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# Advanced International Trade: Theory and Evidence / Edition 1

Advanced International Trade: Theory and Evidence / Edition 1 available in Hardcover

- ISBN-10:
- 0691114102
- ISBN-13:
- 9780691114101
- Pub. Date:
- 12/02/2003
- Publisher:
- Princeton University Press

## Overview

*Advanced International Trade* is the first major graduate textbook in international trade in a generation. Trade is a cornerstone concept in economics, taught in all departments both in the United States and abroad. The past twenty years have seen a number of new theoretical approaches that are essential to any graduate international trade course, and will be of interest in development economics and other fields. Here, Robert Feenstra steps beyond theory to consider empirical evidence as well. He covers all the basic material including the Ricardian and Hecksher-Ohlin models, extension to many goods and factors, and the role of tariffs, quotas, and other trade policies; recent material including imperfect competition, outsourcing, political economy, multinationals, and endogenous growth; and new material including the gravity equation and the organization of the firm in international trade.

Throughout the book, special emphasis is placed on integrating the theoretical models with empirical evidence, and this is supplemented by theoretical and empirical exercises that appear with each chapter. *Advanced International Trade* is intended to bring readers to the forefront of knowledge in international trade and prepare them to undertake their own research. Both graduate students and faculty will find a wealth of topics that have previously only been covered in journal articles, and are dealt with here in a common and simple notation. In addition to known results, the book includes some particularly important unpublished results by various authors. Two appendices describe empirical methods applicable to research problems in international trade, methods that draw on (i) index numbers and (ii) discrete choice models. Thoroughly up-to-date and marked by clear, straightforward prose, this book will be used widely—and enthusiastically.

## Product Details

ISBN-13: | 9780691114101 |
---|---|

Publisher: | Princeton University Press |

Publication date: | 12/02/2003 |

Edition description: | Older Edition |

Pages: | 496 |

Product dimensions: | 6.20(w) x 9.60(h) x 1.20(d) |

## Read an Excerpt

#### Advanced International Trade

#### Theory and Evidence

**By Robert C. Feenstra**

**PRINCETON UNIVERSITY PRESS**

**Copyright © 2016 Princeton University Press**

All rights reserved.

ISBN: 978-1-4008-7376-0

All rights reserved.

ISBN: 978-1-4008-7376-0

CHAPTER 1

**Preliminaries: Two-Sector Models**

We begin our study of international trade with the classic Ricardian model, which has two goods and one factor (labor). The Ricardian model introduces us to the idea that technological differences across countries matter. In comparison, the Heckscher-Ohlin model dispenses with the notion of technological differences and instead shows how *factor endowments* form the basis for trade. While this may be fine in theory, the model performs very poorly in practice: as we show in the next chapter, the Heckscher-Ohlin model is hopelessly inadequate as an explanation for historical or modern trade patterns unless we allow for technological differences across countries. For this reason, the Ricardian model is as relevant today as it has always been. Our treatment of it in this chapter is a simple review of undergraduate material, but we will present a more sophisticated version of the Ricardian model (with a continuum of goods) in chapter 3.

After reviewing the Ricardian model, we turn to the two-good, two-factor model that occupies most of this chapter and forms the basis of the Heckscher-Ohlin model. We shall suppose that the two goods are traded on international markets, but do not allow for any movements of factors across borders. This reflects the fact that the movement of labor and capital across countries is often subject to controls at the border and is generally much less free than the movement of goods. Our goal in the next chapter will be to determine the pattern of international trade between countries. In this chapter, we simplify things by focusing primarily on *one* country, treating world prices as given, and examine the properties of this two- by-two model. The student who understands all the properties of this model has already come a long way in his or her study of international trade.

**RICARDIAN MODEL**

Indexing goods by the subscript *i,* let *ai* denote the labor needed per unit of production of each good at home, while *a*i* is the labor need per unit of production in the foreign country, *i* =1, 2. The total labor force at home is *L* and abroad is *L** . Labor is perfectly mobile between the industries in each country, but immobile across countries. This means that both goods are produced in the home country only if the wages earned in the two industries are the same. Since the marginal product of labor in each industry is 1/*ai*, and workers are paid the value of their marginal products, wages are equalized across industries if and only if *p*1/*a*1 = *p*2/a2/*a*2, where *p1* is the price in each industry. Letting *p* = *p*1/*p*2 denote the *relative* price of good 1(using good 2 as the numeraire), this condition is *p* = *a*1/*a*2.

