Core equivalence and welfare properties without divisible goods

We study an economy where all goods entering preferences or production processes are indivisible. Fiat money not entering consumers’ preferences is an additional perfectly divisible parameter. We establish a First and Second Welfare Theorem and a core equivalence result for the rationing equilibrium concept introduced in Florig and Rivera (2005a). The rationing equilibrium can be considered as a natural extension of the Walrasian notion when all goods are indivisible at the individual level but perfectly divisible at the level of the entire economy.     

Competitive equilibria in economies with multiple indivisible and multiple divisible commodities

In this paper we consider a general equilibrium model with a finite number of divisible and a finite number of indivisible commodities. In models with indivisibilities it is typically assumed that there is only one divisible good, which serves as money. The presence of money in the model is used to transfer the value of certain amounts of indivisible goods. For such economies with only one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity. For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model.     

Existence and description of housing market equilibrium

A rental housing market with finite numbers of non-identical consumers and indivisible housing units, each composed of a vector of attributes, is studied. A partial equilibrium, open city analysis is presented in which all other commodities are perfectly divisible and elastically supplied on national markets. Sufficient conditions for the existence of an equilibrium are rigorously established using a fixed point argument that is based on a bidding arrangement between agents. It is then shown that, although the set of equilibria is not a singleton, all equilibria are similar enough to ensure a strong resemblance between open and closed cities.     

Bankruptcy and optimality in a closed trading mass economy modelled as a non-cooperative game

In this paper we establish the existence of (a) an optimal bankruptcy rule which enables us to describe the Walrasian trading economy as a game with trade in fiat money; and (b) non- cooperative equilibrium points of this game which (in terms of prices and the final allocation yielded) include the competitive equilibrium points, and the accompanying money rate of interest (induced by borrowing at a central bank), when the bankruptcy rule is different from optimal.     

Erratum to “Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only” [J. Math. Econ. 41 (4–5) (2005) 571–601]

We consider a pure exchange economy with a continuum of agents and finitely many indivisible commodities. Every commodity can be consumed only in integer amounts. Thus, agents’ preferences are locally satiated and no commodity bundle has necessarily local cheaper points. We introduce a core which is an intermediate concept between the strong core and the weak core. In our economy, this core is the most natural concept in the sense that it coincides with the set of all exactly feasible Walras allocations.     

Stochastic processes of temporary equilibria

It is the aim of the paper to study within the framework of an ‘overlapping generation model’ the evolution of temporary equilibria. At date t, there are ‘newborn’ agents and ‘old’ agents who were born in previous periods; the old agents hold cash balances (fiat money) that they carried over from the previous period. At the beginning of period t, all agents receive a random endowment of consumption goods. Then the agents exchange these endowments and money on spot markets at date t (trading in future markets is not considered). Once a temporary equilibrium is reached, the economy move to the next date. Agents who were born at date t then become old and meet agents born at period t+1.It is shown that the evolution of temporary equilibria in this model leads to analyse the ergodic properties of a certain class of Markov processes with stationary transition probability.     

Inflationary equilibrium in a stochastic economy with independent agents

We prove the existence of stationary monetary equilibrium with inflation in a “Bewley” model with constant aggregate real variables but with idiosyncratic shocks to the endowments of a continuum of individual agents, when a central bank stands ready to borrow or lend fiat money at a fixed nominal rate of interest and the agents face borrowing constraints. We also find that, in the presence of real micro uncertainty about individual endowments, the rate of inflation is higher (equivalently, the real rate of interest is lower) than it would be in a “certainty-equivalent economy”; to wit, one in which every agent’s endowment is replaced by its expected value. Thus, underlying microeconomic uncertainty and borrowing constraints are shown to generate additional inflation.     

Supply-constrained fixed price equilibria in monetary economies

In this paper we consider an economy with restrictions on the relative prices of non-money commodities. The non-money commodities are partitioned into two groups, index makers and price following commodities. Then two cases are considered, namely that the relative prices of the index makers are fixed, respectively free. In both cases the money prices are flexible, whereas the relative prices of the price following commodities are tied to the prices of the index makers. The existence of a supply-constrained equilibrium is proved with (i) no rationing on the money commodities (stores of value), and (ii) at least one non-money commodity is not rationed. If prices of the index makers are fixed the result strengthens a theorem of Dehez and Drèze, if the prices are free a theorem of Kurz is strengthened. This paper is not only concerned with these existence results, but also with the question whether supply-constrained equilibria should appear more frequently than demand-constrained equilibria.     

Natural oligopolies with exogenous sunk costs: A non-Suttonian result

In a spatial competition model with exogenous fixed costs and divisible goods, we obtain non-Suttonian results. When the economy is infinitely replicated, the number of firms does go to infinity but, as consumers’ income goes to infinity, the equilibrium number of firms tends toward a finite value. This occurs because the global demand to each firm becomes in the limit infinitely sensitive to price differentials since they give then rise to infinitely large differences in purchase expenditure.     

An existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy

We establish an existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani’s fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.     

