Introduction and conclusions

Questions

During our association with universities in Europe and in the United States, we have encountered many questions apt to challenge economists, for instance:

1. Should prices charged in university hospitals reflect (marginal) costs alone, or include a monopolistic markup?

2. Should faculty salaries be determined by a standard scale, or vary with the alternative opportunities of faculty members? (For instance, should the respective salaries of a medical doctor and of a biologist, doing similar work in a research laboratory, reflect the higher opportunity cost of the medical doctor?)

3. How should a university allocate its resources among alternative uses, like education and research?

4. Should universities enjoying an endowment fund aim at spending income and maintaining capital, or at accumulating part of the income, or at depleting the fund at some optimal rate?

5. What rate of discount should be used by a university for decisions about plant and equipment?

6. What should be the attitude of a university toward portfolio risk? Should universities adopt less conservative investment policies than, say, managers of private trust funds? (This was once intimated by officers of a Foundation Oriented toward Research and Development; that foundation has recently reduced its spending, due to a sharp decline in market value of endowment.)

All these questions arise because universities operate under a budget constraint, the level of which is not always set optimally; produce public goods (research); and are sometimes required to sell services below cost (education in state universities).

Introduction

In this paper, we consider an industry supplying a single commodity, the demand for which is uncertain or shifting in time. We show that several standard propositions in the static theory of the firm no longer apply in that context. Consequently, a widely accepted inference about the nature of competition in such an industry becomes unwarranted under our more realistic assumptions.

Section 2 restates the propositions that are challenged later on. A simplified model is introduced in Section 3. Section 4 is devoted to counterparts, for that model, of the propositions listed in Section 2. Four methodological conclusions are presented in Section 6. The appendix collects some properties of the cost function used in the simplified model.

Some propositions from the static theory

Let us consider an industry operating under the following assumptions:

1. a. it produces a single commodity;

2. b. all firms are identical;

3. c. cost for each firm is a function of quantity alone; the total and variable average cost curves of those firms are U-shaped, continuously differentiable, and independent of the number of firms in the industry;

4. d. there is no restriction to entry, and the number of firms is not required to be an integer;

5. e. the quantity demanded at each price is fixed for the industry, independently of the number of firms; the demand function is continuous.

Public projects increasing safety, or entailing risks of human deaths, have inescapably raised the question: ‘How much should a society spend for the safety of its members?’; alternatively stated: ‘What is the social value of a human life?’ Answers provided by economists, public administrators and other scientists have come to be classified under two headings: The ‘human capital’ approach and the ‘willingness-to-pay’ approach. Broadly speaking, the first approach seeks an objective measure of the value of a person's life in his or her earning ability, whereas the second approach takes as its starting point the person's subjective tastes. Some of the literature is directed towards relating the two approaches and in particular towards formulating assumptions under which a person's human capital provides a lower bound to the value placed by that person on his/her life.

It seems to be now generally recognised that ‘willingness-to-pay’ is the logical approach to assessing the benefits of public safety. The approach becomes operational when coupled with the modern theory of public expenditure, initiated by Samuelson (1954). Yet, the methodological foundations of the subjective approach – state-dependent preferences – do not seem to be universally understood, leaving room for occasional doubt or error. This chapter starts (Section 1) with a review of these foundations, which involve preferences revealed through gambling, insurance and life protection. The economics of individual demand for insurance and safety are the subjects of Sections 2 and 3 respectively. The ‘public goods’ aspect is taken up briefly in Section 4.

Labour management

One hundred years ago, the first edition of the Eléments d'Economie Politique Pure by Léon Walras was half-way through printing. This anniversary provides special justification for the presentation of a Walras lecture at our congress. It also places a special burden on the author of the lecture to rationalise the choice of his pet-subject through appropriate references to the life and works of Walras. I will in due course provide such rationalisation for my topic, which is the pure theory of labour management and participatory economies.

This topic currently arouses a great deal of interest – at various levels. For some, labour management, or self-management, is a global project of political, social and economic organisation. For others, it is a form of organisation that meets a basic human aspiration and should be fostered wherever possible, through modest as well as ambitious projects. For our purpose here, a labour-managed economy is an economy where production is carried out in firms organised by workers who get together and form collectives or partnerships. These firms hire non-labour inputs, including capital, and sell outputs, under the assumed objective of maximising the welfare of the members, for which a simple proxy is sometimes found in the return (value added) per worker. The capital can be either publicly or privately owned. To permit easier comparison, I will base this presentation on private ownership.

