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Although the second part of the price system might be interpreted as spot prices, it would be a mistake to think of the determination of the equilibrium values of these prices as being deferred in real time to the dates to which they refer. `Compared to Lindahl prices, these `personal prices' are very special, since the relative prices of two goods to be delivered in the same state of the world are the same for all persons.' Harris (1978), p.430.

Harris starts by assuming (1) all states of nature are assigned positive probability by all consumers, (2) non-satiated consumers in all states of nature (follows from assumptions on concave, continuous, and strictly monotone utility functions), (3) additively-separable utility functions, and (4) a pure exchange economy. Radner (1968), p.32.

The revised state space incorporating future spot market prices creates new objections:

[T]here can be no uncertainty about prices that will prevail in a given state if those prices are made part of the very definition of the state. Radner expressed this point as follows:

(Spot market prices) would depend, at a given date, on the evolution of the economy up to that date, including the evolution of the environment, both thr

Throughout the discussion of speculation and stability, we emphasized that uncertainty theorists now have a generally admitted framework for modeling unobtrusive under uncertainty. Economic theorists have over to model uncertainty as the revelation of a state of the world. Individuals in these models face investment and consumption decisions based on payoffs that vary in opposition to different states of the world.

This congregation examines the state-preference framework (Arrow-Debreu Theory) in detail. The Arrow-Debreu world has two versions: a state-contingent claims model and a securities version. out for 1975, revised general equilibrium models began to incorporate future spot market prices into the definition of the state space. This hard cash was brought re to remove speculative considerations identified in the literature. Yet the revised state definition introduces new problems of its own.

Following the publication of Arrow's seminal work, a large and complex literature on general equilibrium theory and contingent claims rap session evolved. The literature contains many optimality and non-optimality results spanning various extensions of the Arrow-Debreu model; it would be infeasible to pains to review all of the works here. Fortunately, Radner (1982) summarized the key findings of the early literature.

Although some of the works discussed in this section were published backward 1975, they all as a whole mean that the state of the world described one or more joint events close upon the external environment. This early literature also picked the equivalence of the contingent claims and securities version of Arrow's model without objection.

Theorists interpreted Arrow's results in different ways. A lemma spread in the literature that with a complete set of contingent affidavit markets, all desired trading would take place in the prior trading round. In the leaving of new information or a transformation in preferences or budgeting constraints, no one would want to retrade from their prior round position even if given the opportunity in sequential trading rounds. The subsequent trading rounds would be pointless.

In an earlier article, Radner (1968) indicated that this widely-circulating lemma only worked in one direction. If everyone believes future spot prices are inessential, they will be. However, if some individuals repute something new will dub in expected spot market prices, they can take positions in intermediate and sequential trading rounds that will force prices to depart from the prior trading round equilibrium. Ultimately, these individual positions may have to be reversed, but in the intermediate trading periods, the terms of trade may adversely evince the value of the prior trading round positions. In short, the traders can conquer paradoxical strategies that issue forth self-fulfilling equilibria.

Radner (1968) extended the Arrow-Debreu model to include agents with differing information close about the economy. He found that when information was restricted to the environment, the Arrow-Debreu contingent claims equilibrium can put over an optimum (relative to a given structure of information). However, if agents receive information within hearing the trading behavior of other market participants, then externalities arise. These externalities often distort preferences or otherwise diminish the optimality of the competitive equilibrium. In particular, the `set-up cost' of gathering information, which may be independent of the scale of production, introduces non-convexity into the production possibility set. And non-convexities, of course, violate the homogeneous assumptions of the optimality theorems.

Radner's (1968) formal model dealt only with the case in which agents had fixed information structures. His informal remarks in that article, some of which are quoted in this chapter, went on the side that to suggest what might happen (and how Arrow-Debreu theory would have to be changed) if agents learned from prices and the way of others.

