Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Altruistic behavior in a representative dictator experiment

We conduct a representative dictator game in which students and random members of the community choose both what charity to support and how much to donate to the charity. We find systematic differences between the choices of students and community members. Community members are much more likely to write in their own charity, community members donate significantly more ($17), on average, and community members are much more likely (32%) to donate the entire $100 endowment. Based on this evidence, it does not appear that student behavior is very representative in the context of the charitable donations and the dictator game.

---

Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.      

Left-side Relatively Weak Increases in Risk and Their Comparative Statics

This paper proposes a new concept, a left-side relatively weak increase in risk (L-RWIR) order, that extends the definition of a relatively weak increase in risk (RWIR) order. We show that, for the class of linear payoffs, one can obtain an appealing comparative statics result for L-RWIR shifts imposing additional restrictions on risk preferences of a risk-averse decision maker.JEL classification: D81.revised version received October 10, 2003Acknowledgements The authors would like to thank an anonymous referee for insightful comments and useful suggestions.     

What is an ‘endogenous state space’?

Summary. In the literature on choice under unforeseen contingencies, the decision maker behaves as if she aggregates possible instances of future rankings indexed by a set S. The set S is interpreted as a subjective state space even though subsequent rankings need not conform to any one of the aggregated utilities. This paper proposes a definition for a subjective state space under unforeseen contingencies that is topologically unique, derives its existence from preference primitives as opposed to the representation of preferences, and does not commit to an interpretation in which states correspond to future realized rankings. The definition topologically concurs with and extends the identification of the essentially unique subjective state space due to Dekel, Lipman and Rustichini [4].Received: 28 October 2003, Revised: 13 October 2004, JEL Classification Numbers: D11, D81, D91.I thank Eddie Dekel, Alan Kraus, Bart Lipman, Chris Shannon, and the referee for some helpful remarks.     

Core equivalence with congested public goods

Summary This paper examines a model of an infinite production economy with a finite number of types of agents andsemi- public goods, which are subjected to crowding and exclusion. The utility of an agent depends not only on the vector of public commodities produced by the coalition to which she belongs, but also on the mass of agents of her type who are the members of this coalition. The main purpose of the paper is to derive necessary and sufficient conditions on the local degrees of congestion which would guarantee the equivalence between the core and the set of equal treatment Lindahl equilibria. We prove that this equivalence holdsif and only if there are constant returns to group size for each type of agents. It implies that linearity of each agent's congestion function with respect to the mass of the agents of her own type is necessary for the core equivalence to hold.The final version of this paper was written while Shlomo Weber was visiting the Technical University of Dresden as the Fellow of the Alexander von Humboldt Foundation, whose support is gratefully acknowledged. The authors are grateful to Peter Meyer, Nicholas Yannelis and the anonymous referees for useful remarks and suggestions.     

Preference for flexibility in infinite horizon problems

Summary. We consider the extension of the classical problem of preference for flexibility to many periods. Preferences are defined over sets of infinite paths of choices. The main result provides a set of axioms on preferences that yield an additive representation over a subjective state space. This space is the set of preferences over choice today and feasible set tomorrow. The main new axiom, stochastic dominance, is a stronger form of the assumption of monotonicity. Received: September 11 2000; revised version: December 18, 2001     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

Sraffa in historiographical perspective: a provisional statement

The paper explores the theory of the aggregate price, profit, and business fluctuations in Keyne's Treatise for its implications for modern macro-economic analysis. As in the Treatise, profits are first defined within a theory of the agregate price level, as aggregate investment minus saving. Deriving aggregate total revenue and aggregate total cost from this price theory, the paper shows how to construct a version of the Keynesian cross diagram. The cross construction suggests an important qualification for fiscal policy, that total cost does not shift. Then, using a neoclassical definition of profit and the total-cost / total-revenue approach, the paper derives aggregate supply, and then adds aggregate demand in an integrated framework. Comparative statics of the AS-AD analysis and the central role of profit in the Treatise suggest that a focus on profit might be useful in identifying exogenous technology shocks of real business cycle theory.     

Economic Dynasties with Intermissions

We consider a model of successive generations with a fixed proportion of selfish and altruistic members in each individual's offspring. In contrast with the others, selfish members bequeath nothing to their own children. We assume that parents cannot recognize their heirs' types and that negative bequests are forbidden. We study Markov perfect equilibria of this multistage game of incomplete information and their implications for wealth distribution.Journal of Economic LiteratureClassification Numbers: D31, D64, D91, H63.     

Multilateral bargaining: conditional and unconditional offers

Summary. We present a game in which n persons split a cake, where a distinction between conditional and unconditional offers is made. This distinction sheds light on the contrasting results obtained in the previous literature of multilateral bargaining. By allowing the proposer to make both conditional and unconditional offers, we show that the game has a unique subgame perfect Nash equilibrium outcome. Received: March 14, 2000; revised version: March 13, 2001     

A discrete approach to continuum economies

Summary We consider a perfectly competitive economy in which only a finite number of different agents' characteristics can be distinguished. We associate this economy with ann-agents' economy with an ordered Banach commodity space, and we prove that the continuum and the discrete approach to the equilibrium problem can be considered equivalent.The authors are indebted to Javier Ruiz-Castillo for his helpful suggestions to an earlier version of this paper. We would like to thank Nicholas C. Yannelis and an anonymous referee for helpful suggestions and ecomments.     

Sharing health risk and income risk within households: evidence from Japanese data

The question of which household members should consume medical services, and in what quantities, is examined by using Japanese household-level data. Two key concepts are employed, health risk and income risk, and whether family heads or dependants bear these risks investigated. Health risk is the risk that a household member falls ill, while income risk is the risk that future household income decreases. It is found that both heads and dependants make fewer visits to doctors as household size increases. It is also found that only dependants visited doctors less frequently following the reform of the public health insurance system, which raised the co-payment rate of family heads from 10% to 20%. These findings imply that heads and dependants share health risk but dependants bear income risk.     

