Knowledge that Transforms

This paper investigates two aspects of the macroeconomic consequences of market participation decisions of imperfectly competitive firms. First, can there exist multiple, Pareto-ranked Nash equilibria indexed by the level of market participation? That is, can there exist both thin and thick market equilibria? Second, can the variations in the degree of competition that stem from shocks to preferences and technologies help to understand observed fluctuations in the macroeconomy? This paper is part of an ongoing research program intended to understand the macroeconomic implications of the coordination of economic activities in model economies without complete and/or competitive markets. In such environments, the fundamental theorems of welfare economics do not apply and it is quite possible for the economy to have multiple, Pareto-ranked equilibria. Low-welfare equilibria represent situations in which individual agents, acting noncooperatively, are unable to successfully coordinate their activities and reach a preferred equilibrium-this is termed a coordination failure. In equilibria of this type, there are $100 bills lying on the sidewalk but it takes the effort of more than one individual (i.e., coordination) to reap these gains! Our model relates to two important strands of the literature on coordination failures. First are model economies in which the deviation from the Arrow-Debreu paradigm arises from the market power of sellers (see, for example, Oliver Hart, 1982). In these models, the number of active firms is usually taken to be exogenous. Our contribution is, in part, to allow the number of firms to be determined by the costs and benefits of market participation. This allows us to relate the degree of competition in the economy to variations in fundamentals like technology and preferences in addition to exogenous (but self-fulfilling) variations in expectations. Second, our model represents another example of a participation externality in which the gains to participating in an activity, such as entering a market, depend on the number of other agents participating as well. The papers by Peter Diamond (1982), Chatterjee (1988), and M. Pagano (1987; 1988) explore market participation externalities of a different variety. In Diamond's work, these externalities arise through the matching process, while Chatterjee and Pagano (1987) explore the risk-reducing effects of large markets. Similar externalities are found in the industrial organization literature on networks, as in Michael Katz and Carl Shapiro (1985). The model explored in this paper highlights a participation externality arising from the interaction of imperfectly competitive firms.1 tDiscussants: Robert E. Hall, Stanford University; Peter Diamond, MIT; Olivier J. Blanchard, MIT.

This paper examines effects of the legal rules for property division at divorce on investment in human capital during marriage. The authors show that current rules generally lead to suboptimal levels of investment and spousal support, or to inequitable distribution of the returns from such investment, or both. They propose a new rule that performs better than the existing rules on both efficiency and equity criteria and that requires no more information than the existing rules.

Almost since the Expected Utility Hypothesis (EUH) was first introduced, evidence has accumulated that decision makers systematically violate it in various ways. One early response to the evidence was to develop ad hoc alternatives, the best known of which is Prospect Theory (Daniel Kahneman and Amos Tversky, 1979).1 More recent responses have relaxed the independence axiom or other axioms underlying the EUH. See Mark Machina (1987) for a very readable survey of the evidence and responses. Despite the high intellectual caliber of much of this work, there is an important sense in which it has been retrograde: theory is adjusted to the evidence by weakening, not strengthening, its predictive power. In other areas (such as the theory of the firm or the theory of money) economists have followed a different research strategy: more subtle constraints (such as transactions costs or informational imperfections) are sought to explain data that seem anomalous according to received theory. When successful, such a strategy more clearly delineates the realm in which the older theory is applicable and makes new, testable predictions outside that realm. Thus theory is progressively strengthened. To my knowledge, only Jonathan Leland (1986, 1988) has adopted such a progressive strategy in a theoretical investigation of EUH anomalies. The key assumptions of his approximate expected utility theory (AEU) are (1) inexperience and/or cognitive limitations make the true utility function inaccessible, so some approximation must be used; but (2) decision makers efficiently allocate finite resources so as to minimize the resulting errors. He formalizes these assumptions (which he applies to probability assessments as well as to utilities) in terms of a constraint on the number N of steps allowed in a step-function approximation, with the optimal approximation defined as that minimizing expected squared error. His AEU theory is able to explain many of the major EUH anomalies, and reduces to ordinary EUH in areas in which relevant experience accumulates (for example, in competitive markets; as noted by Peter Knez, Vernon L. Smith, and Arlington W. Williams (1985); and Don L. Coursey, John L. Hovis, and William D. Schultze (1987), the prevalence and magnitude of anomalies seems to decline in such settings). The purpose of this note is to present a variant on Leland's AEU. I propose an approximate utility function (or function) in which utility increments are weighted by a sensitivity function. The resource constraint is that overall sensitivity is limited, but (prior to observable decisions) it can be allocated freely along the continuum of potential wealth increments. My approach has three advantages: it predicts an S-shaped value function when agents maximize expected sensitivity at actual choice opportunities, given very plausible assumptions regarding the distribution of such opportunities. Recall that the assumption that decision makers maximize an S-shaped value function, such as that depicted in Figure 1, is the centerpiece of Prospect Theory, *Economics Department, University of California, Santa Cruz, CA 95064. I appreciate the comments of Jonathan Leland. Amos Tversky, and two anonymous referees on earlier drafts of this paper. The usual caveat definitely applies. IThe authors of Prospect Theory call their model as opposed to normative, but do not consider it ad hoc because of its connections with the psychophysical literature. However, no substantial connections of Prospect Theory with generally accepted economic principles (for example, optimality) have previously been demonstrated. It is in this narrow economist's sense that I use the term ad hoc. The more recent work of Ariel Rubinstein (1988) and Tversky and Kahneman (1986) underscores the difficulty of reconciling such a descriptive approach to the expected utility hypothesis.