Moral hazard and general equilibrium in large economies

Summary. The paper analyzes a two period general equilibrium model with individual risk, aggregate uncertainty and moral hazard. There is a large number of households, each facing two individual states of nature in the second period. These states differ solely in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period each household chooses a non-observable action. Higher levels of action give higher probability of the good state of nature to occur, but lower levels of utility. Households' utilities are assumed to be separable in action and the aggregate uncertainty is independent of the individual risk. Insurance is supplied by a collection of firms who behave strategically and maximize expected profits taking into account that each household's optimal choice of action is a function of the offered contract. The paper provides sufficient conditions for the existence of equilibrium and shows that the appropriate versions of both welfare theorems hold. Received: December 7, 1998; revised version: October 25, 1999     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

Peer group effects in applied general equilibrium

Summary. In this paper, I develop an applied general equilibrium environment with peer group effects. The application I consider is schooling. The framework used here is general equilibrium with clubs. I establish the existence of equilibrium for the economy with a finite number of school types. This result is then extended to the case where the set of school types is a continuum. The two welfare theorems are shown to hold for both economies. To compute the equilibrium, I construct a Negishi mapping from the set of weights on individual type's utility to the set of transfers that support the corresponding Pareto allocations as competitive equilibria with transfers. Because this mapping is a correspondence, a version of Scarf's algorithm is used to find a competitive equilibrium. Received: June 9, 1999; revised version: March 13, 2000     

On equilibrium existence in payoff secure games

We propose a single framework for studying the existence of approximate and exact pure strategy equilibria in payoff secure games. Central to the framework is the notion of a multivalued mapping with the local intersection property. By means of the Fan-Browder collective fixed point theorem, we first show an approximate equilibrium existence theorem that covers a number of known games. Then a short proof of Reny’s (Econometrica 67:1029–1056, 1999) equilibrium existence theorem is provided for payoff secure games with metrizable strategy spaces. We also give a simple proof of Reny’s theorem in its general form for metric games in an appendix for the sake of completeness.     

Existence of steady – state equium in an overlapping-generations model with production

Summary This paper establishes an existence theorem of a non-trivial (positive capital stock) steady-state equilibrium in Diamond's (1965) overlapping-generations model with production by employing the steady-state consumption curve introduced in Ihori (1978). The assumptions on preferences and production technologies that ensure the existence of a nontrivial steadystate equilibrium are separated from each other, unlike in Galor and Ryder (1989). We also provide two simple examples which illustrate the importance of two conditions in the theorem.Detailed comments by Tomoichi Shinotsuka and the referees of the journal were quite helpful. We also thank Marcus Berliant, Mark Bus, John H. Boyd III, Ban Chuan Cheah, Rajat Deb, Jim Dolmas, Oded Galor, Greg Huffman, Toshihiro Ihori, Radhika Lahiri, Lionel McKenzie, Arundhati Sen, and the seminar participants at the Midwest Mathematical Economics Conference in Ann Abor and at University of Rochester. The second author gratefully acknowledges the financial supports from the European Community Human Capital Mobility Program.     

Some theorems on the existence of competitive equilibrium

The purpose of this paper is to point out a relationship between theorems on the existence of competitive equilibrium in economies with externalities, and recent results (pioneered by A. Mas-Colell) on the existence of equilibrium for economies in which consumer preferences are neither complete nor transitive. This observation leads both to a substantial strengthening of the theorem on the existence of equilibrium with externalities, and at the same time to a revealing perspective on the Mas-Colell theorem.     

