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Comparative Costs, Autarky General Equilibrium, Trade Patterns, Factor

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Comparative Costs, Autarky General Equilibrium, Trade Patterns, Factor Comparative Costs, Autarky General Equilibrium, Trade Patterns, Factor Endowments, Free Trade Balances, Terms of Trade Surfaces, International General Equilibrium Solutions and Factor Allocations. Bjarne S. Jensen and Jacopo Zotti University of Southern Denmark, Dept. of Environmental and Business Economics University of Trieste, Department of Political and Social Sciences Abstract This paper gives analytical parametric solutions for the basic, two-sector-two-factor-two- country, (2x2x2) model of international trade. Such analytical approach to the involved non-linear economic systems must start with the Cobb-Douglas specifications of sector technologies and consumer preferences. The closed-form expressions provide a unified framework for all traditional basic trade models. The solutions allow for international differences in country sizes, endowments, technology and preferences, encompassing the major "pure trade theories" within a systematic analytic and historical perspective. In this unified framework, we derive the general existence conditions for the solutions under diversification and incipient country specialization. Keywords: Trade models, general equilibrium, terms of trade JEL Classification: F11, F43, E21 1 1 Introduction The pure theory of international trade has always been involved with the fundamental questions of what decides : 1. The commodity pattern (composition) of international trade between countries, 2. The "international values", i.e., the prices of both the free traded commodities and their primary production factors, 3. The gains from foreign trade. Evidently the literature is overwhelming and hence many surveys have been made, Haberler (1936,1961), Mundell (1960), Bhagwati (1964), Chipman (1965-1966). The latter still surpasses all other historical accounts and expositions of theory evolution (to- gether with many references to contemporary authors/discussions). His theory chronology has three periods of main/early contributors : I. Classical theory of comparative advan- tage, gains from trade (Smith, Ricardo, Mill), II. Neo-Classical theory of international trade equilibrium and the equilibrium terms of trade (Marshall, Edgeworth, Haberler), III. Modern theory of factor endowments, factor price equalization, factor income distri- bution, two-sector growth models (Heckscher, Ohlin, Samuelson, Solow, Uzawa, Kemp). Economic laws (theory) governing trade between two countries dawned in Adam Smith - Chapter 11 of restraints upon the importation from foreign countries of goods that can be produced at home, Smith (1776, 1961, p.478): "What is prudence in the conduct of every private family, can scarcely be folly in that of a great kingdom. If a foreign country can supply us with a commodity cheaper than we ourselves can make it, better buy [import] it from them with some part [export] of the produce of our own industry, employed [produced] in a way in which we have some advantage". By scrutinizing the principle of cheapness and advantage in more detail with some illustrations, Ricardo (1817, p.81, p.175), cf. Ruffin (2002, p.743), came up with the law of comparative advantage: "Under a system of perfectly free commerce, each country naturally devotes its capital and labour to such employments [industries, goods, sectors] as are most beneficial to each. This pursuit of individual advantages is admirably connected with the universal good of the whole." Precisely, the Ricardian term comparative advantage means the ability in autarky to produce a good at lower cost/price (relative to other goods), compared to another autarky country. Moreover, the law of comparative advantage (cost) says that a country exports 2 (imports) the good with the low (high) relative (p = P1=P2) autarky price, and it can be expressed an inequality in relative autarky prices : P1A=P2A = pA < P1B =P2B = pB : X1A > 0 (1) The prediction of trade patterns - X1A > 0 : export of good 1 by country A - in open economies by the autarky condition, (1), is (with precise assumptions) not violated in any trade model for : Two countries, two goods [commodities, sectors], two factors, (2x2x2). The world equilibrium terms of trade (p∗) are usually just taken (assumed, not proved) to fall strictly between the two countries relative prices (price ratios) under autarky, i.e., ∗ pA < p < pB (2) ∗ excluding the case of one country (say A) being 'small', hence p = pB . The bilateral rule of comparing relative prices under autarky to determine trade pat- terns, (1), is not valid for a multicommodity (multisector, i ≥ 3) world, as demonstrated by Drabicki and Takayama (1979, p.217). On these "higher dimensional" issues, see Deardorff (1980), Shimomura and Wong (1998). We focus on a full story of the (2x2x2) model, but in contrast to the available literature so far, our objective is to deduce and finally present explicit analytical solutions of the world trade model (2x2x2). While comparative advantage explains why and how trade takes place, it does not explain (give) the terms of trade : relative prices, p∗ in (2). Ricardo's numerical examples, cf. Chipman (1965, p.482), offer no clear size of (p∗) or hints to general answers. It was Stuart Mill, who first gave an analysis of the formation of "international values" [world market prices, determination of p∗ in (2)], that offered a rigorous answer - discussed in detail by Chipman (1965, p.485-86) - upon a pure trade theory example left by Ricardo. Stuart Mill (1875, p.352) stated: "When trade is established between two countries, the two commodities will exchange for each other at the same rate of interchange in both countries", i.e. the "law of one price" that will also be adhered to in our (2x2x2) model. Next Mill (1875, p.359) says: "All trade, either between nations or individuals, is an interchange of commodities, in which the things that they respectively have to sell, constitute also their means of purchase: the supply brought by the one constitutes his demand for what is brought by the other. So that supply and demand are but another 3 expression for reciprocal demand - or named the Equation of International Demand" - or today: the trade balance equation with a zero constraint - which is adopted here, too. To handle the special trade case of Ricardo, Mill assumed that consumers in both countries had identical commodity demand functions of simplest functional form, Mill (1875, p.361): "Let us therefore assume, that the influence of cheapness on demand conforms to some simple law, common to both countries and to both commodities. As the simplest possible and most convenient, let us suppose that in both countries any given increase of cheapness [fall in price] produces an proportional increase of consumption: or, in other words that value expended in the commodity, the cost incurred for the sake of obtaining it, is always the same, whether that cost [expenditure] affords a greater or smaller quantity of the commodity." In short, Mill used here consumer demand functions, generated today by Cobb-Douglas utility functions, as we will do for preferences below. Marshall (1879, 1974) continued the study of Mill's examples with an in-depth analysis of the trade balance equilibrium determination of "international values" (terms of trade) by "reciprocal demand" (offer, net-export) curves of two countries. Let us hear, Marshall (1879, 1974, p.1): "The function of pure theory and models is to deduce definite conclu- sions from definite hypothetical premises. The premises should approximate as closely as possible to the facts with which the corresponding applied theory has to deal. But the terms used in the pure theory must be cable of exact interpretation, and the hypotheses on which it is based must be simple and easily handled. The pure theory of foreign trade satisfies these conditions". Marshall supported his propositions/corollaries with 24 offer-curve diagrams; many now standard, cf. summary in Deardorff (2006, pp.322). While "classical" trade theory (Smith, Ricardo) may have assumed, cf. Chipman (1966, p.18), "constant factor prices and different technologies" among countries, Heckscher (1919, 1991, p.47) examined some : "fundamental assumptions concerning the reasons for differences in comparative costs among countries", i.e. why are in (1) the autarky relative costs (prices) pA and pB different ? As a keen economist, Heckscher correctly argued that countries with same - technologies and relative factor prices - do not trade; since then: "relative costs in one country cannot possibly differ from those in the other. Therefore trade between the countries will not arise", Heckscher (1991, p.47). 4 Hence behind the Ricardian inequality in (1), he saw (emphasized) as a prerequisite an inequality in autarky relative factor prices, !A and !B : ”different relative prices of the factors of production in the exchanging countries", Heckscher (1991, p.48). But next opening free trade would itself affect the relative factor prices and maybe, even under some conditions, bring about not just partial, but full factor price equalization (FPE). As to "modern factor endowment theory", Ohlin (1935, Appendix I) re-examined and extends the general equilibrium equation systems of Walras-Cassel for the mutual interde- pendence pricing of commodities and factors to trading regions (countries). He introduced and emphasized the role of different factor endowments ratios,(kA; kB ), among regions; but Ohlin (1933, p.561-62) opted in most situations for partial factor price equalization. Next Samuelson (1948, p.169) enters the discussion: `In attempting to
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