The inflationary conditions that have prevailed in the industrialized countries in recent years have made investigators aware of the likely relationship between the rate of inflation and the nominal rate of interest. Of the various theories that may bear on this relationship, Fisher's is the one that has attracted most attention. The Fisherian relationship has been analyzed in several recent studies, some of which have subjected it to empirical tests.

In most of these studies, Fisher's theory has been taken at its face value: In testing its empirical validity, researchers have generally ignored important economic and institutional changes since Fisher first proposed his theory. In particular, up to 1975, no attention had been paid to the existence and importance of income taxes, and to the effects that these may have on Fisher's theoretical conclusions, which were formulated and proposed in the United States at a time when the country did not have an income tax.

In a discussion of the interrelationship between income taxes and interest rates under inflationary conditions, one can either pursue an expost analysis emphasizing the inequities and/or distortions associated with taxing the whole nominal income from interest, instead of its real component; or pursue an ex ante, or equilibrium, analysis by discussing the possibility that the existence of income taxes should lead, in the absence of fiscal illusion, to adjustments in the nominal rate of interest.

In Chapter 1, we assumed without justification the existence of demand functions. We provide a basis for that assumption in this chapter by considering individual preferences. In so doing, we seek not only to describe rather more completely the properties of demands but also to establish a framework within which we shall operate for the rest of the book. Section 2.1 discusses the axioms of choice and how they lead to utility functions and to the system of choice described by utility maximization. Section 2.2 is concerned with the transition from utility to the demand functions; the traditional constrained maximization approach is discussed and its drawbacks enumerated. Section 2.3 presents consumer demand in terms of cost minimization rather than utility maximization. Marshallian uncompensated demand functions, defined on prices and outlay, are contrasted with Hicksian compensated demand functions, defined on prices and utility, and the central concept of the cost function is introduced. Section 2.4 uses the apparatus of cost minimization to derive the properties of demand. Symmetry and negativity (the “law of demand”) are presented as is the Slutsky equation linking the price derivatives of compensated and uncompensated demands. The generality of these results is contrasted with those obtained through more traditional approaches. Section 2.5 is concerned with the meaning of “duality” in consumer theory, and we show how the cost function can be used as an alternative to the utility function as a representation of preferences.

The theory presented in Chapter 2 offers a framework within which we can attempt to organize and interpret the data. This chapter begins this task by discussing the application of four particular models, each of which seeks to describe the way in which total outlay is spent. These illustrations not only show how the theory can be made specific but also allow us to check the usefulness of the theory in empirical work. In this context, various problems and difficulties are pointed out as we go along. The identification of them provides much of the motivation for the extensions and modifications of the theory that are begun in the next three chapters.

Although we make no attempt to provide a historical survey of applications of demand theory, the studies will be presented in rough chronological order. This is natural, since there has been a steady growth in the degree to which practical work has based itself upon the theory. In §3.1, we shall discuss some of the methodology and results in Stone's justly famous 1954 monograph, The Measurement of Consumers' Expenditure and Behaviour. This study follows the precedent of virtually all studies up to that time in modeling commodity demands individually, equation by equation, so that, if necessary, the functional form can be varied and special explanatory variables introduced. This approach has the great advantage of flexibility and is undoubtedly the best way of modeling the demand for an individual commodity in isolation.

Developing good theoretical models for applied work in economics is a difficult task and perhaps nowhere more so than in the modeling of the demand for durables, especially in aggregate time series data. On the one hand, a good model ought to be complete; on the other, the essence of a model is abstraction: choosing a small number of characteristics that are supposedly central to behavior. Abstraction is necessitated not only by the need to communicate ideas and information but by the limited discriminatory power of most aggregate time-series data. In the area of the demand for durables, a number of really very different and seemingly contradictory approaches have been put forward, and agreement is far from universal as to what are the central issues.

Perhaps the best way of seeing how complex are the problems is to begin by listing various themes or special features of the demand for durables, all of which have been emphasized by different economists working in the area.

1. (1) There is an extremely important distinction to be made between purchases, on the one hand, and consumption, on the other. Purchases are regarded as adding to stocks, while consumption, which is rendered possible by the existence of the stocks, is responsible for their depletion or physical deterioration. Although it is often assumed that consumption is proportional to the stock of the durable and that the latter physically depreciates at a constant, proportional rate, this is only one particular formulation.

2. […]

This book has analyzed in some detail the effects of inflation on the personal income tax and, to a lesser extent, the effects of inflationinduced increases in personal income taxation on the rate of inflation. It has also discussed various adjustment mechanisms aimed at neutralizing those effects, as well as their use in various countries. The purpose of this chapter is not to summarize the arguments presented in the previous chapters but to draw a few basic conclusions. These will be organized around three sections dealing respectively with political and stabilization, equity and efficiency, and administrative aspects. Particular issues may, of course, involve more than one of these aspects.