Incomplete risk sharing arrangements and the value of information

Summary. The paper constructs a theoretical framework in which the value of information in general equilibrium is determined by the interaction of two opposing mechanisms: first, more information about future random events leads to better individual decisions and, therefore, higher welfare. This is the ‘Blackwell effect’ where information has positive value. Second, more information in advance of trading limits the risk sharing opportunities in the economy and, therefore, reduces welfare. This is the ‘Hirshleifer effect’ where information has negative value. We demonstrate that in an economy with production information has positive value if the information refers to non-tradable risks; hence, such information does not destroy the Blackwell theorem. Information which refers to tradable risks may invalidate the Blackwell theorem if the consumers are highly risk averse. The critical level of relative risk aversion beyond which the value of information becomes negative is less than 0.5. Received: May 14, 2001; revised version: March 5, 2002     

Neutrality in arrow and other impossibility theorems

Summary. Although not assumed explicitly, we show that neutrality plays an important role in Arrow and other impossibility theorems. Applying it to pivotal voters we produce direct proofs of classical impossibility theorems, including Arrow's, as well as extend some of these theorems. We further explore the role of neutrality showing that it is equivalent to Pareto or reverse Pareto, and to effective dictatorship for non-null social welfare functions satisfying the principle of independence of irrelevant alternatives. It is also equivalent to Wilson's Citizens' Sovereignty--which is related to the intuition that symmetry over alternatives makes social preference depend only on citizens' preferences. We show that some of these results are more fundamental than others in that they extend both to infinite societies and to considerably smaller domains of preferences. Finally, as an application of Arrow's theorem, we provide a simple proof of the Gibbard-Satterthwaite theorem.Received: 13 April 2000, Revised: 6 December 2002, JEL Classification Numbers: D71, C70.I thank Salvador Barberá, Luis Corchón, Cesar Martinelli, Eric Maskin, Tomas Sjöström, Ricard Torres, José Pedro Ubeda, and an anonymous referee for feedback. The proofs of Arrow's theorem and two Wilson's theorems come from a note I wrote in 1987 at Universitat Autónoma de Barcelona (Ubeda [16]). In 1996 Geanakoplos [7] wrote a proof of Arrow's theorem similar but not identical to mine. All work in this paper is independent of his.     

Non-marketed options, non-existence of equilibria, and non-linear prices

This paper presents a surprising example that shows that the lattice theoretic properties in Mas-Colell's (1986) seminal work are relevant to the existence of equilibrium even when the commodity space is finite dimensional.The example is a two-period securities model with a three-dimensional portfolio space and two traders. The paper identifies a non-marketed call option that fails to have a minimum cost super-replicating portfolio. Using this option, we construct an economy that satisfies all of Mas-Colell's assumptions, except that the three-dimensional commodity space is not a vector lattice. In this economy, there is no Walrasian equilibrium and the second theorem of welfare economics fails.Our example has important finite- as well as infinite-dimensional implications. It is also an example of a “well behaved” economy in which optimal allocations that are not supported by linear Walrasian prices are decentralized by the non-linear prices studied in Aliprantis-Tourky-Yannelis (2001).     

Two simple proofs of the feasibility of the linear tracing procedure

Summary. Theories of equilibrium selection in non-cooperative games, as well as the notion of risk dominance, depend heavily on the so-called linear tracing procedure. This is the first paper to give direct, simple proofs of the feasibility of the linear tracing procedure. The first proof utilizes a result that is related to Kakutani's fixed point theorem and that is an extension of Browder's fixed point theorem. The second proof shows that it is even possible to avoid the use of correspondences. Received: June 8, 1998; revised version: November 8, 1998     

The Second Welfare Theorem in Economies with Non‐Walrasian Markets

The standard version of the second welfare theorem assumes that market operations produce Walrasian outcomes. Therefore, if there are individuals who can manipulate prices, the conclusion of the second welfare theorem is questionable. In this paper, we address the decentralization of a Pareto‐optimal allocation, when markets are non‐Walrasian. Our objective in this paper is to develop a game which can implement Pareto‐optimal allocations as Nash equilibria of strategic exchange in markets. In this way, we develop a version of the second welfare theorem for economies where markets are strategic.     

