Foundations of Paul Samuelson's Revealed Preference Theory

Stanley Wong

• Publisher: Routledge
• Year: 2006
• ISBN:
  9781134385522
• Edition: 2
• Topic: Commerce
• Subtopic: Commerce Général

Originally published over two decades ago, this classic text within the philosophy of economics is a tour de force against revealed preference. It critically examines the research programme carried out by the Nobel Prize winner Paul Samuelson on the revealed preference approach to the theory of consumer behaviour. It also challenges two essential premises:

* that the programme has been completed
* that the various contributions of Samuelson are mutually consistent.

This text contains a new preface by Wong, in which he provides a detailed insight into the origins of his pioneering text, and a new introduction from Philip Mirowski, analyzing the impact The Foundation of Paul Samuelson's Revealed Preference Theory has had on the discipline of economics as well as explaining why it remains core reading for economists today.

The defining statement of economic method, this book will be of interest to economists everywhere.

Chapter 1

Introduction

1. There is general agreement among economists that Paul Samuelson’s research programme in the revealed preference approach to the theory of consumer behaviour was brought to a successful conclusion when Hendrik Houthakker (1950) proved the logical equivalence of revealed preference theory with ordinal utility theory.¹ This viewpoint, which was first expressed in Samuelson (1950b), owes its popularization to the influential survey on the theory of consumer behaviour by Houthakker (1961) (see also Arrow, 1967; Ekelund et al., 1972; Katzner, 1970; Newman, 1965; Samuelson, 1963).

2. This research programme, which we shall call the ‘Samuelson Programme’, was launched by Paul Samuelson (1938a) in ‘A Note on the Pure Theory of Consumer’s Behaviour’. In an attempt to dispense with the concept of ‘utility’, as well as any other concept which does not correspond to observable phenomena, Samuelson proposed a new theory of consumer behaviour based on a postulate of consistency of behaviour. He believed that his theory, which is now known as revealed preference theory, succeeded in ‘dropping off the last vestiges of utility analysis’ (1938a, p. 62), because it consists only of observational terms, and therefore becomes amenable to empirical verification or refutation.

3. In Samuelson’s opinion, the programme is further developed in ‘Consumption Theory in Terms of Revealed Preference’ (1948), in which the new theory becomes the basis for a method of constructing an individual’s indifference map from observations of his market behaviour. This construction may be seen as an attempt to make operational the concept of ‘preference’, i.e. to specify in terms of observable procedures the method by which an individual’s preferences can be ascertained.

4. The appearance of the Houthakker proof provided Samuelson with the occasion to survey the achievements of his programme. In ‘The Problem of Integrability in Utility Theory’ (1950b), he proclaims that the goal of his programme is finally reached: revealed preference theory (as revised by Houthakker) is shown to be the observational equivalent of ordinal utility theory. The Houthakker proof, writes Samuelson, ‘complete[s] the programme begun a dozen years ago [1938] of arriving at the full empirical implications for demand behaviour of the most general ordinal utility analysis’ (1950b, p. 369).

5. This result, according to Samuelson (1953), implies that the choice between the two theories can be based only on the criterion of convenience:²

The complete logical equivalence of this approach with the regular Pareto-Slutsky-Hicks-Arrow ordinal preference approach has essentially been established. So in principle there is nothing to choose between the formulations. There is, however, the question of convenience of different formulations (Samuelson, 1953, p. 1, emphasis added).

6. The proposition that the Samuelson Programme is completed has gone unchallenged in the literature. Moreover, there does not exist a substantive body of critical literature on the entire revealed preference approach. The criticism of non-specialists, such as Robertson (1951) and Robinson (1962), are largely ignored by specialists, while those by specialists themselves, such as Hicks (1974) and Georgescu-Roegen (1954a, 1973), are scattered in parenthetical remarks, footnotes, or book reviews. However, it must be pointed out that Sen (1973) devoted his inaugural lecture to an examination of the foundations of revealed preference theory.

