Introduction

Consider a group of individuals characterized by the coexistence of the potential benefit of cooperation within the group, and the conflict with respect to the way the fruit thereof is to be distributed among members. In order that this group may form a cooperative society that is organizationally stable as a voluntary association of free individuals, a prior and binding agreement on the rule for resolving such distributional conflicts as may arise among them in the future seems to be definitely needed. An important and distinctive feature of this problem of rule design is that individuals do not, and indeed cannot, necessarily foresee the issues that may possibly be in dispute, nor do they have full information as to the natural abilities and other personal characteristics of each other. The purpose of this chapter is to consider the problem of rule design paying due attention to this informational constraint.

Introduction

Economists, particularly economic theorists, are most often concerned with the analysis of positions of equilibrium. This is most obviously true in microeconomics, where general equilibrium theory stands as the most complex achievement of rigorous analysis; but it is becoming true of macroeconomics as well, where it has become increasingly popular in rational expectations models to assume that markets always clear.

Less attention is given to disequilibrium. In microeconomics, the subject of the stability of general equilibrium is in poor repute. Too many economists (including economic theorists, who should know better) apparently believe that stability theory means tâtonnement - a branch of the subject that died in 1960 and was long ago superseded.1 They regard it as overformal and empty of results, save under the most extreme ad hoc restrictions, and without much relation to the rich and complex world of real economies.

For macrotheorists the concentration on equilibrium manifests itself in other ways. Aside from the rational-expectations-market-clearing position already mentioned, one currently fashionable branch of the subject investigates fixed-price, quantity-constrained equilibria. Such investigations can be very fruitful, but they are not truly disequilibrium investigations, although they are sometimes misnamed as such. They are analyses of equilibria that are non-Walrasian.

Introduction

Some libertarians in the tradition of Locke, Mill, and de Tocqueville would claim that there ought to exist in human life a certain minimum sphere of personal liberty that should not be interfered with by anybody other than the person in question. The question where exactly to draw the boundary between the sphere of personal liberty and that of collective authority is a matter of great dispute, and, indeed, what a libertarian might claim is not unequivocal in the first place. Nevertheless, a claim for the inviolability of a minimum extent of individual libertarian rights seems to be deeply rooted in our social and political ideals.

Granting the existence of a minimum sphere of personal liberty, can we design an otherwise democratic collective choice rule in such a way that each person is empowered to decide what should be socially chosen, no matter what others may claim, in choices over states that specifically concern him?

Walras’ Law

I now move closer to modeling the interaction of agents, building on the theory of the individual agent set forth in the previous two chapters. I begin with a consideration of Walras' Law. Certainly, one expects to find some version of Walras' Law holding for this economy, and, indeed, some version does hold; however, there are some points of special interest as to just what that version is.

Walras' Law in its usual form states that the total value of all excess demands is zero. Here, the excess demands involved will be those for commodities (including bonds), shares, and money. But it is not so clear precisely how the result will turn out. To begin with, demands in this model are distinguished by the dates at which agents expect to exercise them; they are not static. Will Walras' Law hold as a statement about the demands planned for any future moment or only as a statement about the value of all future plans? In fact, the result applies to either case; this is because agents expect at every instant to exchange commodities or shares for money of equal value.

Second, Walras' Law requires that we value all excess demands. In more primitive models, this is straightforward. Such valuation simply uses the common prices. In the present model, however, individuals can have different prices for the same commodity. Even without the individual price offers considered in the preceding chapter, this is true of the prices which agents expect. Not surprisingly, therefore, Walras' Law requires us to value each agent's excess demands at the prices at which that agent personally expects to (or actually does) act on them.

This investigation has come some distance from its origins in the traditional stability literature. Unfortunately, there is still a long way for further research to go before we have a sound foundation for equilibrium economics. I now review some of the road traveled and then consider the nature of the road ahead.

We now know that, under very general circumstances, in a world of rational agents who perceive and act upon a nonexpanding set of arbitrage opportunities cast up by disequilibrium, the economy will be driven to equilibrium as such opportunities disappear. This will occur if new opportunities in a wide sense do not continue to appear or to be perceived to appear. In fact, stability is achieved even with new opportunities, provided that such new opportunities do not appear as favorable surprises, seized by agents as optima the moment they appear. This result - while not nearly as helpful as would be a parallel result as to the effects of the nonappearance of new exogenous opportunities - is nevertheless a basic waystation. It holds both for competitive economies and for some economies including monopoly or monopolistically competitive elements.

This general (if weak) stability result is free of many of the problems which flawed the earlier literature. Consider first the tâtonnement literature. There, to obtain stability it was necessary to restrict excess demand functions very severely; no such restriction is required in the present context. Further, the entire setting of tâtonnement was unrealistic, requiring the absence of any disequilibrium activity save price adjustment with continual recontracting. That is plainly not the case here.

