An Inframarginal Analysis of the Ricardian Model*

Wenli Cheng
Jeffrey Sachs
Xiaokai Yang

REVIEW OF INTERNATIONAL ECONOMICS

RRH: Infra-marginal Analysis of the Ricardian Model
LRH: Wenli Cheng, Jeffrey Sachs and Xiaokai Yang

Abstract

This paper shows that a 2x2 Ricardian model has a unique general equilibrium and the comparative statics of the equilibrium involve discontinuous jumps. If partial division of labor occurs in equilibrium, the country producing both goods would impose a tariff, whereas the country producing a single good would prefer unilateral free trade. If complete division of labor occurs in equilibrium, both countries would negotiate to achieve free trade. In a model with three countries, the country which does not have a comparative advantage relative to the other two countries and/or which has low transaction efficiency may be excluded from trade.

*Cheng: P. O. Box 587, Wellington, New Zealand. Tel: 64 4 472 0590, Fax: 64 4 472 0596, Email: wenlicheng@compuserve.com. Sachs: insert Mailing address, Tel: Fax: E-mail: Yang: insert Mailing address, Tel: , Fax: E-mail: xiaokai_yang/FS/KSG@ksg.harvard.edu. We wish to thank Elhanan Helpman, Lin Zhou, Monchi Lio, Meng-Chung Liu, the referee for Review of International Economics, and the participants of the seminar at Monash University for helpful comments. The financial support from Australian Research Council Large Grant A79602713 is gratefully acknowledged. We are solely responsible for the remaining errors.

JEL classification: F10, F11
Number of Figures: 1 Number of Tables: 3
Address of Contact Author: Xiaokai Yang, insert Mailing address, Tel: , Fax: E-mail: xiaokai_yang/FS/KSG@ksg.harvard.edu

1. Introduction
Ricardo's theory of comparative advantage is regarded as the foundation of modern trade theory. However, the Ricardian model has not attracted the attention it deserves. This lack of attention is attributable to the fact that the conventional marginal analysis is not applicable to the Ricardian model and trade theorists have shown a remarkable insistence on the marginal technique .

There have been only a few non-marginal analyses of the Ricardian model in the literature. Houthakker (1976) proposed a computational method to calculate the equilibrium pattern of division of labor in a two-country, many-commodity Ricardian model. Rosen (1978) applied linear programming to study the optimum work assignment in the presence of comparative advantage. He suggested that the notion of economies of division of labor is not a technical concept, but a concept that describes social interdependence (or "superadditivity" in Rosen's terminology): the more interactions among individuals, the greater scope for productivity improvement .

Rosen's work represents a significant step away from the marginal analysis. However, designed to address a firm's work assignment problem, his model does not immediately relate to international trade. In this paper, we use a non-marginal approach similar to Rosen's (1978) to study the trade patterns and related issues in the Ricardian model. We intend to show that with a non-marginal approach, the original Ricardian model can generate numerous insights in a simple and intuitive way.

We refer to the non-marginal approach in this paper as the infra-marginal analysis. The infra-marginal analysis is, loosely speaking, a combination of marginal and total cost-benefit analysis. We discuss the features of the infra-marginal analysis later in this paper. In particular, we demonstrate that the infra-marginal analysis is consistent with a decentralized decision-making process. We also show that when the infra-marginal analysis is applied, two types of comparative static analyses can be conducted. The first type is the conventional comparative statics which involve continuous changes in endogenous variables in response to a small change in a parameter. The second type involves discontinuous jumps of endogenous variables among different patterns of trade when changes in a parameter exceed certain threshold values.

Using the infra-marginal analysis, we examine several issues associated with international division of labor. Firstly, we incorporate transaction costs into the simple 2x2 Ricardian model and analyze the relationship between transaction costs and the division of labor. According to Adam Smith (1776), the division of labor is limited by the extent of the market (Chapter 3), and the extent of the market is determined by transportation costs (p.31-32). We formalize Smith's conjecture in our model.

Secondly, we examine the effect of tariff in a 2x2 Ricardian model. We show that (1) if partial division of labor occurs in equilibrium, the country that produces both goods chooses unilateral protection tariff, and the country producing a single good chooses unilateral laissez faire policy; and (2) if complete division of labor occurs in equilibrium, both countries would prefer tariff negotiation to tariff war. The tariff negotiation would lead to a bilateral laissez faire regime. This result can be used to explain why unilateral protection tariff and unilateral laissez faire may coexist; and why tariff negotiations may sometimes be essential to achieving free trade. This result also appears to be consistent with our observation of a policy shift from unilateral protection tariff to tariff negotiation and trade liberalization.
Finally, we introduce a third country to the Ricardian model. We show that the country which has no comparative advantage over the other two countries and/or which has the lowest transaction efficiency may be excluded from trade. We use this result to examine the relationship between international competitiveness and the wealth of a nation.

The rest of this paper is organized as follows. Section 2 presents the general equilibrium 2x2 Ricardian model with transaction costs and discusses the implications of the infra-marginal analysis. Section 3 examines the effects of tariff. Section 4 considers a 3x2 model. The concluding section summarizes the findings of the paper and suggests possible extensions.

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