7. Indeed the Houthakker result has become the point of departure for subsequent theoretical research (see, for example, Chipman et al., 1971).³ Moreover, it turned the (neo-classical) theory of consumer behaviour, by which is meant ordinal utility theory and its revealed preference equivalent, into a paradigm for economic theory in general. In the celebrated methodological dispute between Milton Friedman and Paul Samuelson, which was settled in Samuelson’s favour,⁴ the theory of consumer behaviour was cited by Samuelson (1963) as the best example of an economic theory which has been developed to logical perfection. It is indeed surprising that in the time when fundamental issues are hotly debated,⁵ the theory of consumer behaviour should stand out as one area in economics which is free from controversies and where the foundations are not subject to dispute.⁶

8. The current view is that the aim of the revealed preference approach is, and has been, ‘to formulate equivalent systems of axioms on preferences and on demand functions’ (Houthakker, 1961, p. 709). Notwithstanding Samuelson’s position to the contrary, we can discern in Samuelson’s writings at least three different and mutually inconsistent interpretations of the major problem to be solved by the new approach. This raises a problem of understanding the Samuelson Programme.

9. In Samuelson (1938a) the problem is to derive the main results of ordinal utility theory but without using any concept which does not correspond to observable phenomena. As a solution to this problem, Samuelson proposed a new theory of consumer behaviour. However, in Samuelson (1948) the theory becomes a solution to the problem of constructing an individual’s indifference map. The first problem, it appears, is incompatible with the second. If Samuelson does solve positively the second problem, does this mean that he no longer finds objectionable ordinal utility theory? If so, does this not mean that the new approach was founded on an error, namely a misunderstanding of ordinal utility theory? Furthermore, since the second problem requires an antecedent acceptance of a preference-based theory of consumer behaviour, the alleged methodological advantage of the new theory is questionable. Is Samuelson’s theory a new theory, i.e. does it represent a set of ideas which is different from those embodied in ordinal utility theory?

10. In Samuelson (1950b) we find a third interpretation of the central problem of the new approach. Here, it is to find the full empirical implications of ordinal utility theory, by which is meant the observational equivalent of ordinal utility theory. The third problem is incompatible with the first problem of developing a theory of consumer behaviour which does not rely on the concept of ‘utility’. What is the point of seeking the observational analogue of ordinal utility theory if Samuelson intends to ‘develop the theory of consumer’s behaviour freed from any vestigial traces of the utility concept’ (1938a, p. 71)? If there is a positive solution to the third problem, the logical connection with ordinal utility theory is established rather than severed. Moreover, how can two theories be logically equivalent when one is considered observable while the other is not?

11. Samuelson has not addressed himself to these questions, nor has he realized that there are inconsistencies in his interpretations of his programme. Nevertheless, these inconsistencies are fundamental⁷ and place in doubt the consistency of his research programme.

12. The aim of our study is twofold. First, we shall argue that Samuelson’s contributions to the revealed preference approach do not constitute a consistent programme of research. Second, independently of the question of consistency, we shall argue that the Samuelson Programme is not completed because revealed preference theory does not solve any of Samuelson’s three problems: the problem of deriving the main results of ordinal utility theory without the use of utility or any other non-observational concept; the problem of constructing an individual’s indifference map from observations of market behaviour; or the problem of finding the observational equivalent of ordinal utility theory. This implies that the three major claims made by Samuelson for his new approach cannot be maintained:

1. revealed preference theory is a new theory of consumer behaviour;
2. revealed preference theory is an operational method for the construction of an individual’s indifference map; and
3. revealed preference theory is the observational equivalent of ordinal utility theory.

13. This study may be criticized for its narrow definition of the Samuelson Programme, namely the contributions of Samuelson to the revealed preference approach. Thus, even if the criticisms are correct, the study is of limited theoretical interest because more recent writers, for example Arrow (1959), Afriat (1967) and Richter (1966), have proposed satisfactory solutions to the three Samuelson problems. We strongly reject this assessment. As we shall argue in this study, the basic weakness of the programme is inherent to the revealed preference approach. It lies in the conception of the problems themselves. Therefore, the failure of the Samuelson Programme is of fundamental importance to the entire revealed preference approach and not merely of passing historical interest.