Introduction and summary

The purpose of this chapter is to point out that uncertainty about the price elasticity of demand has an effect comparable to that of a kink in the demand curve, for a risk-averse firm; the kink being located at the prevailing price and quantity. The reason for this effect, namely estimation uncertainty, is entirely distinct from the standard reason invoked in the literature on kinky demand curves, since Sweezy (1939), namely asymmetrical reactions of competitors. Thus symmetrical, but imperfectly known, reactions would produce asymmetrical effects. And asymmetrical, but imperfectly known, reactions would produce doubly asymmetrical effects – the asymmetry generated by uncertainty being compounded with that generated by the reactions themselves.

The effect of uncertainty in the context considered here is analogous to the effect of uncertainty about rates of return on savings decisions by consumers. Variance of rates of return affects these decisions in the same way as adverse changes in expected returns – see Drèze and Modigliani (1972) or Sandmo (1974). Thus, uncertainty about rates of return has an effect comparable to that of a kink in the budget line constraining present and future consumption; the kink being located at the endowment point. (The reason for that kink is again distinct from the standard reason, namely a difference between lending and borrowing rates; both asymmetries must again be compounded.)

This chapter briefly summarizes the welfare implications of Walrasian competitive equilibrium. It complements Chapter 3 by highlighting the particular economic assumptions that render the welfare theorems nonvacuous. (A theorem is vacuous if the conditions of its hypothesis cannot be met. For example, if we prove that an equilibrium is Pareto optimal, we have to show that an equilibrium exists for the result to be nonvacuous.) To simplify the exposition, attention will be confined to pure exchange private goods economies. An allocation x specifies a bundle xi of private goods for each household i = 1, 2, …, n. As usual, p denotes a price vector and wi is i's endowment vector.

We begin by recalling some basic definitions. A utility function ui for individual i is self-regarding if it is independent of the consumption of other individuals. It is implicit throughout this chapter that utility functions are self-regarding and that markets are complete: Every good that affects someone's utility is traded in some market. An allocation is Pareto optimal if it is feasible and there is no feasible allocation that would make everyone better off. A feasible allocation is strongly Pareto optimal if there is no other feasible allocation that would make at least one person better off and leave no one worse off. It will usually be implicit that conditions are such that the two definitions are equivalent.

This chapter is concerned exclusively with individual choice. Let X be the universal set of alternatives. We wish to represent the individual's preferences in such a way that his choice from a subset B of X can be obtained from that representation. We begin with choice over two-element sets and build from there.

Definition: A binary relation Q on X is a subset of X × X. If (x, y) belongs to Q, we write xQy, Relation Q is complete if, for all x, y ∈ X, either xQy or yQx holds; Q is transitive if, for all x, y, z ∈ X, xQy and yQz imply xQz. A complete and transitive binary relation is called a weak order and is represented by the letter R.

Since R is complete, we have xRx (set y = x). Since x cannot be strictly preferred to itself, the statement xRy must mean that x is at least as desirable as y: It may be that x is equally desirable as y as in the case y = x, or that x is strictly preferred to y. We can be sure that y is not strictly preferred to x if xRy holds.

If x belongs to B and xRy for all y ∈ B, then x belongs to the set of best (or most-preferred) elements in B. A weak order allows us to determine choice on any finite set from choice on two-element sets.

The two-person, two-commodity exchange economy provides a remarkable amount of insight into resource allocation in general and the market mechanism in particular. Accordingly, assume that production has already taken place and that all net output is owned by households. Each household wishes to exchange goods that it holds in abundance for the goods it lacks.

There are two commodities and two consumers. An allocation x = (x1, x2) assigns a nonnegative commodity bundle xi = (xi1, xi2) to each individual i = 1, 2. Individual i's preference relation is assumed to be strongly monotonic and strictly convex and representable by a continuous and differentiate utility function ui(xi) with positive marginal utilities everywhere (i= 1, 2). These assumptions will be implicit in the hypotheses of both of the theorems to follow.