These results are illustrated in figure 1.1(a) and (b), where we graph the production possibility frontiers (PPFs) for the home and foreign countries. With all labor devoted to good *i* at home, it can produce *L*/*ai* units, *i* =1, 2, so this establishes the intercepts of the PPF, and similarly for the foreign country. The slope of the PPF in each country (ignoring the negative sign) is then *a1*/*a2* and *a1)*/*a2*). Under autarky (i.e., no international trade), the equilibrium relative prices *pa* and *pa*)* must equal these slopes in order to have both goods produced in both countries, as argued above. Thus, the autarky equilibrium at home and abroad might occur at points *A* and *A** Suppose that the home country has a *comparative advantage* in producing good 1, meaning that *a1*/*a2*< *a1**/*a2*)*. This implies that the home autarky relative price of good 1 is *lower* than that abroad.

Now letting the two countries engage in international trade, what is the equilibrium price p at which world demand equals world supply? To answer this, it is helpful to graph the world relative supply and demand curves, as illustrated in figure 1.2. For the relative price satisfying *p*< *pa* = *a1*/*a2* and *pa** = *pa**< *a1** /*a2** both countries are fully specialized in good 2 (since wages earned in that sector are higher), so the world relative supply of good 1 is zero. For *pa*< *p*< *pa)*, the home country is fully specialized in good 1 whereas the foreign country is still specialized in good 2, so that the world relative supply is *L*/*a1)*/(*L**/*a*2*)), as labeled in figure 1.2. Finally, for *p* >*pa* and *p* >*pa)*, both countries are specialized in good 1. So we see that the world relative supply curve has a "stair-step" shape, which reflects the linearity of the PPFs.

To obtain world relative demand, let us make the simplifying assumption that tastes are identical and homothetic across the countries. Then demand will be independent of the distribution of income *across* the countries. Demand being homothetic means that *relative* demand *d*1/*d*2 in either country is a downward-sloping function of the relative price *p,* as illustrated in figure 1.2. In the case we have shown, relative demand intersects relative supply at the world price *p* that lies *between pa* and *pa*,* but this does not need to occur: instead, we can have relative demand intersect one of the flat segments of relative supply, so that the equilibrium price with trade *equals* the autarky price in one country.

Focusing on the case where *pa*< *p*< *pa*)*, we can go back to the PPF of each country and graph the production and consumption points with free trade. Since *p* >*pa,* the home country is fully specialized in good at point *B** as illustrated in figure 1.1(a), and then trades at the relative price p to obtain consumption at point *C*.* Conversely, since *p*< *pa*, the foreign country is fully specialized in the production of good 2 at point *B* in figure 1.1(b), and then trades at the relative price *p* to obtain consumption at point *C*. Clearly, *both* countries are better off under free trade than they were in autarky: trade has allowed them to obtain a consumption point that is above the PPF.

Notice that the home country exports good 1, which is in keeping with its comparative advantage in the production of that good, *a1*/*a2*< *a*1*/ *a*2*. Thus, *trade patterns are determined by comparative advantage,* which is a deep insight from the Ricardian model. This occurs even if one country has an *absolute disadvantage* in both goods, such as *a1* >*a*1* and *a2* >*a*2*, so that more labor is needed per unit of production of *either* good at home than abroad. The reason that it is still possible for the home country to export is that its *wages* will adjust to reflect its productivities: under free trade, its wages are lower than those abroad. Thus, while trade patterns in the Ricardian model are determined by *comparative advantage,* the level of wages across countries is determined by *absolute advantage.*