14. In comparison with most writings on the subject, Samuelson’s contributions are the most illuminating, and are therefore worthy of careful study if we wish to come to a better appreciation of the entire revealed preference approach. Most writers ignore the interpretative aspects and focus almost exclusively on the mathematical structure of revealed preference theory. For example, the important paper by Uzawa (1960), which formalized the Houthakker result, is couched in formalism with a modicum of explanatory text. Samuelson, by contrast, not only created the theory and set out many of its theoretical propositions but also has given an interpretation of its significance and, moreover, has articulated the methodology which underpins the whole approach.

15. There is also a strategic reason why we focus on one writer. If we consider many different writers’ contributions, there is the possibility that we may misconstrue those of any individual writer. It is therefore prudent to minimize this possibility by concentrating on the works of a single contributor. Therefore, except where stated otherwise, our criticisms of Samuelson do not necessarily apply to any other writer on the subject.

16. The Samuelson Programme has not been the subject of an interpretative study. Yet, its importance as a research programme cannot be denied. It lies not only in its continuing influence on research in the theory of consumer behaviour, but, more importantly, in its heuristic value for economics as a whole.

17. The birth of revealed preference theory is an event of great significance in the history of the theory of consumer behaviour. In the words of Arrow (1959, p. 121), it is ‘the first distinctly novel approach’ in the theory of consumer behaviour, long accustomed to the explanation of consumer choice in terms of preferences. With his new theory, Samuelson appears to attain the goal which eluded many economists in the past: namely, to sever the theory of consumer behaviour from the disciplines of philosophy and psychology, freeing the theory from the attendant controversies in which it has been enmeshed almost from its inception as a separate area of study.⁸

18. One of the first economists who expressed misgivings about the logical connection between economics and hedonistic psychology was Irving Fisher, who considered it an unnecessary source of controversy in economics.⁹ To serve as the demarcation line between the two disciplines, Fisher (1892, p. 5) proposed the ‘psychoeconomic’ postulate: ‘Each individual acts as he desires.’ This strategy failed, because, as Sweezy (1934, p. 179) observed, it turns the interpretation of choice into a circular explanation, asserting that ‘each individual acts as he acts’.

19. Another economist who tried to separate economics from psychology was Gustav Cassel (1918). Unlike Fisher he objected to the presence of psychological assumptions in economic theory, because, in his opinion, psychological phenomena do not fall under the purview of economics proper. While he considered the relation between psychology and economics to be worthy of further study, he did insist that in the explanation of prices only assumptions about demand functions are necessary as far as the demand side was concerned. This point of view never found a receptive audience,¹⁰ despite Herman Wold’s observation (1951; 1953, p. 63 and p. 329, n. 5) that the revealed preference approach is the modern legacy of Cassel’s approach.¹¹ Samuelson, the originator of the revealed preference approach, certainly does not regard Cassel as his pre-cursor. Instead, Cassel’s approach earned the following comment from Samuelson: ‘Cassel…rejected utility in favor of demand functions and nothing else, but was never fully aware of what he was thereby assuming or denying about empirical reality’ (1950b, p. 366, n. 1) (see also Houthakker, 1961, p. 706).

20. Although the Samuelson Programme is considered completed with the Houthakker proof, it continues to exert considerable influence on the nature and direction of research in the theory of consumer behaviour. First, the revealed preference theory is now an established part of economic theory. Second, taking the Houthakker result as the point of departure, specialists have undertaken a systematic exploration of the logical relations between preference orderings and demand or choice functions under alternative formulations of ordinal utility theory and revealed preference theory. For example, Chipman et al. (1971) devoted an entire symposium to this line of enquiry, a line which was initiated by Uzawa (1960).