Household i (i = 1, 2) has an endowment vector wi = (wi2, wi2), and w1 + w2 specifies the total stock of each of the two goods available to the community. Allocation,x is feasible if x ≥ 0 and x1 + x2 ≥ w1 + w2. An allocation x ≥ 0 is balanced if x1 + x2 = w1 + w2. Allocation x is Pareto optimal if it is feasible and there is no feasible allocation y such that u1(y1) > u1(x1) and u2(y2) > u2(x2).

The existence theorem proved in Shafer and Sonnenschein (1975) relies on a weaker convexity assumption than condition (6.8), namely, quasi-convexity: Pa is quasiconvex if for all m ∈ M the convex hull of Pa(m) does not contain ma. (A convex combination of members of a set A is any weighted average of a finite number of points in A such that the weights are nonnegative and sum to unity. The convex hull of A, denoted CH(A), is the set of all convex combinations of members of A.) Note that quasicon vexity is implied by conditions (6.8) and (6.9).

Theorem A.7. Suppose that M is a nonempty, convex, closed, and bounded subset of some finite-dimensional Euclidean space [conditions (6.3) and (6.4)]. If, for each a = 1, 2, …, N, Pais quasiconvex and has an open graph [condition (6.7)] and Ba is a continuous [condition (6.5)] and convex-valued [condition (6.6)] correspondence, then there exists some m ∈ M such that ma ∈ Ba(m) and Ba(m) ∩ Pa(m) = ∅, a = 1, 2, …, N.

Proof: For any agent a and any let

The set is closed since Pa has an open graph. Therefore, Ua is well defined. Also, is nonnegative and strictly positive if and only if.

Under ideal conditions an equilibrium of the Walrasian model of a private ownership market economy is Pareto optimal. The fact that these ideal conditions are not met without qualification in the real world does not vitiate the Walrasian approach to welfare economics, if only because Walrasian competitive equilibrium can be viewed as a standard to which policy-makers can aspire. The results of this book would be of little value, however, if it turned out that an equilibrium rarely exists. This chapter examines the conditions under which existence of equilibrium is assured.

Competitive behavior is assumed throughout. Other notions of equilibrium are more plausible in certain situations, but competitive behavior is important enough for a study of competitive equilibrium to constitute a useful introduction to the subject of existence of equilibrium. By assuming competitive behavior, we can be more specific about the features of a resource allocation mechanism. Accordingly, attention will be confined to mechanisms that require each agent to transmit a best response to the messages announced by others. A best response is one that would produce the best outcome for the decision-maker if the messages of others were to remain unchanged. If an agent's strategy has this property, his behavior is said to be competitive.

It is often claimed that proofs of existence of equilibrium constitute a mere mathematical flourish and are not worthy of study by anyone whose interest in economics stems from a desire to understand and prescribe for real-world phenomena.

This book is concerned with the general welfare implications of individual decisions in systems in which some sort of coordination of individual activities is essential to the achievement of a high level of overall welfare. What makes this problematic is the determination of each individual to act in a way that enhances his or her personal well-being. Different configurations of individual decisions produce different outcomes, some of which could be improved upon to the extent of making everyone better off and most of which favor some of the individuals more than others. Even though it will be difficult to claim that a system promotes the general welfare when there will always be some individuals who protest, accurately, that another arrangement would have gone further toward satisfying their material wants, there is no ambiguity in the requirement that a test of welfare be based, somehow, on individual assessments of the outcomes.

We begin, therefore, with a desire to determine which outcomes will emerge and whether these will satisfactorily reflect the tastes and values of the individuals participating in the system. In most economic settings there will be a large number of possible outcomes. It will be assumed at the outset that of all the outcomes that are likely to emerge, only the equilibrium outcomes are worthy of attention. In an abstract model of an economy an equilibrium is a state in which all forces are in balance and there is no tendency to change: No agent wishes to revise his decision having observed this state and, because the decisions do not change, the original outcome is maintained.

A utility function that is sensitive only to the private goods consumption of the agent in question will be termed self-regarding. A firm's technology set is self-regarding if it does not depend on the activities of other agents. We will show that a Walrasian competitive equilibrium allocation is Pareto optimal as long as household utilities and firm technologies are self-regarding and each commodity that affects someone's utility is traded in some market. Section 3.9 demonstrates that self-regarding preferences and technologies are not really required for Pareto optimality, but the assumption of competitive behavior loses its plausibility without it.

