Perturbed utility and general equilibrium analysis

We study general equilibrium theory of complete markets in an otherwise standard economy with each household having an additive perturbed utility function. Since this function represents a type of stochastic choice theory, the equilibrium of the corresponding economy is defined to be a price vector that makes its mean expected demand equal its mean endowment. We begin with a study of the economic meaning of this notion, by showing that at any given price vector, there always exists an economy with deterministic utilities whose mean demand is just the mean expected demand of our economy with additive perturbed utilities. We then show the existence of equilibrium, its Pareto inefficiency, and the upper hemi-continuity of the equilibrium set correspondence. Specializing to the case of regular economies, we finally demonstrate that almost every economy is regular and the equilibrium set correspondence in this regular case is continuous and locally constant.     

A sufficiency result for constrained economies

This paper presents a general sufficiency result for constrained economies. The result shows that, when an equilibrium allocation satisfies the first order necessary conditions for hybrid efficiency (a new type of constrained efficiency), there exists a marginal cost pricing equilibrium in an associated economy. If this equilibrium is Pareto efficient in the associated economy, then the original equilibrium allocation is hybrid efficient. Hence. the necessary conditions are also sufficient.     

On the role of government in a stochastically growing open economy

The relationship between the size of government, economic growth, and volatility in a small open economy is analyzed. First, we characterize the stochastic equilibrium for a centrally planned economy, contrasting it with a closed economy. The role of government consumption expenditure both as a stabilizing and a destabilizing factor is discussed. The optimal size of government is derived and we find that an open economy will have a larger government if and only if it is a net creditor. Second, the stochastic equilibrium in a decentralized economy is characterized and the optimal tax structure derived. Finally, the role of government production expenditure and its impact on risk is briefly discussed.     

Trends and cycles in small open economies: making the case for a general equilibrium approach

Economic research into the causes of business cycles in small open economies is almost always undertaken using a partial equilibrium model. This approach is characterized by two key assumptions. The first is that the world interest rate is unaffected by economic developments in the small open economy, an exogeneity assumption. The second assumption is that this exogenous interest rate combined with domestic productivity is sufficient to describe equilibrium choices. We demonstrate the failure of the second assumption by contrasting general and partial equilibrium approaches to the study of a cross-section of small open economies. In doing so, we provide a method for modeling small open economies in general equilibrium that is no more technically demanding than the small open economy approach while preserving much of the value of the general equilibrium approach.     

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.     

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.     

Can harmful events be another source of environmental traps?

This paper aims to present a new explanation for environmental traps through the presence of endogenous hazard rate. We show that adaptation and mitigation policies affect the occurrence of environmental traps differently. The former could cause environmental traps, whereas the latter could help society avoid such traps by decreasing the probability of a harmful event occurring. As a result, we present a new trade-off between adaptation and mitigation policies different than the usual dynamic trade-off that is highlighted in many studies and is crucial to developing countries. Contrary to the literature, when an economy is in a trap, an economy with a high environmental quality equilibrium tends to be more conservative in terms of resource exploitation than an economy with a low environmental quality equilibrium, which implies a heterogeneous reaction against the endogenous hazard rate.     

Approximate equilibrium in pure strategies for a two-stage game of asset creation

The paper studies a two-stage economy where consumers choose first the asset structure and then use it in a standard general equilibrium framework to transfer wealth across time and states of nature. The financial structure is chosen by maximizing indirect utility functions, using continuous random selections from the second-stage equilibrium correspondence. We depart from Bisin (J Econ Theory 82:19–45, 1998) where an endogenous beliefs approach was used and the asset creation was left to financial intermediaries. Moreover, our approach allows us to go beyond a mixed strategies result as we obtain an approximate equilibrium in pure strategies for the economy with incomplete information about future endowments.     

No-arbitrage condition and existence of equilibrium with dividends

In this paper we first give an elementary proof of existence of equilibrium with dividends in an economy with possibly satiated consumers. We then introduce a no-arbitrage condition and show that it is equivalent to the existence of equilibrium with dividends.     

Existence of a competitive equilibrium when all goods are indivisible

This paper investigates an economy where all consumption goods are indivisible at the individual level, but perfectly divisible at the overall level of the economy. In order to facilitate trading of goods, we introduce a perfectly divisible parameter that does not enter into consumer preferences — fiat money. When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce the rationing equilibrium concept and prove its existence. Unlike the standard Arrow–Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up, if the initial endowment of fiat money is dispersed, then a rationing equilibrium is a Walras equilibrium. This result implies the existence of a dividend equilibrium or a Walras equilibrium with slack.     

A simple proof of the existence of an equilibrium when the weak axiom holds

An elementary proof of the existence of a competitive equilibrium is given for economies where the weak axiom holds. It is shown by an induction argument on the number of goods that the problem is reduced to the question of the existence of an equilibrium in a two-good economy.     

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.     

