A Geometry of Specialization

Division of labor models have become a standard analytical tool, along with competitive general equilibrium models (Ricardian, HOS, Ricardo-Viner), in public finance, trade, growth, development, and macroeconomics. Yet unlike the earlier models, specialization models lack a canonical representation. This is because they are both new and complex, characterized by multiple equilibria, instability, and emergent structural properties under parameter transformation. We develop a general framework for such models, illustrating results from current research on specialization models, and explaining why one sub-class of these models is particularly difficult to illustrate easily. JEL classifications: [F12],[O12],[O41] keywords: specialization, trade and development, location of industry, agglomeration Thanks are due to Kym Anderson, Richard Baldwin, Jan Haaland, Mary Lovely, Anthony Venables, and the participants at the CEPR sponsored European Research Workshop in International Trade (ERWIT), held in Helsinki. While working on this paper, the authors benefitted from support provided by the Tinbergen Institute (Nelson) and the Center for International and Economic Studies at the University of Adelaide (Francois) while visiting those institutions. All remaining errors are due to confusion on the part of the authors. address correspondence to: J.F. Francois, Faculty of Economics H8-23, Erasmus University Rotterdam, postbus 1738, 3000DR Rotterdam, NETHERLANDS. Fax: +31 10 452 5808. Email: [email protected]. A Geometry of Specialization NONTECHNICAL SUMMARY One of the great traditions in the analysis of international trade is the use of canonical models: Ricardian, Ricardo-Viner, and Heckscher-Ohlin-Samuelson. Furthermore, each of these models has a simple graphical representation, useful for both intuition generation and for pedagogical purposes. Over the last fifteen years, two additional classes of model have joined the big three. These are strategic trade models and division of labor models. The strategic trade models entered the literature with simple graphical representations developed in the industrial organization literature, while the division of labor models have proven to be considerably more resistant to simple representation. The recent specialization literature leans on special models built around specific functional forms, and often involves numeric simulation. Even so, a set of general results (low level equilibrium traps, catastrophic adjustment, agglomeration effects) does stand out from this somewhat diverse collection of special models. Because our starting point in this paper involves examination of this class of models in the context of relatively general functional forms and technologies (linear homothetic, concave, etc.), we are able to offer a generalized treatment that links this pattern of results to the general properties of models with increasing returns due to specialization. In the process, we demonstrate that important results in the recent literature depend critically on the stability and transformation properties that characterize the general framework highlighted here. These properties are closely related to those explored in the context of scale economy models by an earlier generation of trade and development economists. We begin with two versions of national production externality (NPE) models. In the first, a closedeconomy version of the model, we develop the basic elements of the Ethier-type division of labor model in the simplest environment. Even in this simple context, we are able to illustrate basic mechanisms that have been highlighted in the literature on endogenous growth and development. From there we develop a NPE model of trade in final goods only, and demonstrate that this model is operationally identical to standard models of trade with national external economies of scale. The greatest conceptual and analytical difficulties emerge with international production externalities (IPE), which surface once trade in differentiated goods is permitted. The graphical analysis makes the locus of this difficulty clear. In addition, we develop a new graphical apparatus that is directly analogous to the Baldwin envelope for the case of division of labor models. The general treatment of IPE models is followed by an examination of trading costs (an important issue in the recent literature) in Ricardian and Heckscher-Ohlin versions of the IPE model. 1 A Geometry of Specialization