21. Outside the theory of consumer behaviour, the major impact of the Samuelson Programme is on methodology. Here, it enjoys a wider and, perhaps, more lasting influence in economics. The success of the Samuelson Programme has been attributed by Houthakker (1961) and by Samuelson (1963) himself to an underlying methodology which requires a scientific theory to be expressed solely in observational terms, devoid of philosophical elements. The importance of Samuelson’s methodology is indisputable. A vast majority of economists have adopted Samuelson’s methodology to the point of regarding it as the scientific methodology appropriate to economics. This is borne out by the fact that in awarding Samuelson the Nobel Memorial Prize in Economics for 1970 the Swedish Royal Academy of Sciences cited him thus:¹² ‘By his many contributions, Samuelson has done more than any other contemporary economist to raise the level of scientific analysis in economic theory.’

22. It is clear that our study depends fundamentally on the accuracy of our understanding of the Samuelson Programme and of its individual contributions. Accordingly, in chapter 2 we present and discuss in detail a method of understanding theoretical work. This method, which is known as ‘situational analysis’ or the method of ‘rational reconstruction’, regards a theory as a solution to a problem. To understand a theory is to conjecture the problem to which it is a tentative solution and to explain why the solution may be considered satisfactory, or otherwise significant, to the theorist. We propose to use this method throughout this study.

23. In chapter 3 we present an interpretation, along the lines of rational reconstruction, of John Hicks and R.G.D.Allen’s formulation of ordinal utility theory. Its purpose is threefold. It sets up the background to which the Samuelson Programme must be compared, since Samuelson first proposed his theory as a replacement for ordinal utility theory. Second, it serves to illustrate our method of study. Third, it draws attention to a number of difficulties in the Hicks-Allen theory which warrant further investigation.

24. The core of our study is to be found in chapters 4, 5 and 6. Because we are evaluating the consistency of the various contributions to the Samuelson Programme, the problem of understanding the Samuelson Programme is partitioned into three problems. In chapter 4 we tackle the problem of understanding revealed preference theory as presented in Samuelson (1938a). In chapter 5 we examine the problem of understanding revealed preference theory as presented in Samuelson (1948). Finally, in chapter 6 we consider the problem of understanding revealed preference theory as presented in Samuelson (1950b). As a solution to each problem of understanding, we shall propose a rational reconstruction of the problem-situation of Samuelson. In addition, we shall criticize each (reconstructed) problem-situation from within and without.

25. Chapter 7 summarizes the results of our study. We conclude with a rational reconstruction of our study, outlining a procedure by which our criticisms of the Samuelson Programme may be criticized in turn. This should be seen as a demonstration of the power and fruitfulness of the method of rational reconstruction in the study of theoretical work.

Chapter 2

Understanding and criticism

2.1 Introduction

1. Any criticism of a theory (or of a theoretical work, in general) is founded on an understanding of the theory. Because the validity of the criticism is to a large extent dependent on the correctness of that understanding, there is merit in making explicit the understanding upon which the criticism is to be constructed. This explicitness aids the task of criticism in two important ways. Where the criticism is valid, the critic can point out directly which parts of the theory are affected, which parts are left untouched, and, consequently, which parts should be replaced. Where the criticism is invalid, the critic or others can identify more easily the sources of the misunderstanding(s) that led to the invalidation of the criticism.

2. Our study of the Samuelson Programme is based upon solutions to two general problems: the problem of understanding any particular theory; and the problem of criticizing it. It is the purpose of this chapter to present our solutions to these problems. These solutions will then be applied to subsequent chapters concerning the investigation of the Samuelson Programme.

3. Our solution to the problem of understanding a theory emphasizes, above everything else, the objectives that the theorist, qua theorist, wishes to achieve. In other words a theory is interpreted as a solution to a problem, i.e. the creation of a theory is seen as being goal-directed or as a rational action.¹ We are therefore seeking to understand why the theorist regards his theory as an adequate response to the problem-situation as he sees it. The problem-situation or logical problem-situation comprises the objectives and their logical interrelations. Thus, the problem of understanding a theory becomes a problem of understanding a problem-situation in the context of which the theory was proposed.²

4. The task of understanding a theory is to reconstruct the problemsituation of the theorist as he saw it and to show that, i...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Foreword
• New preface and acknowledgments
• Preface from the original edition
• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7
• Notes
• Bibliography