**TWO-GOOD, TWO-FACTOR MODEL**

While the Ricardian model focuses on technology, the Heckscher-Ohlin model, which we study in the next chapter, focuses on factors of production. So we now assume that there are two factor inputs — labor and capital. Restricting our attention to a single country, we will suppose that it produces two goods with the production functions *yi* = *fi*(*Li,**Ki,[i* = 1, 2, where *yi* is the output produced using labor *Li* and capital *Ki* These production functions are assumed to be increasing, concave, and homogeneous of degree one in the inputs (*Li,**Ki)*. The last assumption means that there are *constant returns to scale* in the production of each good. This will be a maintained assumption for the next several chapters, but we should be point out that it is rather restrictive. It has long been thought that *increasing returns to scale* might be an important reason to have trade between countries: if a firm with increasing returns is able to sell in a foreign market, this expansion of output will bring a reduction in its average costs of production, which is an indication of greater efficiency. Indeed, this was a principal reason why Canada entered into a free-trade agreement with the United States in 1989: to give its firms free access to the large American market. We will return to these interesting issues in chapter 5, but for now, ignore increasing returns to scale.

We will assume that labor and capital are *fully mobile* between the two industries, so we are taking a "long run" point of view. Of course, the amount of factors employed in each industry is constrained by the endowments found in the economy. These resource constraints are stated as

L1 + L2 ≤ L, K1 + K2 ≤ K. (1.1)

where the endowments *L* and *K* are fixed. Maximizing the amount of good 2, *y*2 = *f*2 (*L*2, *K*2, subject to a given amount of good 1, *y*1, = *L*(*f*1) (*L*1 [*K*1), and the resource constraints in (1.1) give us *y*2 = *h(y*1), *L*1*K*1). The graph of *y*2 as a function of *y*1 is shown as the PPF in figure 1.3. As drawn, *y*2 is a *concave* function of *y*1, [partial derivative]2*h*(*y*1, *L,K*) [partial derivative] *y*12< 0. This familiar result follows from the fact that the production functions *fi (Li, Ki)* are assumed to be concave. Another way to express this is to consider all points *S* =(*y*1), *y*2 that are feasible to produce given the resource constraints in (1.1). This production possibilities set *S* is *convex,* meaning that if *ya=(y1a, ya* and *y*1*b = yb, yb*) are both elements of *S,* then any point between them λ *ya* +(1-λ) *yb* is also in *S,* for 0 [less than or equal to] λ ≤ 1.

The production possibilities frontier summarizes the technology of the economy, but in order to determine where the economy produces on the PPF we need to add some assumptions about the market structure. We will assume perfect competition in the product markets and factor markets. Furthermore, we will suppose that product prices are given *exogenously:* we can think of these prices as established on world markets, and outside the control of the "small" country being considered.

**GDP FUNCTION**

With the assumption of perfect competition, the amounts produced in each industry will maximize gross domestic product (GDP) for the economy: this is Adam Smith's "invisible hand" in action. That is, the industry outputs of the competitive economy will be chosen to maximize GDP:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2)

To solve this problem, we can substitute the constraint into the objective function and write it as choosing y1 to maximize *p*1*y*1 + *p*2*h(y*1, *L, K*). The first-order condition for this problem is *p*1 + *p*2 [partial derivative] *h* /[partial derivative] *y*1= 0, or,

p = p1/p2 = - [partial derivative] h/[partial derivative]hy1 = - [partial derivative]y2/[partial derivative]y1. (1.3)

Thus, the economy will produce where the relative price of good 1, *p = p*1/*p*2, is equal to the slope of the production possibilities frontier.5 This is illustrated by the point *A* in figure 1.4, where the line tangent through point *A* has the slope of (negative) *p.* An increase in this price will *raise* the slope of this line, leading to a new tangency at point *B.* As illustrated, then, the economy will produce more of good 1 and less of good 2.

The GDP function introduced in (1.2) has many convenient properties, and we will make use of it throughout this book. To show just one property, suppose that we differentiate the GDP function with respect to the price of good *i,* obtaining It turns out that the terms in parentheses on the right of (1.4) sum to *zero,* so that [partial derivative]G/[partial derivative]pi = yi. In other words, the derivative of the GDP function with respect to *prices* equals the *outputs* of the economy.