Toward an Improved Definition of the Wealthy*

A definition of the wealthy was proposed in this journal [Eisenhauer, J. G. (2008). An economic definition of the middle class. Forum for Social Economics, 37, 103–113]. According to the definition, “the wealthy” are people who could live poorly for a year while living off the interest on their wealth. This paper suggests a more general definition of the wealthy, which encompasses that definition as well as ones based on the ability to live at higher standards of living than the poverty level over longer periods of time than one year while living off interest income alone. Previous empirical work is revisited to show new insights offered by the new definition. The evidence points to the reemergence of a rentier class.     

Monotonic Knowledge Models,Cycles, Linear Versions and Auctions with Differential,Finite Information

In games of incomplete information where each player's information is represented by a partition of the state space, this paper presents a characterisation of monotonic models in terms of connected partitions and another in terms of versions . A model is monotonic if and only if there is a linear version, and this is true if and only if there is a real‐valued function on the state space such that every partition of the model is connected with respect to this function. These results help us understand the strength of the connectedness assumption on common‐value, second‐price auctions with differential, finite information. We offer a simple sufficient condition for non‐monotonicity to check if models are monotonic.     

Preference for Flexibility and Dynamic Consistency

Dekel, Lipman, and Rustichini [3] characterize preferences over menus of lotteries that can be represented by the use of a unique subjective state space and a prior. We investigate what would be the appropriate version of Dynamic Consistency in such a setup. The condition we find, which we call Flexibility Consistency, is linked to a comparative theory of preference for flexibility. When the subjective state space is finite, we show that Flexibility Consistency is equivalent to a subjective version of Dynamic Consistency and that it implies that the decision maker is a subjective state space Bayesian updater. Later we characterize when a collection of signals can be interpreted as a partition of the subjective state space of the decision maker.     

Public Good Contributions Between Communities

The four fundamental determinants of voluntary contributions to public goods are taste, community size, wealth, and wealth distribution. This paper argues that for policy purposes it is important to discriminate between the four hypotheses. To do this, it is necessary to consider the comparative static effects of the above determinants not only on total contribution, but also on per capita contribution and the participation rate. Furthermore, just as members of a smaller community would contribute more than their identical counterparts in a larger community, we show that members of a community that has more poor members would also contribute more than their identical counterparts in a community that has more rich members.     

Preference profiles sustaining Arrow's theorem

Summary. Arrow's theorem is proved on a domain consisting of two types of preference profiles. Those in the first type are “almost unanimous": for every profile some alternative x is such that the preferences of any two individuals merely differ in the ranking of x, which is in one of the first three positions. Profiles of the second type are “appropriately heterogeneous”, with preferences similar to those generating the “paradox of voting”. Received: March 9, 2000; revised version: June 7, 2001     

Cooperation,stability and social welfare under majority rule

We resolve collective irrationality in the stability set, a solution concept for voting games proposed by Rubinstein (J Econ Theory 23:150–159, 1980) to resolve the well-known paradox of voting in the core. A lack of cooperation within winning coalitions prevents their members from eliminating an alternative globally less preferred to another one when they observe the rational behavior defining the stability set. Allowing for the possibility of accompanying a coalitional vote with a binding solidarity agreement is a natural response to this cooperation failure. This leads to a new standard of behavior and a new solution concept called stability set with binding solidarity agreement or S _c -stability set. It is shown that the S _c -stability set and a newly defined version of the Mas-Colell bargaining set for simple games are not comparable with respect to set inclusion. The S _c -stability set includes the core, is included in the stability set and contains only Pareto-optimal alternatives. When individual preferences are complete linear orders, the S _c -stability set is always non-empty.      

Semicollusion vs. Full Collusion: The Role of Demand Uncertainty and Product Substitutability

We examine the profitability of two different cartel organizational forms: full collusion, under which firms collude on both price and quality, and semicollusion, under which firms collude on price only. We show that, in the presence of demand uncertainty that cannot be contracted upon in the cartel agreement, firms may be better off limiting their collusive agreement to price only. However, a positive relationship between demand uncertainty and the relative profitability of semicollusion exists only for low levels of demand substitutability. The converse is true for high levels of demand substitutability. Therefore, if demand substitutability is sufficiently high, no level of demand uncertainty will make semicollusion the optimal organizational form. In contrast, semicollusion is guaranteed to be optimal for a sufficiently low level of demand substitutability. The market structure described is motivated by and closely parallels that of shipping cartels. Received September 29, 2000; revised version received December 10, 2001 Published online: November 11, 2002     

A class of multipartner matching markets with a strong lattice structure

Summary. For a two-sided multipartner matching model where agents are given by path-independent choice functions and no quota restrictions, Blair [7] had shown that stable matchings always exist and form a lattice. However, the lattice operations were not simple and not distributive. Recently Alkan [3] showed that if one introduces quotas together with a monotonicity condition then the set of stable matchings is a distributive lattice under a natural definition of supremum and infimum for matchings. In this study we show that the quota restriction can be removed and replaced by a more general condition named cardinal monotonicity and all the structural properties derived in [3] still hold. In particular, although there are no exogenous quotas in the model there is endogenously a sort of quota; more precisely, each agent has the same number of partners in every stable matching. Stable matchings also have the polarity property (supremum with respect to one side is identical to infimum with respect to the other side) and a property we call {\it complementarity}. Received: May 5, 2000; revised version: January 25, 2001