Equilibrium theory with a measure space of possibly satiated consumers

Walras equilibria may not exist when consumers’ preferences are possibly satiated. To overcome this difficulty, several extended notions of equilibria have been proposed and all reduce to Walras equilibria under nonsatiation and free disposal. This includes the notions of equilibria with slack (also called dividend equilibria) as by Drèze and Müller [J. Economic Theory 23 (1980) 131], Makarov [J. Mathematical Economics 8 (1981) 87], Aumann and Drèze [Econometrica 54 (1986) 1271], Mas-Colell [Equilibrium theory with possibly satiated preferences, in: Majumdar, M. (Ed.), Proceedings of the Essays in Honour of David Gale on Equilibrium and Dynamics, Macmillan, London, pp. 201–213], monetary equilibria as by Kajii [J. Mathematical Economics 25 (1996) 75], or weak equilibria as by Polemarchakis and Siconolfi [J. Mathematical Economics 22 (1993) 85], which are all defined when there are finitely many consumers. This includes also the notion of free disposal equilibrium, when markets clear in a weak sense, allowing free disposal. Our paper considers an economy with a measure space of consumers and provides a general existence result of equilibria for the various existing notions. This result extends in particular the result by Hildenbrand [Econometrica 38 (1970) 608] on the existence of Walras equilibria.     

A graph theoretic approach to markets for indivisible goods

Many important markets, such as the labor market and the housing market, involve goods that are both indivisible and of budgetary significance. We introduce new graph theoretic objects ideally suited to analyzing such markets. We show that the minimum equilibrium price is characterized by a certain optimization problem on these graph theoretic objects.     

Voluntary contributions to multiple public goods in a production economy with widespread externalities

In a production economy, multiple public goods are produced by firms in competitive markets, and provided by the government together with contributions from consumers. There are widespread externalities: all consumers’ consumption and contributions and all firms’ production enter into utility functions. Public goods can be imperfect substitutes or complements, and they can be local public goods or club goods. Zero bounds that require consumers to make nonnegative contributions complicate the differentiable approach. Applying the transversality theorem for smooth economies in a regular parameterization, we obtain the existence of equilibrium in such an economy, and generically equilibria are regular and locally unique.     

Spatial differentiation,divisible consumption and the pro-competitive effect of income

We analyze a spatial differentiation model with divisible consumption under one-stop shopping. Each consumer who visits only one store, chooses the quantities of the goods which maximize his/her utility function under the budget constraint (namely consumption expenditures must equal income minus transportation costs), choosing the store which provides him/her with the largest indirect utility. We derive the equilibrium price when the firms are located at the two extremities of Hotelling’s linear city and show that income increases have a pro-competitive effect.     

Equilibrium theory under ambiguity

We extend the classical results on the Walras–core existence and equivalence to an ambiguous asymmetric information economy; that is, an economy where agents maximize Maximin Expected Utility (MEU). The interest of considering ambiguity arises from the fact that, in the presence of MEU decision making, there is no conflict between efficiency and incentive compatibility (contrary to the Bayesian decision making). Our new modeling of an ambiguous asymmetric information economy necessitates new equilibrium notions, which are always efficient and incentive compatible.     

Stationary Markovian equilibrium in overlapping generation models with stochastic nonclassical production and Markov shocks

This paper provides new sufficient conditions for the existence and computation of Markovian equilibrium for a large class of OLG models with Markov shocks to production. The economies considered allow for a very large class of “reduced-form” production functions, including those that are nonclassical, encompassing stochastic OLG models with social security, income redistribution policies, taxation, valued fiat money, production nonconvexities, and monopolistic competition. Our approach combines aspects of both topological and order theoretic fixed point theory and provides globally stable successive approximations algorithms for computing extremal Markovian equilibrium objects.     

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.     

Between Wicksell and Hayek

A bstract Mises' Theory is grounded on the "ultra-Wicksellian" idea that the pure credit system represents the working of a modern monetary economy, and that forcing banks to raise the rate of money interest does not need to operate through some binding bank-liquidity constraint. It is the rise in the relative price of consumption goods against production goods that accounts for the end of inflation. According to Mises, it is in the power of the banks to resist this readjustment; in this event, the only end to hyperinflation comes from the breaking of the monetary system. Hayek develops the second side of Mises'argument, the capital-allocation effect, while the first side, the ultra-Wicksellian picture of the monetary economy, is either weakened or taken for granted. Wicksell's 1914 reaction to Mises'book is recalled. Some criticism of Mises'readjustment mechanism from a Keynesian-Schumpeterian point of view is offered in the concluding remarks.     

Comparative statics in markets for indivisible goods

This paper builds upon Caplin and Leahy (2014), which introduced a new mathematical apparatus for understanding allocation markets with nontransferable utility, as such covering the housing market and other markets for large indivisible goods. In the current paper we complete the study of comparative statics initiated therein. We introduce homotopy methods to characterize how equilibrium changes in response to arbitrary parameter changes. Generically, we show that there can be five and only five qualitatively distinct forms of market transition: Graft; Prune and Plant; Prune and Graft; Cycle and Reverse; and Shift and Replant. Our path-following methods identify new algorithms for computing market equilibria.     

Anonymous price taking equilibrium in Tiebout economies with a continuum of agents: Existence and characterization

We introduce a model of a local public goods economy with a continuum of agents and jurisdictions with finite but unbounded populations, where the set of possible projects for each jurisdiction/club is unrestricted in size. Under boundedness of per capita payoffs, which simply ensures that equal treatment payoffs are bounded above, we apply results of Kaneko and Wooders (1986) to obtain nonemptiness of the core of the economy. We then demonstrate, under the stronger condition of strict small group effectiveness, that the equal treatment core coincides with the set of price-taking equilibrium outcomes with anonymous prices—that is, prices for public goods depend only on observable characteristics of agents. Existence of equilibrium follows from nonemptiness of the core and equivalence of the core to the set of equilibrium outcomes. Our approach provides a new technique for showing existence of equilibrium in economies with a continuum of agents.