Instability of equilibria in experimental markets: upward-sloping demands, externalities, and fad-like incentives.

• Author: Plott, Charles R.

1. Introduction

   This paper addresses four questions: (i) Can an upward-sloping demand be successfully created in a laboratory environment through the introduction of an externality, similar to fad-like preferences? (ii) In the presence of such special characteristics, do markets equilibrate to the classical intersection of the demand and supply curves? (iii) Can both stable and unstable equilibria be observed? This is a rather deep question since it asks if markets obey laws of dynamics similar to those that have been observed in physics. (iv) If markets do exhibit instability, which of the two classical concepts of stability, Marshallian stability or Walrasian stability, does the best job of predicting the conditions under which instability will be observed? Both of these theories are based on very general models of market behavior and so should apply to the simple and special case of an experimental setting. Indeed, the theories should apply to an experimental setting with the same force that would be applied to any other setting. Thus, experimental methods are a perfect way to address the issues, especially when no alternative method seems to exist.

   The questions posed are natural. First, a fundamental part of neoclassical theory of market adjustments resides in the presumption that markets can be unstable. Thus, there is a natural intellectual curiosity about whether or not the presumption is correct. Second, there is a practical motivation for an interest in stability. Multiple equilibria often appear in models, causing difficulty with model specification. The conventional solution to the problem is to discard the equilibria that are unstable under the presumption that unstable equilibria cannot be observed, that is, they are removed from all consideration. It is only natural to ask if this convention is justified. The third question stems from an issue about the relationship between the competitive model of markets and game theory. The most basic principles of economics are being replaced by principles of game theory and related solution concepts. Do phenomena exist in markets that will be very difficult if not impossible to capture with the static solution concepts of game theory? In particular, game theory and the associated concepts of solutions tend to be equilibrium theories, without any accompanying notion of dynamics or equilibration. Thus, since disequilibrium is a primary feature of instability, it is a rather obvious place to look for challenges to the static equilibrium concepts of game theory.

   Notice that the motivations for this study are essentially unrelated to parameters that might be found in the U.S. economy, or any other economy, for that matter. The motivations are not about the economy; they are about economics and the underlying principles of economics that we use as tools to understand the economy. At this stage, the investigation is strictly of a laboratory nature. While the study suggests many interesting questions about the nature of markets found in the field, they are not addressed here. For example, the question of the relative frequency or instances of instability are not addressed. Measures that might indicate when a market is perched at an unstable equilibrium are not sought. This study is about the nature of the laws that govern whether or not an equilibrium is stable, and the focus is on the behavior of markets in the laboratory.

   Once one decides to look for instability, the neoclassical theory itself suggests where to search. According to the ideas, the curves must have a perverse shape in the sense that the demand curve should slope upward or the supply curve should slope downward. Neoclassical theory also suggests two types of underlying economic circumstances that can produce such perversities. One set of circumstances is related to income effects. Both the famous Giffen good of upward-sloping demands and the labor-leisure tradeoff that produces backward-bending (downward-sloping) supply curves are related to the income effect. A second set of circumstances is related to externalities or external economies, as Marshall called them. On the supply side, downward-sloping supplies are thought to be produced by efficiencies that might be produced by expanding industrial scale. On the demand side, a similarly constituted externality can produce the upward-sloping demand curves that are thought to be produced by preferences such as desires to mimic the behavior of others.

   This paper employs the second set of circumstances, the use of externalities to create an upward-sloping demand.(1) Markets were created in which the value of the units to any one person increased with the level with which the units are purchased by others. The more others do it, the more any particular individual wanted to do it. The general interpretation could be preferences that result in a desire to mimic others or it could be some sort of belief formation process in which the beliefs or expectations of agents about some underlying state of nature are influenced by the buying behavior of other agents. The result of the preference inducement was to create a market that can be modeled as having an upward-sloping market demand curve even though individual demand curves are downward sloping. With such a demand, an opportunity arose to observe whether or not instability presents itself.

   Based on previous research, a presumption exists that Marshallian stability and not Walrasian stability will be observed. Plott and George (1992) studied markets in which the supply was downward sloping due to a Marshallian externality and found that the Marshallian model of market stability provided the appropriate conditions under which instability could be observed. The Walrasian concept of stability was found to be completely inappropriate for that type of economic environment. Since an upward-sloping demand is a mirror image of the Marshallian downward-sloping supply, the current study is a test of both the replicability and the robustness of the Plott and George experimental results.

   The results are easy to summarize. Unstable equilibria can exist in markets. They exist at the intersection of demand and supply, as do other classical market equilibria. Where the perverse curves are due to an externality, the Marshallian model and not the Walrasian model define the conditions under which unstable equilibria exist. The experiments replicate and extend the results previously reported by Plott and George.

   Aside from classical discussions, the literature about the possibility of upward-sloping demands is not extensive. Papers by Becker (1991) and Karni and Levin (1994) both addressed issues of fad-like preferences. (For brevity, we will refer to them as B&KL.) Interestingly enough, both sets of authors, B&KL, failed to realize that they were dealing with a classical Marshallian external economy on the demand side as opposed to the supply side. After translation to the demand side, the model of B&KL differs from Marshall and Plott and George (1992) (PG) in only two substantive respects. The first is the structure of the externality and the second is the assumed industrial organization.

   First, with respect to the structure of the externality, B&KL do not require that the level of market activity be the vehicle that carries the externality, as do Marshall and PG. Instead, B&KL fads allow market demand to be the vehicle of the externality independent of whether or not the demand resulted in trades or whether adequate supply exists. By contrast, the formal representation of the externality used in PG depends on actual volume traded in the market (Marshallian fads). In B&KL fads, the utilities of agents depended on the number of people that want to do something rather than the incidence of them actually doing it, as is the case in Marshall fads and in PG.

   Second, with respect to the industrial organization, B&KL assume that there are only a small number of well-informed sellers and many myopic buyers. By contrast, Marshall and PG assume that there is symmetry between the buying and selling sides of the market. The implications of these differences are rather dramatic. Marshall and PG apply the competitive model on the one hand and with it can characterize notions of stable and unstable markets together with possible dynamic adjustment processes. By contrast, B&KL allow the demand side to behave much like competitors, from which a demand function can be derived in the same way that it is derived in this paper. However, that is where the similarity ends. In this paper, the supply is also derived by application of the competitive model. In B&KL, the sellers are fully informed of the behavior of the demand side of the market and are able to solve for various equilibria using standard game theoretic logic. The problem posed by B&KL is then one of selecting the appropriate equilibrium by appeal to solution concepts.

   While both sets of authors, B&KL, mention stability, they do not use the term in a classical sense. In fact, it is interesting to note that, to the extent that the term stability makes sense, they identify instability with Walras and not Marshall. Thus, as the data reported in this paper show, the intuitive ideas of instability that they apply are exactly the opposite of what they should use.

   The organization of the paper is as follows. Section 2 is a review of the two competing models of market adjustment, Marshallian and Walrasian. This section is also used to introduce the major features of the experimental design. Sections 3 and 4 are brief summaries of the formal structure of the externality model and the associated concepts of demand and equilibrium from the point of view of the individual and the market, respectively. Section 5 is a discussion of the market supply functions. Section 6 is an outline of the experimental design and the predictions of the models, given the parameters imposed. Section 7...