Trading equilibrium in a public good economy with smooth preferences and a mixed measure space of consumers

Lindahl and Nash equilibria are often used in the theory of public good. Shitovitz and Spiegel (1998) present an example of 2-person economy with one private good and one pure public good, where the core efficient Lindahl allocation does not Pareto dominate the (inefficient) Nash allocation. In this paper we introduce the new concept of Trading equilibrium for a general public good economy with smooth preferences and a mixed measure space of consumers. We obtain that this economy admits a unique Trading equilibrium. Moreover, the Trading equilibrium induces a core allocation that strictly Pareto dominates the Nash allocation.     

The hybrid equilibria and core selection in exchange economies with externalities

This paper introduces a hybrid equilibrium concept that combines the elements of cooperative and non-cooperative behaviors in an exchange economy with externalities. For a fixed coalition structure (or a partition of traders), the hybrid equilibrium is a price and consumption bundle such that each coalition chooses a core solution from its budget set and the consumption bundles are feasible. It becomes the competitive equilibrium when the position is the finest, and it selects a core allocation when the partition is the coarsest. The paper provides sufficient conditions for the existence of a hybrid equilibrium for any coalition structure.     

Evolution in a General Equilibrium framework

In this paper, we consider a general equilibrium model in which the economies are characterized by the distribution of firms on a set of branches of production; we will show that based on the decisions of the managers of the firms, it is possible to build a dynamic system whose solutions reproduce the possible trajectories of the economy. Once the initial state of an economy is known, that is, the initial distribution of firms, we will have a unique solution for this dynamic system, which will coincide with the evolution of the economy, that is, the evolution of prices and equilibrium allocations.The investment decisions of the administrators of the companies will change the distribution over the set of existing productive branches, which in turn will produce changes in the wealth of consumers who are also shareholders of the companies and then as a consequence, their demand will change, and therefore the equilibrium allocations and prices will too.In most cases, these decisions lead to an improvement in the efficiency of the productive side of the economy and an increase in the welfare of the economy as a whole, but, as we will show, under some particular circumstances, even when it comes to rational decisions from the point of view of administrators, this can lead to undesirable repercussions on the welfare of consumers. Besides, in a neighborhood of a critical economy, even when these decisions may involve small changes in the distribution of companies, they can cause abrupt and unexpected changes in the behavior of the economy, or in other words, they can cause an economic crisis. These are characterized by large changes in the prices, in the demand, and in the supply of goods. In contrast, in a sufficiently small neighborhood of a regular economy, small changes in the distribution of firms produced by the investment decisions of managers do not lead to large changes in the subsequent behavior of the economy. We will exemplify these statements with several numerical examples.     

Equilibria in markets with a Riesz space of commodities

We present a new proof of the existence of competitive equilibrium for an economy with an infinite dimensional space of commodities.     

Competitive General Equilibrium with network externalities

We identify sufficient conditions for existence of competitive equilibrium with network externalities and indivisibilities. Such combination of externalities and indivisibilities is present in many goods and services with network effects, and it makes existence of equilibrium non-trivial. We provide an existence theorem in a model with a measure space of consumers. Key conditions for existence are anonymity of network effects and dispersion in the economy’s income distribution.     

Uniqueness of competitive equilibrium with solvency constraints under gross-substitution

Under a gross substitution assumption, we prove existence and uniqueness of competitive equilibrium for an infinite-horizon exchange economy with limited commitment and complete financial markets. Risk-sharing is limited as only a part of the private endowment can be used as collateral to secure debt. The unique equilibrium is Markovian with respect to a minimal state space consisting of exogenous shocks and Negishi’s welfare weights. We represent equilibrium dynamics via a monotone operator acting on entire wealth distribution functions. We construct a fixed point of this operator generating a lower and an upper orbit and proving coincidence of accumulation points.     

Equilibrium price dynamics in an overlapping-generations exchange economy

An extension to the Yaari (1965)–Blanchard (1985) continuous time overlapping generations model for an endowment Arrow–Debreu economy with an age-structured population is presented. It is proved that Arrow–Debreu equilibrium prices are represented by a double linear integral equation, and depend on the age-distributions of population and endowments. For an economy with a balanced growth, and logarithmic utility, we prove that bubbles may exist if endowments are distributed earlier than some critical age.     

Fiscal policies in open cities with firms and households

This paper provides an equilibrium numerical model of an open city economy with mobile firms and resident workers. Given household preferences and firm technologies and an exogenous configuration of city tax rates and national grants and fiscal mandates, the model calculates equilibrium values for aggregate city economic activity, factor prices, and finally, local tax bases, revenues, and public goods provision. The model is calibrated to the Philadelphia economy for Fiscal Year 1998. We then explore the economic and fiscal consequences of raising city tax rates and the city’s ability to finance rising local welfare payments. We find the city to be incapable of bearing significant increases in local responsibility for welfare transfers.