Ead will denote the largest family of environments for which all utility functions and technology sets are self-regarding. Section 3.4 proves that a Walrasian competitive equilibrium allocation is Pareto optimal if the environment belongs to Ead. There are many members of Ead for which an equilibrium does not exist, however; this issue is taken up in Chapter 6, which shows that there is a very wide class E* of environments overlapping Ead for which equilibria exist. Therefore, the result of Section 3.4 is not vacuous. Section 3.6 will show that for every economy e in E* ∩ Ead and any Pareto-optimal allocation f of e there is an economy e′ in E* ∩ Ead that is the same as e except with respect to endowments and profit shares and such that f is a Walrasian competitive equilibrium allocation for e′ An other words, e′ is obtained from e by redistributing wealth.

This book was inspired by my economic theory lectures to first-year Ph.D. students at the University of Toronto. The point d'appui is that any economic system or mechanism is essentially a communication process. Each agent transmits messages to which other agents respond as self-interest dictates. A successful mechanism must harness this self-interest so that each agent, without necessarily understanding the overall process, is induced to cooperate in the determination of a satisfactory (or optimal) menu of goods and services. Adam Smith, of course, is the founder of this approach to the study of economics. This book employs the formal, and abstract, general equilibrium model of resource allocation pioneered by the nineteenth-century economist Léon Walras. Its modern formulation was developed over the last three decades, particularly by Professors K. J. Arrow, G. Debreu, L. Hurwicz, and R. Radner.

Our “mechanism design” approach to economic theory begins with the tacit supposition that the author and the reader have met to design a resource allocation mechanism that will deliver a satisfactory menu of goods and services. Nothing is taken for granted and the designers are not necessarily committed to the existing institutions. As a result, any theorem that does point to a particular system, say, to the private ownership market economy, will have that much more cogency.

The mechanism approach brings into prominence the issue of the criteria by which the performance of an economic system is to be judged, particularly those criteria relating to the interplay between individual incentives and individual messages.

Uncertainty affects individual welfare in a variety of ways. This chapter deals with one of the most important consequences of the vicissitudes of nature, the randomness of initial endowments and of the input–output relationship in production. A career choice, for example, is a decision to acquire certain skills that become part of one's endowment and that can be more or less rewarding depending on occurrences that are random from the standpoint of the individual decision-maker. Bad weather can affect crops, and a farmer will not know with certainty the size of the harvest even though he or she knows how much seed was planted. Fire and flood can destroy homes. The first and last examples are consistent with a change in a person's preferences for commodities. However, we will simplify by supposing that individual preferences do not change as random events are realized even though a serious injury, say, can cause a change in preference because it affects one's ability to participate in some activities. Subject to this simplifying assumption, the Arrow–Debreu interpretation of the market mechanism is easily extended to accommodate uncertainty. All that is required is a reinterpretation of the notion of a commodity. Just as we distinguish an automobile delivered at one date from the same physical object at another date, insisting that they be identified as two different goods, so we also distinguish between an automobile delivered at one date when one specific random event is realized and the same automobile available at the same date under a different realization.

This chapter presents three important results on the possibility of designing a resource allocation mechanism that gives each agent the incentive to follow the rules in every situation.

The proof that a Walrasian competitive equilibrium is Pareto optimal does not assume a large number of agents. It does assume that agents take prices as given. Section 5.1 shows that this assumption is suspect: Any mechanism that improves the well-being of each agent and yields Pareto-optimal outcomes can be manipulated. Someone, in some situation, will have an incentive to violate the rules governing the behavior of agents. Section 5.2 proves that any gain from a violation of the rules of the Walrasian mechanism will be miniscule if each commodity has a large number of suppliers. Therefore, it will not be worth anyone's while departing from prescribed behavior in that case. The last section shows that manipulation – a rule violation that cannot be detected – is inevitable in mechanisms that determine the Pareto-optimal supply of a public good and, unlike the case of the Walrasian mechanism, the difficulties do not fade as the number of agents increase, whatever mechanism is used.

The phenomenon on which to focus attention is the ability of an agent to influence prices by taking into consideration the effects of his decision on demand or supply. The most easily understood instance is that of a monopoly. The monopoly will optimize by producing at the point where marginal revenue equals marginal cost.