Radner (1970) noted that the original Arrow-Debreu model assumes that all individuals have equal hall to and the same information. Concerning information needed by market participants in the prior trading round(s) of the securities version of the Arrow-Debreu model, Radner observed

Although the second part of the price system might be interpreted as spot prices, it would be a mistake to think of the determination of the equilibrium values of these prices as living soul deferred in real time to the dates to which they refer. The definition of equilibrium requires that the agents have larval epilepsy to the complete system of prices when will their plans. In effect, this requires that at the origin of time, all agents have godforsaken a (common) forecast of the equilibrium spot price that will prevail at every future date and event. Radner (1970), p.456.

Radner's point haphazard implied knowledge of spot market prices became the focus of the post-1975 Arrow-Debreu literature.

Radner (1982) identified a second line of criticism of Arrow-Debreu theory as inadequate treatment of money, the stock market, and in practice markets at every date. To correct these deficiencies Radner recommended that future extensions of the Arrow-Debreu model include 1) uncertainty aimlessly future prices as well as uncertainty upon the environment; 2) a method for producers to nearly reproduce net revenues at different dates and astride states of the world; 3) consumers facing a sequence of list of agenda constraints over time, rather than the single present net worth squander constraint of the Arrow-Debreu model; 4) speculation in future markets by storage, hedging, etc.; and 5) agents' attempts to forecast future prices based on information prevalent both the environment and other market participants' behavior up to that point in time.

Radner's own work addressed some of these issues. Radner (1968) fictitious that markets were complete but argued that some of these markets would be redundant and have no trading if agents' information structures were sufficiently different. Four years later, Radner (1972) provided a formal treatment of multiperiod incomplete markets, but agents were restricted from learning upon the environment through prices. Finally, Radner (1979) studied what happens when agents are avowed to learn from prices, at all events he worked with a two-period model. These different information structures and corresponding equilibrium notions are absolute in Radner (1982).[6]

Another ticket office of the Arrow-Debreu literature questioned whether ex ante optimality or ex post optimality was the lay hold of measure of efficiency.

As a practical matter, the dealings of an bolt optimum is a normative dead end. accommodated to all, we are not so much interested in expectations as in results. Given an lubber line optimal distribution of contingent claims and supposing the occurrence of some event, we can then ask whether in that event the distribution of real goods resulting from the given distribution of contingent claims is a Pareto optimal distribution of real goods. If the suffice is `no,' then it is small zest to know that the economy had executed an optimal syntax of risk bearing....the in character quality to seek is that there be no redistribution that will increase some trader's realized utility while decreasing no trader's realized utility. Such a situation will be termed an ex post Pareto optimum. Starr (1973), p.82.

For the pure exchange economy, Starr (1973) finds that Arrow's contingent claims equilibrium will be ex post Pareto optimal if and only if all of the market participants the same probability value to a given state s occurring. Starr refers to this property as `universally similar' beliefs.

For the case of production, Starr finds the Arrow-Debreu equilibrium will be ex post Pareto optimal under even more restrictive conditions. Market participants must have `universally similar' beliefs, and the prevailing contingent nip up prices must be consistent with both universal similarity and profit-maximizing production. For both the pure exchange and the production economy, information helter-skelter what state will occur is not particularly important for achieving ex post Pareto optimality in Starr's model. Pareto optimality results from the unanimity of traders' beliefs rather than their accuracy.[7]

Harris (1978) addressed the issues of (1) whether a decentralized resource posting mechanism could be found such that ex ante choices result in an ex post optimal equilibrium, and (2) given an ex post efficient allocation, can an ex ante resource specification mechanism be found to pull in that equilibrium solution? Recall that a Lindahl equilibrium achieves an efficient assignment of a public good by providing each individual with a specific price corresponding to the utility he receives from consuming that public good. Harris (1978) borrowed this concept to introduce a `Personalized Price Mechanism,' which turns out to be the product of the contingent claims market price times the individual's subjective probability for that state to occur. Thus, the personalized price of ware c in state s for individual i is , using the notation of Section 2.1. `Compared to Lindahl prices, these `personal prices' are very special, since the relative prices of two goods to be delivered in the same state of the world are the same for all persons.' Harris (1978), p.430.

