Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

On the structure of the set of fixed price equilibria

Working in the framework suggested by Drèze, this paper studies the number of fixed price equilibria and their continuity with respect to the price system. In an exchange economy, the concept of a rationing scheme is introduced, which specifies how shortages are shared among agents. For given utility functions and a given rationing scheme, under standard assumptions, an existence theorem is recalled, and it is shown that the graph of the equilibrium correspondence, when prices and initial endowments vary, is a piecewise continuously differentiable manifold. Moreover, generically, the number of equilibria for an economy, at given prices, is finite and the set of equilibria varies continuously with the price system and the initial endowments.     

Competitive equilibria in general choice spaces

This paper primarily demonstrates the existence of Arrow-Debreu equilibria in a general class of topological vector spaces of commodity bundles. Two conditions based on production possibilities, preferences, and the topological nature of bounded sets are shown to substitute, in any locally convex space, for the advantages of the Euclidean topology. Examples fulfilling these conditions are supplied. The approach is that of Bewley, demonstrating equilibria on finite dimensional sub-economies and establishing a net of these equilibria that converges to an equilibrium on the whole commodity space. An example of equilibrium with a storage technology is given. An auxiliary result concerns the price support of efficient allocations.     

Equilibria with coordination failures

This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

Spatial market equilibria with flow-dependent supply and demand: The single commodity case

Existence and uniqueness of spatial price equilibria are analyzed for a single commodity market network in which supply and demand levels are allowed to depend on commodity flows as well as market prices. This framework makes possible the explicit incorporation of flow-dependent shipment costs into market supply and demand functions. Moreover, since many quantity signals are also expressible as flow-dependent variables, it is possible to incorporate a number of recent models of supply and demand behavior which allow for quantity signals as well as price signals. In this context, the main result of the paper is to establish the existence of spatial price equilibria for such market networks under quite general conditions. In addition, certain uniqueness results are established for the case of arc-generated networks.     

Spanning with indexes

This paper presents several approximation theorems of a general contingent claim in terms of index options. We demonstrate that any contingent claim on the primitive securities in an infinite state economy can be approximated arbitrarily close by a portfolio of index options. In addition, these index options are associated with the same payout function, which belongs to a large and explicit class of one-variable measurable functions. I also characterize the layer structure of a general contingent claim.     

Equilibria in Banach lattices without ordered preferences

This paper establishes a very general result on the existence of competitive equilibria for exchange economies (with a finite number of agents) with an infinite-dimensional commodity space. The commodity spaces treated are Banach lattices, but no interiority assumptions on the positive cone are made; thus, the commodity spaces covered by this result include most of the spaces considered in economic analysis. Moreover, this result applies to preferences which may not be monotone, complete, or transitive; preferences may even be interdependent. Since preferences need not be monotone, the result allows for non-positive prices, and an exact equilibrium is obtained, rather than a free-disposal equilibrium.     

General consumption constraints and regular economies

In the spirit of Smale’s work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowments. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has a finite number of equilibria, which locally depend on endowments and possibility functions in a continuous manner.     

Pareto ordering of distributions

In this paper, the state of an economy is described by a production plan and a distribution on the product space of agents' characteristics and the commodity space. An ordering on the set of states will be introduced and after a study of the structure of this ordering it will be shown that the close relationship between price equilibria and optimal states remains true in this framework.     

Price functionals with bid–ask spreads: an axiomatic approach

In Jouini and Kallal [Jouini, E., Kallal, H., 1995. Martinagles and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1) 178-197], the authors characterized the absence of arbitrage opportunities for contingent claims with cash delivery in the presence of bid–ask spreads. Other authors obtained similar results for a more general definition of the contingent claims but assuming some specific price processes and transaction costs rather than bid–ask spreads in general (see for instance, Cvitanic and Karatzas [Cvitanic, J., Karatzas, I., 1996. Hedging and portfolio optimization under transaction costs: a martinangle approach. Mathematical Finance 6, 133-166]). The main difference consists of the fact that the bid–ask ratio is constant in this last reference. This assumption does not permit to encompass situations where the prices are determined by the buying and selling limit orders or by a (resp. competitive) specialist (resp. market-makers). We derive in this paper some implications from the no-arbitrage assumption on the price functionals that generalizes all the previous results in a very general setting. Indeed, under some minimal assumptions on the price functional, we prove that the prices of the contingent claims are necessarily in some minimal interval. This result opens the way to many empirical analyses.     

Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.     

Existence of equilibria with infinitely many consumers and infinitely many commodities: A theorem based on models of commodity differentiation

This paper presents a general result on the existence of competitive equilibria in exchange economies in which consumers and commodities are both infinite in number. The result shows that — in this framework at least — the added assumptions necessary to handle models with infinitely many agents are remarkably similar to the additional restrictions needed when only finitely many commodities are available for trade.It is shown that the results apply, in a straightforward manner, to two of the common models of consumer choice when commodity differentiation is an important consideration.     

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

The strong sequential core for two-period economies

The strong sequential core for two-stage economies with a possibly incomplete set of assets in period zero and trade in commodities in period one consists of those goods allocations that are in the classical core and moreover, after realization of the state of nature, in the core of the economy where executed asset contracts serve as initial endowments. The strong sequential core coincides with the classical core when all possible state-contingent contracts may serve as an asset. For finance economies it is shown that the strong sequential core is generically empty when there is an incomplete set of assets. Outside the setting of finance economies, we show that the strong sequential core can be empty even if there is a complete set of assets. If the set of constrained feasible allocations resulting from trading in assets, is enlarged to include also allocations outside the agents’ consumption sets, then a complete set of assets is sufficient for the equivalence of the resulting semi-strong sequential core and the classical core.     

Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

Equilibria in large economies with a separable Banach commodity space and non-ordered preferences

The purpose of this paper is to provide an existence result of equilibria for economies with a measure space of agents, a non-trivial production sector and an infinite dimensional commodity space. The commodity space is modeled by an ordered separable Banach space whose positive cone has a non-empty interior. The discretization approach proposed in this paper, allows us to extend the existence results in Khan and Yannelis [Equilibrium in markets with a continuum of agents and commodities. In: Khan, M.A., Yannelis, N.C. (Eds.), Equilibrium Theory in Infinite Dimensional Spaces. Springer, Berlin, 1991] and Podczeck [Economic Theory 9 (1997) 585] to economies with a non-trivial production sector and with possibly non-ordered but convex preferences as well as partially ordered (possibly incomplete) but non-convex preferences.     

The no-arbitrage condition and financial markets with heterogeneous information

This paper examines the role of the no-arbitrage condition in financial markets with heterogeneous expectations. We consider a single-period, state-contingent claims model, withM risky securities andS states. There exist two types of heterogeneously informed investors, where the information heterogeneity is defined with respect to either the security payoff matrix, the state probability vector, or state partitions. When the information heterogeneity is defined with respect to either the security payoff matrix or state partitions, the no-arbitrage condition imposes a constraint on the dispersion of information between informed and uninformed investors. Further, the no-arbitrage condition is useful in ascertaining the patterns of heterogeneity among investors that are consistent with equilibrium. However, when the information heterogeneity is defined with respect to state probabilities, the role of the no-arbitrage condition is severely restricted. Finally, the no-arbitrage condition may have important implications for the (necessary and sufficient) conditions for the existence of an equilibrium price vector in financial markets with heterogeneous expectations.     

Functional sunspot equilibria

Consider a one step forward looking model where agents believe that the equilibrium values of the state variable are determined by a function whose domain is the current value of the state variable and whose range is the value for the subsequent period. An agent’s forecast for the subsequent period uses the belief, where the function that is chosen is allowed to depend on the current realization of an extrinsic random process, and is made with knowledge of the past values of the state variable but not the current value. The paper provides (and characterizes) the conditions for the existence of sunspot equilibria for the model described.     

Price equilibria for markets with supply rigidities and demand heterogeneity

Price equilibria are studied for markets characterized both by supply rigidities and demand heterogeneity. Typical examples include rental housing markets in which vacancy rates remain close to zero over time. In such markets, where total demand and supply are essentially identical, the primary role of prices is to allocate available commodity types among consumer types. Hence the central objective of this paper is to establish conditions for the existence and uniqueness of such price-allocation equilibria. These general results are then applied to the types of random-utility specifications of demand which have most frequently been employed to model such markets.