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3. General Equilibrium Dynamics of Basic Trade Models for Growing Economies
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CHAPTER 3 General Equilibrium Dynamics of Basic Trade Models for Growing Economies Bjarne S. Jensen and Chunyan Wang 1. Introduction In the literature on the pure theory of trade, the two-factor, two-sector, two-country framework has provided a fundamental general equilibrium structure for static and comparative-static analyses of many issues related to factor allocation, output composition, relative prices, and trade patterns. Although the work on two-sector growth models has long ago been extended to trading economies, stability issues and non-steady-state dynamics have to be further analyzed. As is well known, many results and theorems of both static and dynamic trade theory rest on the assumption of incomplete specialization. A major purpose of this chapter is to study the conditions that will in the long-run preserve the diversification of a small trading economy and two large trading economies. However , when the parametric conditions of diversified steady state growth are not satisfied, we give, for a small country, special attention to various forms of endogenous (persistent) growth per capita. Basic (prototype) dynamic trade models will be analyzed in detail. A small trading economy, owing to the given terms of trade, can be conceived of as being restricted (by the outside world and competitive pricing) to operating with fixed-coefficient technologies. Nevertheless, the long-run stability of the diversification of a small trading country does not depend entirely, as in a closed economy, on the ranking of sectorial factor intensities. Alternative trade patterns give the growing two-sector economy some opportunities to remain diversified. However, besides technology, the domestic demand composition is of critical importance for preserving domestic production of both tradable goods. For two large trading countries, the long-run stability of incomplete specialization is likewise critically dependent on demand side parameters. Dynamic trade theory was initiated by Oniki and Uzawa (1965), who studied the effects of capital accumulation and labor growth on international equilibrium over time for two large countries. In this area, 77 78 Dynamics, Economic Growth, and International Trade other studies were Bardhan (1966, 1970), Kemp (1969), Findlay (1970), Takayama (1972), Woodland (1982), Gandolfo (1994). Our work may especially be seen as extensions of the contributions of Stiglitz (1970), Deardorff (1971, 1973, 1974, 1978, 1994), and Smith (1976, 1977, 1984). In section 1, we present the general equilibrium structure of the trade models. Section 2 is devoted to dynamic two-sector models for small trading economies. As to capital accumulation, we consider proportional , classical, and optimal saving models. Section 3 presents a dynamic analysis of a two-sector growth model for two large countries with the terms of trade ofinternational equilibrium endogenously determined. It may be called a two-factor Ricardian trade model, as we also allow for different sector technologies in the two countries. The parametric conditions of preserving diversification in both countries are obtained. Final comments are offered in section 4. 2. Structure of Two-Sector Trade Models The structure of the two-sector trade models are formed by the basic assumptions of international immobile production factors, full employment , competitive prices, and trade balance equilibrium. The elements of a competitive two-sector economy with homogenous production functions will subsequently determine and impose important restrictions upon the character and parameters of the actual homogenous dynamic systems for a small or large economy trading in both goods. 2.1 Domestic Production and Factor Endowments Consider an economy consisting of a capital good industry (sector) and a consumer good industry (sector), labelled 1 and 2, respectively. The two-sector general equilibrium model is characterized by the following assumptions. The sector technologies are described by production functions exhibiting constant returns to scale, (1) where !i(ki), i =1,2, have the properties 'Vki > 0: IHki) =dli(ki)/dki > 0, 1I'(ki) =d2Ii(ki)/dk; k2 : - kl : Y2 kl 0, that is,£ == dL/dt =dLI/dt +dL2/dt =£1 +£2 =Ln == Lf(k). (25) The domestic stock of capital goods increases by savings (investment demand). Depreciation of capital is ignored. Hence, with proportional saving, domestic capital accumulation (absorption) is described by the equation, cf. (21), (16), k == dK/dt = Ql =sY/Pl =S[YI +Y2/pl =L(s/Pl)y =LS[Ylll + (Y2/P)121 == L g(k). (26) Thus, with the factor endowments, L and K, as state variables, the complete description of the growth process in the small trading economy is given by the dynamic system, (25)-(26). This system (25)-(26) applies to growth processes with "fixed coefficient " sector technologies operating within...