The fact that the terms in parentheses sum to zero is an application of the "envelope theorem," which states that when we differentiate a function that has been maximized (such as GDP) with respect to an exogenous variable (such as *pi)*, then we can *ignore* the changes in the endogenous variables (*y*1 and *y*2) in this derivative. To prove that these terms sum to zero, totally differentiate *y*2 = *h(y*1, *L,K*] with respect to *y*1 and *y*2 and use (1.3) to obtain *p*1*dy*1 = - *p*2*dy*2, or *p*1*dy*1+ *p*2*dy*2 = 0 This equality must hold for any small movement in *y*1 and *y*2 around the PPF, and in particular, for the small movement in outputs *induced* by the change in *pi*. In other words, *p*1([partial derivative] *y*1/[partial derivative] *p*1)+ *p*2([partial derivative]y2/ [partial derivative] *p*1) = 0, so the terms in parentheses on the right of (1.4) vanish and it follows that [partial derivative]G/ [partial derivative] *p*1 = *y*1.

**EQUILIBRIUM CONDITIONS**

We now want to state succinctly the equilibrium conditions to determine factor prices and outputs. It will be convenient to work with the *unit-cost functions* that are dual to the production functions (*fi Li,Ki*). These are defined by.

*(Continues...)*

Excerpted fromAdvanced International TradebyRobert C. Feenstra. Copyright © 2016 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.

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## Table of Contents

Acknowledgments ix

Preface xi

Chapter 1

Preliminaries: Two-Sector Models 1

Chapter 2

The Heckscher-Ohlin Model 31

Chapter 3

Many Goods and Factors 64

Chapter 4

Trade in Intermediate Inputs and Wages 99

Chapter 5

Increasing Returns and the Gravity Equation 137

Chapter 6

Gains from Trade and Regional Agreements 174

Chapter 7

Import Tariffs and Dumping 209

Chapter 8

Import Quotas and Export Subsidies 254

Chapter 9

Political Economy of Trade Policy 300

Chapter 10

Trade and Endogenous Growth 338

Chapter 11

Multinationals and Organization of the Firm 371

Appendix A. Price, Productivity, and Terms of Trade Indexes 410

Appendix B. Discrete Choice Models 429

References 443

Index 475

## What People are Saying About This

**Bin Xu**

No other book in advanced international trade matches this one in providing a clear, complete, up-to-date, balanced, and systematic summary of international trade theory and evidence. Its impact on the graduate education and scholarly research of international trade will be felt for years to come.

— *Bin Xu, University of Florida*

**Donald Davis**

Feenstra covers his topics fabulously. I hope—for the sake of our field—that this book will help to complete a revolution already underway in turning the study of international trade from speculation into a science.

— *Donald Davis, Columbia University*

**Douglas Irwin**

This book is a tremendous contribution. It will quickly become 'the' main textbook in graduate international trade classes, and will be a useful reference for many others interested in the field. It is very up-to-date and is unique in emphasizing empirical testing and results, precisely what most trade economists are doing these days.

— *Douglas Irwin, Dartmouth College, author of "Free Trade Under Fire"*

**Daniel Trefler**

In fifteen years of teaching this material I have never used a textbook. Thanks to Robert Feenstra, my students are about to experience a dramatic change for the better. When I have a question about international trade I immediately turn to Rob Feenstra for answers and insights. He is the most distinguished empirical researcher in the field today. Not surprisingly, this book reflects both his awesome scholarship and his ability to communicate ideas simply.

— *Daniel Trefler, University of Toronto*

## Recipe

"No other book in advanced international trade matches this one in providing a clear, complete, up-to-date, balanced, and systematic summary of international trade theory and evidence. Its impact on the graduate education and scholarly research of international trade will be felt for years to come."—Bin Xu, University of Florida

"In fifteen years of teaching this material I have never used a textbook. Thanks to Robert Feenstra, my students are about to experience a dramatic change for the better. When I have a question about international trade I immediately turn to Rob Feenstra for answers and insights. He is the most distinguished empirical researcher in the field today. Not surprisingly, this book reflects both his awesome scholarship and his ability to communicate ideas simply."—Daniel Trefler, University of Toronto

"This book is a tremendous contribution. It will quickly become 'the' main textbook in graduate international trade classes, and will be a useful reference for many others interested in the field. It is very up-to-date and is unique in emphasizing empirical testing and results, precisely what most trade economists are doing these days."—Douglas Irwin, Dartmouth College, author of *Free Trade Under Fire*

"Feenstra covers his topics fabulously. I hope—for the sake of our field—that this book will help to complete a revolution already underway in turning the study of international trade from speculation into a science."—Donald Davis, Columbia University