Political and stabilization aspects

The basic political argument related to the indexation of income taxes concerns the “proper size of the public sector” and thus has divided liberals from more conservative writers. As we saw in earlier chapters, in the absence of indexation and of substantial lags in collection, an increase in nominal income – whether due to inflation or growth – will increase the ratio of tax revenue to national income. Governments will have more money to spend without having to raise taxes. As a consequence the public sector is likely to be, or become, larger when no indexation is present. An individual's attitude toward this expansion is likely to depend on his political views. Liberals are likely to favor it while conservatives are likely to oppose it.

Index numbers of prices, output, and welfare are part of the common parlance of economic debate. Yet the theory of economic index numbers, which has attracted some of the best minds in economics over the years, had until very recently been rather unfashionable. Few modern texts include more than passing references to index number theory, and the topic seems to be regarded as a rather unimportant backwater. However, the increase in rates of inflation in recent years has brought renewed interest in the measurement of price indices, while the realization that inflation affects different groups differently had rendered the quantification of these differentials an important element in assessing inequality between households or individuals.

In the context of consumers, economic index numbers attempt to construct a single ratio that measures one of two things. The first, the cost-of-living index, measures the relative costs of reaching a given standard of living under two different situations, while the second, the real consumption index, compares two different standards of living in some appropriate units. As we shall see, the most convenient scale with which to measure welfare is the expenditure necessary, at constant prices, to maintain the various welfare levels being considered. These concepts, which use money to measure changes in welfare, can only be applied to situations where money and welfare are uniquely linked. This will not be the case where goods that are important for consumers' well-being are not purchased through the market; examples are health care, public parks, clean air, a noise-free environment, or some kinds of education.

Consumer index numbers • Household characteristics, demand, and household welfare comparisons • Social welfare and inequality

The problems faced by consumers when there is uncertainty have frequently arisen in our discussion to date. Indeed, uncertainty is pervasive in almost all decision making and is inevitable whenever an action or decision and its consequence are separated by a space of time, however short. Even for consumption decisions involving the most highly perishable commodities, some uncertainty is always present. An ice cream may melt before it can be eaten; its quality or flavor may be very different from that anticipated, or it may or may not cause indigestion at some unpredictable time after consumption. All these are trivial enough, but become of the greatest importance in considering any sort of intertemporal decision making, whether buying a car, planning savings, or choosing the assets in which to hold wealth. Because of such considerations, a fully satisfactory treatment of consumers' behavior would allow for uncertainty right from the start. However, as we shall see, although a consistent and well-articulated theory for choice under uncertainty does exist, its applications to date are partial in coverage and are very considerably more complex than the corresponding results under certainty. Moreover, the omnipresence of uncertainty does not imply that it is always important.

Only in the last twenty years, dating essentially from the work of Savage (1954), has a full, axiomatic treatment of choice under uncertainty been available, although, as in the case of the axioms of choice under certainty, there has been considerable refinement by later writers.

Households differ in size, age composition, educational level and other characteristics and, in general, we would expect households with different characteristics to have different expenditure patterns. Just as we are interested in modeling the effects on demands of differences in prices and budget levels, so is it legitimate and useful in summarizing a great deal of information to model the effects of household characteristics. In cross-section studies, either rather aggregated data for a few household types are available or, more rarely, a great deal of truly microeconomic information. Modeling the effects of household characteristics is useful in both situations provided that the model is plausible: in the former case, we obtain more precise estimates of the price and budget responses by pooling scarce data; in the latter, the model provides a convenient way of summarizing information that otherwise would take the form of a different demand system for each of the many household types.

In general, we can model differences in behavior by making demand depend not only on prices and total expenditure but also on some list of household characteristics. Most frequently modeled are the effects of household composition, the number, types, and ages of household members, but in principle any other characteristics can be included. As we shall see, this can be done in a wide variety of ways. One of the crudest, other than ignoring such effects altogether, is to deflate both demands and total outlay by household size so that, in per capita terms, consumption is the same function of the budget and prices for all households.

So far, this book has focused on the relationship between price level changes and the income tax. The impact of changes in real incomes have thus been ignored. However, the interplay of the progressivity of the tax with growth in real income can have effects that a country may wish to avoid. For example, adjustments for changes due to inflation alone may still leave a country with a growing ratio of revenue from income tax to personal (or national) income which can create a fiscal drag that might hinder the growth of the economy. This chapter and the next deal with some of the issues created by growth in real income. At this point, it is perhaps worthwhile to emphasize the basic difference between growth-related and inflation-related distortions. Unlike inflation-related distortions, those due to growth result exclusively from the progressivity of the tax. There is thus no problem of capitalincome distortions. If the tax were truly proportional, no growth related problem would exist.