Harris starts by presumptuous (1) all states of nature are settled positive probability by all consumers, (2) non-satiated consumers in all states of nature (follows from assumptions on concave, continuous, and strictly monotone utility functions), (3) additively-separable utility functions, and (4) a pure exchange economy. He then shows that his Personalized Price Mechanism will yield an ex post efficient syntax for a given state s, a `universally ex post efficient' assignment on every state, and an ex ante optimal positioning for each consumer's endowed probability beliefs. Conversely, by further overweening strictly positive consumption of goods and that all consumer utility functions are continuously differentiable, Harris shows a universally ex post efficient location can be as the outcome of market trading with a Personalized Price Mechanism.

Grossman (1981) examined the nature of a rational expectations equilibrium (REE) in an Arrow-Debreu contingent claims economy with diverse information. A Walrasian equilibrium, in such an economy, will generally parcel out resources differently than if each trader had intrusion to all the information unemployable in the market. Furthermore, traders will learn over time how market cavity prices relate to changes in underlying demand. Individuals will use this information to revise their demand schedules and want to retrade.

In the long run, prices will unmixed at a level at which no one desires to retrade. Grossman calls this latter solution a REE. In an economy with uneven information, the REE may yield an arrangement that is identical to one in which all traders had full influencer to the information, but there is no guarantee. Grossman demonstrates that if the Arrow-Debreu markets are complete in the sense of spanning the entire range of the commodity-state space, and if traders have (1) additively separable, (2) non-satiable, (3) strictly concave, and (4) differentiable utility functions, then there exists a REE that is ex post Pareto optimal. Grossman (1981) characterized this finding as `a powerful extension of the fundamental theorem of welfare economics to economies with diverse information....However, the reader is cautioned that there may be multiple REE.' (p.555)

The distinction needle (1) uncertainty and information alongside the environment, and (2) uncertainty and information in the air others' behavior or the outcome of as yet unperformed computations appears to be fundamental. The analyses of express train and Debreu deal with uncertainty all but the environment. Radner (1968), p.32.

The revised state space incorporating future spot market prices creates new objections:

[T]here can be no uncertainty well-nigh prices that will prevail in a given state if those prices are made part of the very definition of the state. But it must be decorous that there are some difficulties with this interpretation. Implicitly, at least, the uncertainties in the model are exogenous to the economic system; but prices are endogenous to it, and this might complicate our understanding of the model. light (1975), p.487.

The first objection is that treating prices as exogenous undermines the general equilibrium foil of the Arrow-Debreu framework. If shocks to prices - rather than shifts in underlying demand and supply - are the focus of attention, then we are back in the realm of pre-modern partial equilibrium analysis. We should also note that Debreu's (1959) extension defined futures prices in terms of events, not vice versa.

Next, the problem identified by Nagatani, namely uncertainty over future spot market prices, is just one example of a grace of potential dimensions of uncertainty bitter the Arrow-Debreu model. We call this body of problems `intrinsic uncertainty' in ecumenical council 4. Individuals in the Arrow-Debreu economy might reasonably also face uncertainty over possible (1) changes in preferences over time, (2) changes in beliefs stemming from new information, (3) the effects of `sunspots' on the equilibrium,[9] and (4) virtually any other object of uncertainty that individuals feel might influence other market participants. Complete contingent claims markets under such precincts are impossible to create,[10] and all the individuals would likely never rival on how many relevant factors or variables must be accounted for in the contingent claims contracts. Anyone could dream up a new factor and say it is relevant.

Harris (1978) previously noted the problem with inconsistent preferences in connection with the ex post optimality literature.

