ricardian case of constant costs, but as Drabicki and Takayama (1979) and Dixit and Norman (1980, pp. 95-96) have shown, it need not hold in less special cases. However, the more paradoxical aspects of their counter-examples rely on the presence of strong complementarity in demand. In any case, whatever the pattern of substitutability or complementarity, the principle of comparative advantage may be reformulated in terms of a correlation between differences in autarky price levels and net export volumes for different commodities, as Deardorff (1980) and Dixit and Norman (1980) have shown. While the principle of comparative advantage may thus be defended as a basic explanation of trade patterns, it is not a primitive explanation, since it assumes rather than explains inter-country differences in autarkic relative prices. Much of trade theory is therefore concerned with investigating alternative sources of these differences, and each such source has implications in turn for the effect of the opening up of trade on the structure of production and on the domestic distribution of income. The same questions can also be posed not in terms of a comparison between autarky and free trade but in the context of disturbances to an initial trading equilibrium, la discussing these and other issues, our strategy into present in Section 2 an overview of a number of alternative models, stressing the complementarity between them and the differences in the questions which each is well suited to answer. For the most part, this section stays within what we call the "Classical paradigm." This encompasses not only the Classical assumptions about goods and factor mobility already mentioned, but also neglects intermediate stages in the production hierarchy and assumes that all agents are atomistic, operating in an undistorted and competitive environment in which technology exhibits constant returns to scale. More recent work which relaxes these assumptions, allowing for trade at different levels of the production spectrum and for departures from competitive behavior, is reviewed in Sections 3 and 4 respectively. Inevitably, throughout the chapter there is some overlap with other contributions to this volume (though not on empirical matters, which we leave to Chapter10). In general, we go into less depth on individual topics than other contributors, attempting instead to fit recent extensions into an overall framework which provides a coherent view of the field. Moreover, a survey of a wide field such as this cannot hope to be anything other than highly selective. Without attempting to provide a comprehensive coverage, therefore, we hope to give the flavor of a subject which remains a vibrant and fruitful source of theoretical insight and testable hypotheses. 2. Models of trade Although the theory of international trade combines elements of demand behavior with production structure in a general-equilibrium context, it is primarily variations in the specification of the production side that distinguish the basic models of trade. Section 2.1 describes the uses to which the "exchange model" has been put; this model can be interpreted as one in which each of two factors is used to produce a separate commodity so that no intersectoral factor mobility is allowed. Section 2.2 describes the Ricardian model, the polar opposite of the exchange model in that only one productive factor (labor) is employed, but this factor can be freely reallocated between sectors so as to maximize its earnings. Section 2.3 presents the basic propositions of the Heckscher-Ohlin model, the model most frequently used in positive trade theory, whereas Section 2.4 deals with the specific-factors model, which focusses on asymmetry in the degree of factor mobility between sectors. Finally, Section 2.5 extends these models to consider some properties of higher dimensional cases as well as the possibility of joint production. The production structures of the basic trade models discussed in this section have many properties in common. For each country it is possible to relate the value of the national product, Y, to the vector of factor endowments, v, and the vector of final commodity prices, p, where competition ensures that the composition of output (shown by the vector, x) maximizes the value of Y at those prices. Formally, Y=g(p, v)= maxx[p'x: F(x, v)< 0], where the aggregate production possibilities set defined by the function F(x, u) is convex. The national product function was introduced by Samuelson (1953) and its properties have been examined under a variety of assumptions by Chipman (1972), Diewert (1974), and Dixit and Norman (1980) among others. Price-output responses are normal, in the sense that no commodity ran fall in supply if its price rises (and all other prices and endowments remain constant). Similarly, an increase in the endowment of any factor of production cannot raise that factor's return if commodity prices and all remaining endowments are held constant. Furthermore, a basic relationship- that of reciprocity- equates the effect which an increase in the endowment of factor i The reciprocity relationship is due to Samuelson (1953) and discussed, inter alia, by/ones and Scheinkman (1977). Referring to the previous footnote, outputs and factor prices are reflected in the partial derivatives of the national product function when these are well defined (as when the number of factors is at least as great as the number of commodities): x =g p and w= g v. g is a concave function of v (implying gvv, or aw/av, is negative semi-definite) and a convex fmlction of p (implying ax/ap is positive semi-definite). Reciprocity follows from the symmetry of the matrix of second derivatives of g. has on the output of commodity j (all commodity prices constan) to the effect which an increase in commodity j’s price has on the return to factor i. The models of trade described in Sections 2.1-2.4 differ from one another in the specification of the numbers of factors and commodities and the degree of intersectoral mobility of the factors, They all share, however, the requirement that the economy's demand for inputs 'to produce commodities not exceed the avail- ability of factors in the endowment base, and the stipulation that in a competitive equilibrium the unit costs in any activity do not fall short of market price. Furthermore, we postpone our discussion of intermediate goods and joint production Section 2.5 considers joint production, while Section 3.1 allows the existence of intermediate goods in the production spectrum as international trade in these goods. . Throughout we generally assume that factor endowments are given. This rules out international trade in productive factors (see Section 3.2), the possibility that the local supply of factors may respond to changes in factor rewards, For a discussion of variable supply, see Walsh (1956), Kemp and Jones (1962), and Martin and Neary (1980). or the possibility that current production affects future factor supplies. This latter possibility is made explicit in neoclassical growth models in which capital is one of the Productive factors and is currently produced. See Oniki and Uzawa (1965) and the discuss/on of Findlay (1970) in Section 2.3. If all final commodities are traded on world markets, the commodity price vector, p, as well the factor endowment vector, v, can be treated as exogenous for a small open economy. But often trade models allow a subset of commodities to enjoy only a national market; even for a small open economy the pj's for non-traded goods thus depend endogenously upon local demand conditions. The study of models with non-traded goods has expanded enormously in recent years, in part because of their relevance to macroeconomic policy in small open economies.The implications of non-traded goods for trade models have been considered by McDougall(1965
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