Restrictions on preferences • The theory of market demand

We have already discussed, in Chapter 4, the straightforward extension of the neoclassical utility maximizing model to problems involving choice over consumption in different time periods. In this chapter, we extend the analysis in several directions. Section 12.1 considers various aspects of intertemporal planning, especially in the context of the individual's life cycle. First, the model is extended to allow simultaneous choice of consumption and labor supply, and we discuss how, given freedom of choice, we might expect consumers to vary their work and consumption levels in response to variations over the life cycle in prices and wages. We then turn to the more conventional case of constrained labor supply as discussed in Chapter 4, and illustrate the derivation of the consumption function with a model based on the AIDS of Chapter 3. The relationship between the consumption function and systems of demand equations is also briefly considered. Liquidity constraints in the form of borrowing restrictions or different rates of interest on borrowing and lending are then discussed, and their influence in raising the marginal propensity to consume is emphasized. Finally, we discuss the implications of the analysis for the relationship between the aggregates of consumption, income, and wealth. Section 12.2 considers the dynamics of the link between income and consumption, not only within the full intertemporal model but also taking into account other explanations and the econometric evidence. Section 12.3 is concerned with questions of imperfect information.

The preceding two chapters have been concerned with the analysis and measurement of the welfare of individual households. We now turn to questions of the welfare of society as a whole. The two topics which make up the title of this chapter are both major fields of economic investigation in their own right, and we cannot hope to give more than an outline of them here. Indeed, we are more concerned with illustrating one of the major themes of the book, that consumer theory as we have presented it is of great analytical value in other branches of economics. Social welfare functions have obvious conceptual links with individual utility functions and we shall explore these ideas in §9.1. We shall use our previous analysis to discuss possible structures for social welfare functions, and we shall argue that the index number concepts discussed in Chapters 7 and 8 can be used to provide natural units for making interpersonal comparisons of welfare. Section 9.2 is concerned with the measurement of inequality. The approach described is based on an explicit link with social welfare, pioneered by Kolm (1969, 1976) and Atkinson (1970), and we show how the analysis of §9.1 can be used to adapt the conventional measurement of income inequality to the more fundamental purpose of measuring welfare inequality.

Social welfare functions and their arguments

The social welfare function is an essential tool of welfare analysis and this section is concerned with its development and its properties. It will be used in §9.2 in specific practical contexts.

Consumer behavior is frequently presented in terms of preferences, on the one hand, and possibilities on the other. The emphasis in the discussion is commonly placed on preferences, on the axioms of choice, on utility functions and their properties. The specification of which choices are actually available is given a secondary place and, frequently, only very simple possibilities are considered. In this book, we shall have a great deal to say about preferences, and discussion of them begins in Chapter 2. We begin, however, with the limits to choice rather than with the choices themselves. Unlike preferences, the opportunities for choice are often directly observable so that, to the extent that variations in behavior can be traced to variations in opportunities, we have a straightforward and objective explanation of observed phenomena. It is our view that much can be so explained and that the part played by preferences in determining behavior tends to be overestimated. Hence, this first chapter considers what can be said about behavior without detailed consideration, of how choices are made. A large part of this book, from Chapters 2 to 9, works with one very special assumption about the opportunity set, namely that choices are constrained by fixed, known prices in such a way that the total value of the objects chosen should not exceed some predetermined total. In this case, we say that the consumer faces a linear budget constraint.

No part of economics is more contentious and more interconnected with the rest of the subject than is labor economics. We shall here attempt to separate the analysis of labor supply from labor economics as a whole, but it is inevitable that, to some extent, we shall be drawn into wider issues. One aspect of the contentiousness of the subject is the range of different approaches to it, from the institutionalists, on the one hand, to those who apply a narrow version of the neoclassical paradigm, on the other. Our approach is analytical, but we think not narrow and, as throughout the book, our aim is to formulate models relevant for good empirical work.

The chapter is divided into three sections. The first extends Chapter 4's discussion of the basic neoclassical model of labor supply to deal with the case where the individual chooses not to work at all. The choice between working and not working is referred to as the participation decision, and in §11.1, we show how it can be analyzed in terms of the divergence between the actual and an appropriately defined “shadow” wage rate. We also discuss the implications of this theoretical analysis for econometric studies of participation rates and of the labor supply of those who do work. Section 11.2 considers the effects of abandoning the linear budget constraint of the neoclassical model and takes a more realistic view of the constraints faced by households.

