The chapters are largely Independent. The growth and fluctuations sections are almost entirely self-contained (although Chapter 4 builds moderately on Part A of Chapter 2). There IS also considerable independence among the chapters in each secnon. New growth theory (Chapter 3) can be covered either before or after the Ramsey and Diamond models (Chapter 21, and Keynesian models (Chapters 5 and 6) can be covered either before or after real-busmess-cycle theory (Chapter 4). Finally, the last four chapters are largely self-contained lalthough Chapter 7 relies moderately on Chapter 2, Chapter 9 relies moderately on Chapter 5, and Chapter 10 rehes moderately on Chapter 6).

A solutions manual prepared by Jeffrey Rohaly is available for use with the book.

The main subject of Chapter 10 is the determinants of an economys natural rate of unemployment. The chapter also investigates the impact of fluctuations in labor demand on real wages and employment. The main theories considered are efficiency-wage theories, contracting and insider/outsider theories, and search and matching models.

Macroeconomics is both a theoretical and an empirical subject. Because of this, the presentation of the theories is supplemented with examples of relevant empirical work. Even more so than with the theoretical sections, the purpose of the empirical material is not to provide a survey of the literature; nor is it to teach econometric techniques. Instead, the goal is to illustrate some of the ways that macroeconomic theories can be applied and tested. The presentation of this material is for the most part fairly intuitive and presumes no more knowledge of econometrics than a general familiarity with regressions. In a few places where it can be done naturally, the empirical material includes discussions of the ideas underlying more advanced econometric techniques.

Each chapter concludes with an extensive set of problems. Tlie problems range from relatively straightforward variations on the ideas in the text to extensions that tackle important new issues. The problems thus serve both as a way for readers to strengthen their understanding of the material and as a compact way of presenting signiftcant extensions of the ideas in the text.2

The fact that the book is an advanced introduction to macroeconomics has two main consequences. The first is that the book uses a series of formal models to present and analyze the theories. Models identify particular features of reaUty and study their consequences in isolation. They thereby allow us to see clearly how different elements of the economy interact and what their implications are. As a result, they provide a rigorous way of in-\ estigating whether a proposed theory can answer a particular question and whether it generates additional predictions.

The book contains literally dozens of models. The main reason for this multiplicity is that we are interested in many issues. The features of the economy that are crucial to one issue are often unimportant to others. Money, for example, is almost surely central to inflation and is probably not central to long-run growth. Incorporating money into models of growth vould only obscure the analysis. Thus instead of trying to build a single

4 INTRODUCTION

model to analyze all of the issues we are interested in, the book develops a series of models.

An additional reason for the multiplicity of models is that there is considerable disagreement about the answers to many of the questions we will be examining When there is disagreement, the book presents the leading views and discusses their strengths and weaknesses. Because different theories emphasize different features of the economy, again it is more enlight-emng to investigate distinct models than to build one model incorporating all of the features emphasized by the different views.

The second consequence of the books advanced level is that it presumes some background in mathematics and economics. Mathematics provides compact ways of expressing ideas and powerful tools for analyzing them. The models are therefore mainly presented and analyzed mathematically. The key mathematical requirements are a thorough understanding of single-variable calculus and an introductory knowledge of multivariable calculus. Tools such as functions, logarithms, derivatives and partial derivatives, maximization subject to constraint, and Taylor-series approximations are used relatively freely. Knowledge of the basic ideas of probability-random variables, means, variances, covariances, and independence-is also assumed.

No mathematical background beyond this level is needed. More advanced tools (such as simple differential equations, the calculus of variations, and dynamic programming) are used sparingly, and they are explained as they are used. Indeed, since mathematical techniques are essential to further study and research m macroeconomics, models are sometimes analyzed in more detail than is otherwise needed in order to illustrate the use of a particular method.

In terms of economics, the book assumes an understanding of microeconomics through the intermediate level. Familiarity with such ideas as proht-maximization and utility-maximization, supply and demand, equilibrium, efficiency, and the welfare properties of competitive equilibria is presumed. Little background m macroeconomics itself is absolutely necessary. Readers with no prior exposure to macroeconomics, however, are likely to find some of the concepts and terminology difficult, and to find that the pace is rapid (most notably in Chapter 5). These readers may wish to review an intermediate macroeconomics text before beginmng the book, or to study such a book m conjunction with this one.

The book was designed for first-year graduate courses in macroeconomics. But It can be used in more advanced graduate courses, and (either on Its own or m conjunction with an intermediate text) for students with strong backgrounds in mathematics and economics in professional schools and advanced undergraduate programs. It can also provide a tour of the field for economists and others working in areas outside macroeconomics.

Chapter 1

THE SOLOW GROWTH MODEL

1.1 Theories of Economic Growth

Standards of living differ among parts of the world by amounts that almost defy comprehension. Although precise comparisons are difficult, the best available estimates suggest that average real incomes in such countries as the United States, Germany, and Japan exceed those in such countries as Bangladesh and Zaire by a factor of twenty or more. There are also large differences in countries growth records. Some countries, such as South Korea, Turkey, and Israel, appear to be making the transition to membership in the group of relatively wealthy industrialized economies. Others, including many in South America and sub-Saharan Africa, have difficulty simply in obtaining positive growth rates of real income per person. Finally, we see \ast differences in standards of living over time: the world is much richer today than it was three hundred years ago, or even fifty years ago.

The implications of these differences in standards of living for human welfare are enormous. The real income differences across countries are associated with large differences in nutrition, literacy, infant mortality, life expectancy, and other direct measures of well-being. And the welfare consequences of long-run growth swamp any possible effects of the short-run fluctuations that macroeconomics traditionally focuses on. During an average recession in the United States, for example, real income per person falls by a few percent relative to its usual path. In contrast, the productivity slowdown-the fact that average annual productivity growth since the 1970s has been about 1 percentage point below its previous level-has reduced real income per person in the United States by about 20 percent relative to what it otherwise would have been. Other examples are even more startling. If real income per person in India continues to grow at its postwar average rate of 1.3 percent per year, it will take about two hundred years for Indian real incomes to reach the current U.S. level. If India achieves 3 percent growth, the process will take less than one hundred years. And if it achieves Japans average growth rate, 5.5 percent, the time will be reduced to only fifty years. To quote Robert Lucas (1988), "Once one starts to think about [economic growth], it is hard to think about anything else."