One of the most difficult areas in consumer theory is that which concerns itself with intertemporal choice. Theory which ignores uncertainty lacks credibility while theory taking it into account is complex and hard to implement. On the empirical side, the analysis of the consumption function and of durable goods presents all the classic time-series problems of dynamics, seasonally and serial correlation. Even after 40 years of continual econometric activity, and in spite of their contemporary treatment as standard classroom examples of applied econometric analysis, both durable goods and consumption functions are still subject to lively controversy.

Much the most influential work on what is still called the ‘modern’ theory of the consumption function is that of Modigliani and Brumberg (1955a, b) on the life-cycle model, although the ideas go back to Fisher and Ramsey. The life-cycle model has the inestimable advantage of viewing the theory of the consumption function as a part of consumption theory in general. This work, together with that of Friedman (1957), provided the basic model of the consumption function which has dominated theoretical and empirical discussion ever since. In its applied form at least, the basic regression is one of consumption on its own lagged value and on income although a number of other variables (lagged income, wealth, liquid assets, the distribution of income) make periodic appearances.

Introduction

The development of complete systems of demand functions has been one of the most important trends in research on consumer demand in the last couple of decades. Richard Stone's Linear Expenditure System and the theoretical approach which he used in establishing this system have been instrumental in this development. The LES system has been widely used both in its original form and in forms modified and generalized in various directions. Several other systems have also appeared. There is no doubt that great advances have been achieved. It seems to me, however, that research in this field has, voluntarily, put on a strait-jacket. I have in mind the requirement that all demand functions constituting the system shall be ‘of the same form’, differing only in the values of the parameters. The purpose of the present paper is to suggest approaches which may help to free theory and applied work from this strait-jacket.

The idea that it would be sound and useful to abandon the requirement that all functions in the system should be of the same form is not entirely uncontroversial. L. J. Lau has argued that such uniformity ‘is desirable because it allows all commodities to be treated symmetrically’. This kind of symmetry does of course possess a sort of aesthetic value, and it is also convenient from a mathematical and computational point of view.

Introduction

The literature on index numbers is so vast that we can cover only a small fraction of it in this chapter. Frisch (1936) distinguishes three approaches to index number theory: (i) ‘statistical’ approaches, (ii) the test approach, and (iii) the functional approach, which Wold (1953, p. 135) calls the preference field approach and Samuelson and Swamy (1974, p. 573) call the economic theory of index numbers. We shall mainly cover the essentials of the third approach. In the following two sections, we define the different index number concepts that have been suggested in the literature and develop various numerical bounds. Then in section 4, we briefly survey some of the other approaches to index number theory. In section 5, we relate various functional forms for utility or production functions to various index number formulae. In section 6, we develop the link between ‘flexible’ functional forms and ‘superlative’ index number formulae. The final section offers a few historical notes and some comments on some related topics such as the measurement of consumer surplus and the Divisia index.

Price indexes and the Konüs cost of living index

We assume that a consumer is maximizing a utility function F(x) subject to the expenditure constraint where x ≡ (x1, …, xN)T ≥ 0N is a non-negative vector of commodity rentals, p ≡ (p1, …, PN)T ≫ 0N is a positive vector of commodity prices and y > 0 is expenditure on the N commodities.

Introduction

The study of labour supply and commodity demands has, for the most part, proceeded on separate lines. There has been an extensive literature, much of it inspired by the work of Sir Richard Stone (see, for example, Stone 1954), on the estimation of commodity demand systems; and there has been a recent growth of interest in labour supply equations. However, there have been relatively few attempts to estimate jointly labour supply and commodity demand relationships. At a theoretical level, the main contribution to linking these two aspects of household decision-making has been in the work on household production. The ‘activities’ approach, developed particularly in Becker's theory of the allocation of time (1965), provides considerable insight, but has not been widely adopted in empirical research. In this paper we build on Becker's theoretical work and develop the activities approach as the basis for an econometric investigation of the joint determination of labour supply and commodity demand in the United Kingdom.

We begin in section 2 by discussing the household allocation of income and time, and relating it to the theory of rationing. To illustrate the extension of the standard consumer demand model, we take in section 3 the case of the linear expenditure system. This provides the basis for the empirical work, which uses data on expenditure by commodity category, and hours of work, contained in the Family Expenditure Survey for the United Kingdom.

One of the most significant developments in economics over the past twenty years has been the increasing extent to which economists have been prepared to apply the basic tools of consumer theory to areas other than just the demand for goods. A particularly notable example is the analysis of labour supply, where utility theory has been successfully used in the empirical analysis of a wide range of phenomena, including the supply decisions of primary and secondary workers, the decision whether or not to participate, and the type of behaviour which results from the complex rules of modern tax and social security systems. For a discussion of this material see, e.g. Killingsworth (1981) or Deaton and Muellbauer (1980, chapter 11). More generally, the ‘characteristics’ or household production model has been applied to a wide variety of economic problems. Amongst the earliest examples is Gorman's famous 1956 paper on eggs, although it was Lancaster (1966a, b) whose work firmly established the methodology in the literature. In part one of this volume, the chapter by Theil and Laitinen can be interpreted as a characteristics model with the transformed goods as the characteristics, but much wider applications are possible. In particular, the model has been applied to the analysis of human capital formation, of fertility, of the use of time, of sexual and racial discrimination, of quality, and of health, to name only a few topics.