Cap and trade policies in the presence of monopoly and distortionary taxation

We extend an analytical general equilibrium model of environmental policy with pre-existing labor tax distortions to include pre-existing monopoly power as well. We show that the existence of monopoly power has two offsetting effects on welfare. First, the environmental policy reduces monopoly profits, and the negative effect on income increases labor supply in a way that partially offsets the pre-existing labor supply distortion. Second, environmental policy raises prices, so interaction with the pre-existing monopoly distortion further exacerbates the labor supply distortion. This second effect is larger, for reasonable parameter values, so the existence of monopoly reduces the welfare gain (or increases the loss) from environmental restrictions.     

Monopolistically competitive equilibria with differentiated commodities

Summary. An existence theorem of monopolistically competitive equilibrium of the economy in which commodities are subject to differentiation will be proved. We start with the existence theorem of Negishi (1961) and extend it to the commodity space of measures on a compact metric space. In so doing, we have to handle the price normalization carefully. Received: December 2, 1996; revised version: May 6, 1999     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

Outsiders' threat and consecutive offers

Summary. We study the effects of outsiders' threat and consecutive offers in the two-person bargaining model of Shaked and Sutton (1984). In our first model, there are no outsiders and the firm can make two consecutive offers for every given number of periods. Our first model has the same unique equilibrium as in Shaked and Sutton (1984). In our second model, the firm can switch between rival partners but cannot change the alternating proposing sequence. Our second model has the same perfect equilibrium as in Rubinstein (1982). So the key factor that leads to the equilibrium of Shaked and Sutton (1984) is the possibility of firm's consecutive offers, not the outsiders' threat. Received: 23 December 1998; revised version: 21 May 1999     

Injecting rational bubbles

This paper proves two theorems about economies with a finite number of infinitely lived agents who trade a complete set of one-period Arrow securities and several infinitely lived securities at each date, subject to short-sales constraints. The first theorem in the paper considers an equilibrium to an economy of this kind. It proves that there exists another economy with perturbed short-sales constraints in which there is an allocation-equivalent equilibrium in which asset prices have a bubble. The second theorem extends to the result to the case in short-sales constraints are endogenously determined in the sense of Alvarez and Jermann [Efficiency, equilibrium, and asset pricing with risk of default, Econometrica 68 (2000) 775-797].     

Linear and non-linear price decentralization

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consumption sets are the positive cone of arbitrary ordered Fréchet spaces—dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prices and for ω-proper economies they are both sufficient and necessary.     

Theorems on correspondences and stability of the core

In this note two theorems strengthening Grodal's (1971) Theorem on correspondences are proved. The first drops the convexity assumption. The second strengthens that theorem further for the case when the range is the positive orthant. In this case, the conclusion of Grodal's Theorem - the intersection of the integral with the interior of the range being open- is modified to read as the integral being a relative open subset of the positive orthant. An example is provided to show that, such a strengthening is not valid in general. This allows us to dispense with the requirment of convexity of preferences in Grodal's (1971) theorems on the closedness of the set of Pareto optimal allocations, the core, and the continuity of the core correspondence for pure exchange economies. We apply this result to show that blocking coalitions in a large economy are stable. Received: September 30, 1998; revised version: September 18, 2001 RID="*" ID="*" The author is grateful to an anonymous referee for helpful comments. The usual disclaimer applies.     

Learning buyers' valuation distribution in posted-price selling

Summary. For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution. Received: July 22, 1997; revised version: December 11, 1997     

Comments on John Roemer’s first welfare theorem of market socialism*

Abstract

In this comment on John Roemer’s “theory of cooperation with an application to market socialism”, I extend Roemer’s first welfare theorem of market socialism in two directions. First, I prove a version of the theorem that deals with non-linear taxation. Second, I offer a connection between the theorem and welfare equality. I then argue that the models and questions that Roemer contribute to bring to welfare economics raise questions that go much beyond the research on socialist ethics. In particular, I introduce a positive model of moral behavior that yields different predictions from Roemer’s Kantian model. I conclude that individual morality should become a central concern of welfare economists.