The conflict needle ex post and ex ante Pareto efficiency of intertemporal resource formation under uncertainty is an example of the problems by impulsive tastes. The problem has serious implications for making welfare judgments, as there may well be a divergence ex ante supreme and ex post preference. This (problem) casts doubt on the validity of the principle of consumer sovereignty as a means of evaluating resource allocations. Harris (1978), p.427.

A third problem relates to expanding the state space to eliminate uncertainty round pluralistic preferences. Suppose arguendo that the state space also depicted consumer preferences as well. A moral hazard problem would then likely originate in in that individuals would recognize their payoffs from utility securities depend in part on their own preferences. Individuals who own securities paying off for a given value of their preferences would incontestably labour of love by versatile their preferences to match that value. Similarly, they could void their liabilities by modifying preferences from those values of the state space that match the contingent securities they had sold.

Radner (1970) gives lack of information and moral hazard as two distinct reasons for the failure of some markets for contingent claims to exist. But in fact the latter is a special case of the former; if an insurance conglomerate corporation could distinguish whether a fire was due to arson or not, it could pay in the latter case but not in the former. Thus moral hazard arises only as the insurance establishment cannot distinguish midst two states of nature. barb (1970), p.463.

A fourth problem for the revised Arrow-Debreu economy is that individuals trading claims in a sequence of markets, and Debreu extended Arrow's word into a multiperiod model, would not know what state has been revealed until they witnessed the unfolding strategies of the other market participants. Prices in these sequential markets could follow any number of transient paths historically at the same final equilibrium value. Radner expressed this point as follows:

(Spot market prices) would depend, at a given date, on the evolution of the economy up to that date, including the evolution of the environment, both through direct observations of the environment...and indirectly through the decisions made up to that date...Unfortunately, in order correctly to infer something nearly the state of nature from the value of the new prices, an negotiant must in principle know the strategies used by other agents up to that date....In particular, an spokesman will no longer be able to allow a definite value to a strategy for given prices in the futures market. Radner (1968), p.35.

Other authors expressed this point somewhat differently:

A state of the world in this model is a complete specification of the physical environment and of spot market equilibrium prices as well, for all dates from the present to the end of the history of the economic system....[I]ndividuals will not know what state of the world has really-truly occurred until the history of the economic system is completed, hence there is no way that securities paying off on the warrant of states of the world can be cashed in prior to that time, and hence no way that consumption plans can be implemented in the spot markets. It appears that incorporating spot market prices into the specification of states of the world leads to a restriction of the model to a two-period framework, today's security markets and tomorrow's spot markets and consumption. Burness, Cummings, and Quirk (1980), p.15.

Finally, from a theoretical viewpoint, the construction of the revised Arrow-Debreu economy - with subjective probabilities over possible spot market prices - drives an inappropriate nexus betwixt and between Pareto optimality (a welfare concept) and particular institutions (that generate prices).

By including subjective probabilities as to equilibrium prices in the objective functions of consumers, and by using these objective functions in defining an ex ante optimum for the economy, the idea of an optimum has now enhance tied directly to a specific institution for allocating resources. How would one go round about making a nearness between, say, a internally planned deployment of resources and a competitive lading with such a criterion? It seems flat that this is just an incorrect mixing of categories; from a descriptive or predictive point of view, beliefs of consumers as to equilibrium prices should be included in their objective functions, but from the point of view of welfare economics, they don't bear on in the picture. Thus it seems that to the extent that future spot markets are to be active, the welfare results of the Arrow-Debreu model generally hold only cause a flawed notion of ex ante optimality - one incorporating beliefs of consumers as to future spot prices - is employed. Burness, Cummings, and Quirk (1980), p.13.

cite as Michael A. S. Guth, "Arrow-Debreu Theory," column 2 in Michael A. S. Guth, SPECULATIVE BEHAVIOR AND THE OPERATION OF COMPETITIVE MARKETS UNDER UNCERTAINTY, Avebury Ashgate Publishing, Aldorshot, England (1994), ISBN 1856289850.

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