In this chapter, the determinants of the sensitivity of the yield of the personal income tax will first be analyzed. Then a method for measuring that sensitivity will be described and applied to United States data.

The analysis of the sensitivity of the individual income tax to changes in national income has been a subject that for many years has attracted considerable attention. For a time, this attention was directed toward the contribution that this sensitivity made to stabilization.

This book is about the economic theory of consumer behavior and its uses in economic analysis. It is about the tools and language of utility theory and their application to a field that ranges from empirical work on commodity demand to abstract questions of social choice. The basic theory is the familiar one, although we have made extensive use of cost functions and related “duality” concepts to present it in a way that simplifies what is often seen as difficult or inaccessible material. This, and the range of subject matter, broader than any previous book on consumer behavior, are the most distinctive features of the book. Our main purpose in writing it is to provide in. one place a complete toolbox of utility theory together with a demonstration of the power of these tools in action over a wide front of economics. Although the use of utility theory runs as a common thread throughout the book, only a fraction of the space deals with the standard textbook model of choice subject to a linear budget constraint. In recent years, important work has been done in many areas of economics by applying consumer theory to nonstandard situations, for example, to discrete choice, to rationing, to labor supply, to fertility, to quality choice, to choice with complex nonlinear budget constraints resulting from tax and benefit systems, liquidity constraints, uncertainty, and so on. Most of this work emphasizes careful modeling of the constraints that consumers face, including the statistical and econometric consequences.

The model of consumer behavior developed in Chapter 2 and applied in Chapter 3 is clearly limited both in scope and in realism. The process of extending and improving the model in various directions will occupy much of the rest of the book and is the particular subject matter of Part Four. In this chapter, we make a start on these extensions but only in a very limited way. In particular, in §4.1 and §4.2, we show how labor supply decisions, savings behavior, and purchases of durable goods can be handled within the framework of utility maximization subject to a linear budget constraint, provided the arguments of the utility function and the constraint are appropriately redefined. We shall refer to these models as neoclassical, a name we use to label the assumption of linear budget constraints with fixed, known prices. In the present context, none of the neoclassical models turns out to be very realistic and hence the substantial attention paid to their improvement in Part Four. Nevertheless, it is extremely important to understand them. First, they play an important part in much contemporary economic analysis, and it is essential to understand exactly the assumptions on which their theoretical validity depends. Second, they yield important insights that we ignore at our peril and, in Part Four, they will be the platform on which we attempt to build more realistic and relevant models.

Whether inflation is, or is not, the work of the devil is an issue on which I would rather not make a pronouncement; however, it is the theme of this book that inflation respects appearances while destroying reality. Inflation distorts tax systems and, in the process, affects the level of taxation and its incidence among taxpayers. But these distortions are often not obvious and, at times, are so subtle that not only unsophisticated observers but even highly sophisticated ones may be deceived into concluding that nothing has changed in reality. This book deals with these distortions, with respect to income taxes, and with what can be done, or has been done in various countries, to deal with them. As the subject is of considerable interest to policymakers around the world, I have preferred to emphasize the practical, rather than the purely theoretical, side of the problems. This, however, does not imply that this book will be of no interest to academic economists or to students of taxation. The problems are simply too important and complex to be left just to policymakers. This book includes thirteen chapters ranging from fairly theoretical to eminently practical ones. In all cases, the perspective is an international one, although because of greater availability of data for the United States, some issues are illustrated with examples for that country.

In Part I, we saw how the theory of choice, initially developed for application to the allocation of a fixed total expenditure over a number of goods, could be extended to deal with labor supply, the allocation of income between saving and consumption, and the purchase of durable goods. So far, we have looked at these extensions as separate problems, but in principle, each consumer has to deal with all of them simultaneously. At any given time, current assets and current and future income must be allocated over nondurable and durable goods for current and future periods, while for consumers who are free to do so, plans must be made for allocating time between work and leisure in the present and the future. There are also the complications of choosing types of real and financial assets as well as the problems of dealing with uncertainty. All of the parts of this allocation problem may interact: changes in future wage rates may alter retirement plans with important consequences for durable good purchases now; an anticipated increase in asset values three years hence may cause an elated investor to buy more of his favorite dinner, and so on. Such interactions pose formidable problems, not only for the consumer but also for the economist who attempts to describe consumer behavior. If making today's purchases requires knowledge of the price of bootlaces 30 years from now, daily living is close to impossible. Nor is there much hope of predicting behavior if all such possible interactions must be allowed for.

The quality of goods and household production theory • Labor supply • The consumption function and intertemporal choice • The demand for durable goods • Choice under uncertainty