One of the most important developments in recent applied economics has been the increased availability of data on large samples of individual households, particularly in the United States. Although the analysis of such data poses formidable problems of its own, it is possible, at least in principle, to apply the microeconomic theory of the preceding chapters. If, however, as is frequently the case, the data are available only for aggregates of households, there are no obvious grounds why the theory, formulated for individual households, should be directly applicable. The transition from the microeconomics of consumer behavior to the analysis of market demand is frequently referred to as the “aggregation problem.” Aggregation is seen as a nuisance, a temporary obstacle lying in the way of a straightforward application of the theory to the data. In this view, the role of aggregation theory is to provide the necessary conditions under which it is possible to treat aggregate consumer behavior as if it were the outcome of the decisions of a single maximizing consumer; this case we shall refer to as that of exact aggregation. These aggregation conditions often turn out to be stringent, which has tempted many economists to sweep the whole problem under the carpet or to dismiss it as of no importance. Some economists, indeed, see for example Hicks (1956), have held the view that microeconomic theory has greater relevance for aggregate data, arguing on largely intuitive grounds that the variations in circumstances of individual households average out to negligible proportions in aggregate, leaving only the systematic effects of variations in prices and budgets.

In Chapter 1, we suggested that the end result of the study of the microfoundations of macroeconomics would look different to different kinds of economists. The objectives of a microeconomist might be met by presenting a reasonably detailed structure in which various well-understood market failures would lie at the heart of macroeconomic conundrums like inflation and unemployment. To a macroeconomist, a successful reconciliation of micro and macro might entail a return to Marshallian price theory, or a well worked out statement of individual behavior in a non-optimizing framework. To a historian of thought, it would be a reasonable sort of endeavor if it could explain how the neo-Walrasian and Keynesian research programs grew, grew apart, and what features of each made them appear incompatible.

After our efforts in Part II, however, matters become somewhat clearer. Stripping the idea of general equlibrium theory down to models of interrelated and systemic interaction, there is almost an embarrassment of riches in the sense that it is no longer the case that a general equilibrium framework itself determines uniquely the kind of macroeconomics one can do. Gone are the days when general equilibrium theory required only numeraire money, no production, fulfilled expectations, Walras' Law, tatonnement price adjustments, reversible time, futures markets for all commodities, an equilibrium defined by market clearing, etc. To argue that general equilibrium theory provides no theory of unemployment because the theory assumes Walras' Law may have been a useful way to indulge oneself in the late 1930s, but it is irrelevant to general equilibrium theory today.

It may be useful to recall the outlines of the Arrow–Debreu–McKenzie general equilibrium model, since this can be regarded as the starting point for subsequent work.

1. (1) There is a class of agents, called consumers, who have preferences over different bundles of final goods.

2. (2) The consumer preferences are sufficiently regular so that preferences can be represented by utility indicators.

3. (3) Consumers' income comes from sale of factor services and distributed profits of firms.

4. (4) Members of another class of agents, called firms, have preferences over output configurations, which lead to profits.

5. (5) Consumers, taking product and factor prices as given, attempt to maximize utility subject to their income constraint.

6. (6) Firms, taking product and factor prices as given, attempt to maximize profits subject to a technology constraint.

Under a variety of economic restrictions it can be shown that there exists a set of factor prices and product prices such that, if consumers and firms were to simultaneously optimize at those prices, the output and purchase of goods that would result entails those same prices. That is, there exists a set of prices (a competitive equilibrium) that could logically reconcile the potentially conflicting choices of all the economic agents. (The allocation of goods that corresponds to the competitive equilibrium is called the competitive allocation.)

This basic construction is far from concerns about speculative demands for money, real versus nominal interest rates, and flexible versus naive accelerators.

It is always difficult to appraise current research in an area, especially in a technical area, for a non-specialist. Recent work on problems associated with the microfoundations of macroeconomics present severe difficulties since the literature is intrinsically integrative, albeit abstract. The particular set of abstractions, or models, have their roots in the separate concerns of microeconomists, general equilibrium theorists, macroeconomists, and monetary theorists and as such cannot be fully appreciated without a sense of how these areas have developed and interacted up to the present time.

In a discipline like economics, where progress can be identified with sequences of models each successively better suited to the current issues, but each always developing from a predecessor, an understanding of what is “modern” requires too an understanding of what is no longer “modern.”

The basic structure of Part I represents what must be an imperfect attempt to trace the development and interlocking nature of two scientific research programs (in the sense of Lakatos), macroeconomic theory and (general equilibrium) neo-Walrasian theory. Since much that is currently being done in the various microfoundations literatures can be identified as the symbiosis of these two programs, their separate developments should be part of the mental baggage of modern economists.

