On the uniqueness of local equilibria

The purpose of this paper is to define a new notion of local equilibrium in an exchange economy, where the consumers face lower bounds on net trades. Then, we show that the local equilibrium is unique if the lower bounds are closed enough to 0. By the way, we also provide a convergence result of local equilibrium price toward Walras equilibrium price of a suitable tangent linear economy.     

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.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Slack in incomplete markets with nominal assets: A symmetric proof

In this paper, we provide an equilibrium analysis in the framework of incomplete markets where some agents’ preferences are possibly satiated at some state of the nature. We will consider nominal assets with exogenously fixed asset prices. We extend the notion of equilibrium with slack – introduced by Drèze and Müller [Drèze, J., Müller, H., 1980. Optimality properties of rationing schemes. Journal of Economic Theory 23, 150–159] in a fixed price setting – to the GEI framework.     

No unbounded arbitrage,weak no market arbitrage and no arbitrage price system conditions; Equivalent conditions

Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162] prove that the no unbounded arbitrage (NUBA), a special case of a condition in Page [Page, F.H., 1987. On equilibrium in Hart’s securities exchange model. Journal of Economic Theory 41, 392–404], is equivalent to the existence of a no arbitrage price system (NAPS) when no agent has non-null useless vectors. Allouch et al. [Allouch, N., Le Van, C., Page F.H., 2002. The geometry of arbitrage and the existence of competitive equilibrium. Journal of Mathematical Economics 38, 373–391] extend the NAPS introduced by Werner [Werner, J., 1987. Arbitrage and the existence of competitive equilibrium. Econometrica 55, 1403–1418] and show that this condition is equivalent to the weak no market arbitrage (WNMA) of Hart [Hart, O., 1974. On the existence of an equilibrium in a securities model. Journal of Economic Theory 9, 293–311]. They mention that this result implies the one given by Page and Wooders [Page Jr., F.H., Wooders, M., 1996. A necessary and sufficient condition for compactness of individually rational and feasible outcomes and existence of an equilibrium. Economics Letters 52, 153–162]. In this note, we show that all these conditions are equivalent.     

Satiation and existence of competitive equilibrium

In this paper, we introduce a new assumption concerning the (non)satiation property of preferences and establish the existence of a competitive equilibrium under it. The assumption is weaker than the standard nonsatiation assumption and “weak nonsatiation” introduced by Allouch and Le Van (2008). In particular, it allows preferences to be satiated only inside the set of individually rational feasible consumptions, while the two nonsatiation assumptions do not. It is also worth noting that just like the two nonsatiation assumptions, our new assumption depends solely on the characteristics of consumers.     

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.     

Direct perturbations of aggregate excess demand

We complement the Sonnenschein–Mantel–Debreu results by establishing that an exchange economy, i.e., preferences and endowments, that generates a given aggregate excess demand (AED) function is close to the economy that generates a perturbation of this AED. As a consequence, genericity and determinacy results obtained by direct perturbation of an AED are as strong as results obtained by perturbing preferences and endowments.     

The Jevons double coincidence condition and local uniqueness of money: An example

Jevons’s double coincidence of wants condition is derived as the result of household level transaction costs in general equilibrium where N   commodities are traded at (1/2)N(N−1)$(1/2)N(N-1)$ commodity-pairwise trading posts. Each household experiences a set-up cost on entering an additional trading post. Budget constraints are enforced at each trading post separately implying demand for a carrier of value between trading posts, commodity money. General equilibrium consists of prices so that each trading post clears. Existence and local uniqueness of commodity money in equilibrium can follow from the scale economy implied by the household set-up cost.     

Equilibrium in a mixed economy of arrow-debreu type

The functioning of the current NIS economies is severely affected by regulatory interferencies with supply and demand for many commodities. In particular, the presence of dual markets is characteristic for these economies. On the first market, typically the “low-price sector” of the economy, prices are fixed and the allocation of goods is determined by rationing schemes and governmental orders. On the second market, flexible prices resulting from the market mechanism coordinate demand and supply. It is allowed that any surplus of good purchased on the first market can be sold on the second market at the then prevailing market prices.     

An index formula for production economies with externalities

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)^L−1${(-1)}^{L-1}$ where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.     

Club theory and household formation

The relationship between our general equilibrium model with multi-member households and club models with multiple private goods is investigated. The main distinction in the definitions consists in the equilibrium concepts. As a rule, competitive equilibria among households where no group of consumers can benefit from forming a new household and valuation equilibria prove equivalent in the absence of consumption externalities, but not in their presence.     

Excess demand function around critical prices in incomplete markets

We show that the aggregate excess demand function in an economy with incomplete real asset markets can be characterized by Walras’ law, homogeneity, and continuity around critical prices that cause one-dimensional drop of the dimension of the budget set.     

A family production overlapping generations economy

This paper provides a theoretical analysis of an overlapping generations economy in which production decisions and input–output allocations are all carried out at the family level. I consider a single class of output allocation schemes and various degrees of knowledge about the production technology. Under complete knowledge, I show that a family organizational structure in which everyone receives his marginal contribution to output, invests less in physical capital than under a perfectly competitive equilibrium environment. Under incomplete knowledge, I analyze and compare how beliefs about the input–output relationship affect the physical capital accumulation dynamics and the long-run standards of living.     

Extreme points of two digraph polytopes: Description and applications in economics and game theory

In this paper, we introduce two polytopes that respect a digraph in the sense that for every vector in the polytope every component corresponds to a node and is at least equal to the component corresponding to each successor of this node. The sharing polytope is the set of all elements from the unit simplex that respect the digraph. The fuzzy polytope is the set of all elements of the unit cube respecting the digraph. The main results are characterizations of the extreme points of the above described two digraph polytopes. We also give an economic application of the result on the sharing polytope and a game-theoretical application for the fuzzy polytope.     

Intertemporal coordination in two-period markets

This paper studies the stability of the intertemporal coordination dynamics when the common knowledge of individual expectations of future prices is perturbed in a neighborhood of a perfect foresight equilibrium. The main forces that affect stability are: (i) the effect of a change in asset demand on second period spot market prices, and (ii) the effect on asset demand of a small change in second period prices. In an intertemporal market game whose interior Markov perfect equilibria correspond to perfect foresight equilibria, it is shown that though M-rationalizability implies the stability of the intertemporal dynamics, the converse is not always true.     

Instability in the cobweb model under the BNN dynamic

The cobweb model where firms choose between rational and naive forecasting strategies has a 2-cycle when the slope of supply is greater than the slope of demand for a number of different dynamics describing the evolution of strategy choices. This paper proves that the 2-cycle is exponentially unstable under the learning dynamic of Brown et al. (1950). Issues arising in the analysis of piecewise smooth discrete time maps are discussed.     

Geodesics on the equilibrium manifold

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.