Introduction

Consider the problem of dividing a cake among three individuals once again. Reliance on the Pareto efficiency criterion in finding an appropriate division will be of no help, because all divisions that leave nothing to be wasted will be Pareto-efficient. If we take recourse to the simple majority decision rule, our choice will be narrowed down, but the outcome thereby arrived at may well be strongly unappealing, as we have illustrated by Example 4.5. Invoking the no-envy concept of equity, we can also narrow down the range of eligible divisions.

In concluding this study, a few general observations that might shed further light on the nature of our problem may be in order. We would also like to add some qualifications on the analysis presented in this work.

Many reputable welfare economists have been strenuously denying the relevance of Arrovian impossibility theorems to welfare economics. Some of them have gone as far as to purge social choice theory altogether from the sacred realm of economics. Although we are in full agreement with Arrow's response (1963, p. 108) to the effect that “one can hardly think of a less interesting question about [Arrow's] theorem than whether it falls on one side or another of an arbitrary boundary separating intellectual provinces,” the reason for which Arrow's result has been denied any legitimacy in welfare economics is worth our examination, which seems to bring about an important clarification.

Introduction

According to Dahl (1956, p. 36), “no one has ever advocated, and no one except its enemies has ever defined democracy to mean, that a majority would or should do anything it felt an impulse to do. Every advocate of democracy of whom I am aware, and every friendly definition of it, includes the idea of restraints on majorities.” Therefore, it may well be claimed that a difficulty identified by Example 4.5, which comes to the fore only when we apply the simple majority decision rule mechanically, can hardly be attributable to this rule as its intrinsic defect.

Introduction

The analysis of the previous chapter proceeded as though agents always expect to be able to complete their planned transactions with no difficulty. This is hardly a reasonable assumption in a disequilibrium model where agents constantly find their plans thwarted. Further, given the absence of any subjective uncertainty, the fact that transactions of all sizes are assumed to be costlessly made leads the otherwise very sensible speculation results of the previous chapter to be of the “bang-bang” sort: agents rush discontinuously from one arbitrage opportunity to another, switching from buying to selling large amounts in pursuit of even very small speculative profits. It is plainly time to deal with such matters.

In fact, there is more than one matter to deal with here; there are three, and they are related in somewhat different ways.

The first issue is the analysis of transaction costs, that is, difficulties in transacting that prevent the “bang-bang” property just described from arising. Such costs may be thought of either as effort which must be expended in the search for trading partners or as a partial substitute for the effects of subjective uncertainty, which is otherwise conspicuously absent from the model. As we shall see, incorporating this kind of transaction difficulty into the analysis is easy to do; it has some interesting consequences, but it raises no very deep problems.

Introduction

The matters discussed in the previous chapter are all quite complex, and it is best to deal with them one at a time where possible. In the present chapter, I explore the behavior of individual agents where disequilibrium consciousness is allowed and production and consumption take place out of equilibrium. To do so, I first ignore the (welcome) complications which arise from the realization by agents that they may not be able to complete their transactions. Further, I postpone consideration of how prices (and price expectations) are set. These and other matters are introduced later on.

I thus begin with the general setup of the model and the analysis of the optimizing behavior of agents who believe that prices will change. The analysis is complicated, but the results are appealing, being both interesting in themselves and required for what follows. The complexity seems inescapable if we are to deal with models in which time is essential and arbitrage over time takes place. No suitable, complete treatment of these matters seems available in the literature.

Because it seems desirable to continue to make the discussion accessible to relatively nontechnical readers without at the same time sacrificing continuity for those interested in a more rigorous treatment, this and succeeding chapters are organized a bit differently from the earlier ones. Each subject is discussed in one or more nontechnical sections. Those sections are followed by one or more technical ones, which are indicated by asterisks.

Toward a more sensible model

It is now time to consider developing the models so far considered in the direction of our final goal. We must allow production and consumption to take place out of equilibrium. More important, we must allow agents to realize that they are not in equilibrium and to act on arbitrage opportunities as they occur. This fundamentally requires that agents be permitted to do two things. First, they must recognize that prices may change. Second, they must recognize that they may not be able to complete their desired transactions. In forming their consumption and production plans, agents must take these things into account.

The fact that agents may not be able to complete their transactions is not unrelated to the fact that prices can change. Agents who believe that they face transaction constraints are also likely to believe that prices in markets with such constraints will change. This is particularly likely in a Hahn Process world of orderly markets in which agents can take their own inability to purchase as reflecting a general short supply. Moreover, agents facing such constraints may themselves make price offers to get around them.

Handling all of this is a tall order and is best done in pieces. In the present chapter, I consider in general how the analysis so far developed can be adapted to deal with these matters. The details - which are often very interesting indeed - are explored later on.

Introduction

Traditionally, the concept “democracy” often has been construed to mean neither more nor less than rule by the majority of individuals. Suffice it to quote a passage from Bryce:

In view of this strong doctrinal association between democracy and majority rule, which we cannot simply neglect, it is important to have in hand an analysis of majority rule as a collective choice mechanism.