In Chapter 1, then, a case is built that the set of problems being considered ramifies in a multitude of ways into the daily thinking of professional economists who believe themselves quite free of, and apart from, the arcane concerns of mathematical economists.

The precursors: equilibrium

Although Cournot's insight remained largely unexplored until Walras, the modern developments of the theory probably proceed from Gustav Cassel. In his Theory of the Social Economy he set out in a tractable form a simplified Walrasian system and noted that “the pricing problem is essentially a single problem extending over the whole of the exchange economy and [this fact] gives the pricing prices process an intrinsic consistency which can only be expressed by a system of simultaneous equations” [Cassell, 1932, p. 148].

The analysis was straightforward even by modern standards although the mathematics was used more to achieve expositional clarity than to uncover new features of the system. It was as if economists had to agree on the modelling procedures, the structure of the problem, before mathematical analysis could be utilized.

There is an analogue, for Edgeworth models, to disequilibrium analysis in Walrasian models. Instead of examining the market price adjustment mechanism, one could examine the patterns of exchange that individual traders create and face when required to complete transactions out of equilibrium. If the Walrasian framework is a model of how the institutions of a competitive market serve to organize and stabilize economic activity, then the Edgeworth system, which abstracts from the price mechanism, may appear as neoinstitutionalism.

There are two distinct themes to this literature: (1) problems of coordination, of resource allocation proper, in systems without competitive markets or (2) problems of monetary theory, like the role of money in a dynamic exchange setting.

In this chapter we will examine how disequilibrium trading models can generate systemic coordination successes and failures. This family of models has something to contribute to the microfoundations of macroeconomics literature. It is possible to design institutional arrangements for the conduct of disequilibrium activity in such a way that, under one set of arrangements, trading activity leads to coherent outcomes, but under alternative structures, coordination failures abound. We can formalize the role of the medium of exchange money as a systemic coordinator and identify its place among alternative transactions facilitators.

Before we proceed, however, we must note one terminological muddle. In many surveys and discussions, “Edgeworth process” refers to a disequilibrium adjustment mechanism which utilizes a variant of the tatonnement in which there are two state variables, prices and individual stocks of commodities.

J. R. Hicks' Value and Capital, published in 1939, is rightly considered a classic in economics for its rigorous treatment of household and firm behavior under competitive conditions. What is less frequently appreciated today is that it was an attempt to lay the conceptual groundwork for macroeconomics in a well specified Walrasian system.

The structure of Value and Capital itself reflects Hicks' absorption with microfoundations topics. Initial chapters present the theory of consumer behavior and general equilibrium of exchange.

The relationship between microeconomic theory and macroeconomic theory has been stormy. The subject has been ignored, discovered, settled and ignored again. The literature is replete with polemics, calls to action, and technical preciousness which obscure the central ideas. Consequently this book is a survey organized around the question “Are the concerns and models of microeconomic theory logically consistent with the concerns and models of macroeconomic theory?”

My biases should be recognized. I consider economic theory to be a scientific discipline. I believe that our knowledge is more secure if our insights can be developed in terms of formal models. I believe that progress occurs in terms of sequences of models which have assumptions that are clear and conclusions that are falsifiable either by empirical tests or by tests of congruence with other theoretical constructs.

Having been trained as a mathematician, I am less impressed with mathematical virtuosity than some economists. However that same training leaves me suspicious of analyses that begin with an ideologically “correct” view and end with conclusions which support that view.

My own approach to microfoundations issues can be summed up by Axel Leijonhufvud's observation, noted in Chapter 5, that

In this part attention will be directed to the various ways in which general equilibrium theory has been, and is being, modified to provide a conceptual base for the formulation of macroeconomic concerns.

Two major approaches can be identified: the first focuses on interdependent optimization by the various agents, the second is more concerned with the mechanisms for exchange or transactions. Abusing both language and history a bit, the former will be termed (neo-)Walrasian analysis, the latter (neo-)Edgeworthian. A further bifurcation will be between equilibrium theory and disequilibrium theory, or whether the analysis is directed to the possibility of pre-reconciled choice or the attainment of terminal states in real time.

There are thus four “pigeonholes” in which to place recent and current work. The taxonomy consists of Walrasian equilibrium (Chapter 6), Walrasian disequilibrium (Chapter 7), Edgeworthian equilibrium (Chapter 8), and Edgeworthian disequilibrium (Chapter 9).