In this chapter I present a mathematical theory of institution creation. Being only a theory as opposed to the theory, it cannot be considered the only possible approach that one could take. However, it is my feeling that the model presented here does contain two elements that any successful theory of institution creation must contain. The first is a theory of norm creation and change which must be included in any theory that tries to depict the process of the creation of social institutions as we have defined them (i.e., as commonly adhered to regularities in behavior created to solve recurrent societal problems), because it is upon these norms that the regularities in behavior we are calling social institutions can be built. More precisely, we have defined social institutions or conventions as regularities (R) in the behavior of members of a population when they are agents in recurrent situations, Γ, which are such that:

1. Everyone conforms to R.

2. Everyone expects everyone else to conform to R.

3. Either everyone prefers to conform to R on condition that the others do if Γ is a coordination problem, in which case uniform conformity to R is a coordination equilibrium, or

4. If anyone ever deviates from R, it is known that some or all of the others will also deviate and the payoffs associated with the recurrent play of Γ using these deviating strategies are worse for all agents than is the payoff associated with R.

Now, notice that for a social institution or regularity R to be a well-functioning one, everyone must “expect everyone else to conform to R.”

This book considers the nature, function, and evolution of economic and social institutions. Most simply, it is a first step in an attempt to liberate economics from its fixation on competitive markets as an all-encompassing institutional framework. It views economic problems as evolutionary ones in which economic agents have finite lives and pass on to their successors a wide variety of social rules of thumb, institutions, norms, and conventions that facilitate the coordination of economic and social activities. In time, the institutional structure of the economy becomes more and more complex as more and more social and economic institutions are created and passed on from generation to generation. In some instances these institutions supplement competitive markets, and in some instances they totally replace them. Some of the institutions are explicitly agreed to and codified into law; others are only tacitly agreed to and evolve spontaneously from the attempts of the individual agents to maximize their own utility. Some lead to optimal social states; others are dysfunctional. In any case, each arises for a specific reason. It is the purpose of this book to investigate these reasons and analyze the types of institutions that evolve.

But what are social institutions, and what functions do they serve? These questions can be answered only by viewing economic problems in an evolutionary light. Doing this, as Veblen (1898) points out, takes the emphasis away from equilibrium analysis and places it on the disequilibrium aspects of the economic process. The proper analogy to make is between the evolution of an economy and the evolution of a species.

Ideas, once conceived, often undergo long gestation periods and are brought forth with great pain. When in the process they grow into monographs or books, one must realize that despite their mature appearance they are still only infants. This book presents a theory of social institutions that is still in its infancy and in no way purports to be fully mature. However, it does, I think, capture the essence of the phenomenon under investigation and present a formal way of dealing with it.

In judging the pages that follow, we must first ask what it is that a theoretical social scientist can attempt when he tries to make sense out of a particular aspect of the real world. It is my feeling that the first step he must take is to strip the phenomenon under study of its misleading worldly trappings and to lay bare its true nature. What may often be discovered is that the exotic phenomenon under investigation is isomorphic to a phenomenon with which we are quite familiar and comfortable. It is in the identification of these structural similarities that the essential qualities of the phenomenon are discovered and it is this process that any social scientific theory must attempt before going on to deal with more complicated questions. This is exactly what I have attempted to do in this book. I have tried to lay bare the essence of social institutions and the structure of the evolutionary problems they are called upon to solve.

One of the demands that confronts social scientists is the demand for relevance. For many, this demand is a curse because it robs social scientists of their ability to justify total abstraction. The inevitable question in social science is always: “So what? What difference does this make to the real world?”

It is my belief that there are two methodological responses to this demand. One is a response in which the social scientist makes his work directly applicable to meaningful empirical questions. This is what the layman usually sanctions as “relevant” social scientific research. The other approach, however, and one that I feel is equally relevant, is an approach that aims not to change the real world directly but rather to alter the way we view the real world by changing the prevailing theoretical paradigm existing among scholars. In other words, one approach is to theorize directly about the real world, whereas the other is to theorize about the theory existing to describe the real world (i.e., to be metatheoretical). My aim in this book was closer to the latter approach than to the former. What I have written may not be as directly applicable to the real world as it is to the way we view that world. I have tried to broaden the institutional frame of reference that we use to analyze empirically relevant social phenomena and to open up a new set of questions that could be asked about such phenomena. Consequently, the theory presented here is one step removed from direct application, yet still potentially applicable.