On the General Structure of Ricardian Models with a Continuum of Goods: Applications to Growth, Tariff Theory, and Technical Change

Abstract

A continuum of goods is introduced into the general Ricardian model of international trade. By looking at the derived demand for labor, it is demonstrated that the analysis of the model can be reduced to the analysis of an equivalent model of pure exchange in which each country essentially trades its own labor for the labor of other countries. Furthermore, unlike the case where the number of goods is finite, the derived demand for labor becomes a differentiable function of the relative wages of the different countries. How this facilitates the analysis of comparative statics exercises is illustrated by establishing a number of propositions in the theory of growth, technical change, and tariffs. THE RICARDIAN MODEL IS perhaps the simplest formulation in which the technology can be explicitly incorporated into an analysis of international trade. In a general form, it consists of an arbitrary number of countries each of whom use only one factor of production, called labor, to produce an arbitrary number of goods. Each country has a constant returns to scale technology but they differ in the relative amounts of labor required to produce different goods. This generates an incentive for each country to specialize in the production of only certain goods which in turn generates the gains from trade. Although the model is frequently employed to illustrate many of the basic principles of international trade, it is not commonly used to examine those issues which require a detailed analysis of comparative statics. Questions such as how a shift in demand affects the pattern of trade and the relative prices of goods, or the corresponding impact of a tariff, technical change, or growth in the labor force are generally analyzed either with simpler models which do not explicitly incorporate the technology at all or else more sophisticated models which include a technology with several factors of production. The problem with the Ricardian model is that the qualitative properties of the results typically depend upon the pattern of specialization. In order to determine the general equilibrium effect of a small change in the tariff rates, for instance, we must know precisely which countries are completely specialized in the production of which goods and which goods are jointly produced by more than one country. A general analysis of any of these issues, therefore, will require a separate analysis for each possible pattern of specialization. Even with two countries and two goods, there are generally several cases to examine. An even more serious defect is the fact that the first order effect in any one of these cases tells only part of the story of what happens in a world with many goods and discrete parameter changes. In general, a change in some