The Structure of Equilibrium in an Asset Market with Variable Supply

This note presents new results on existence of rich Fubini extensions. The notion of a rich Fubini extension was recently introduced by Sun (2006) and shown by him to provide the proper framework to obtain an exact law of large numbers for a continuum of random variables. In contrast to the existence results for rich Fubini extensions established by Sun (2006), the arguments in this note don’t use constructions from nonstandard analysis.

Informative Voting and the Samuelson Rule

We study the classical free-rider problem in public goods provision in a large economy with uncertainty about the average valuation of the public good. Individual preferences over public goods are shaped by a skill and a taste parameter. We use a mechanism design approach to solve for the optimal utilitarian provision rule. The relevant incentive constraints for information aggregation ensure that individuals behave as if they were engaging in informative voting over the level of public good provision. It is shown that the use of information by an optimal provision rule is inversely related to the polarization of preferences which results from the properties of the skill distribution

Finitely additive representation of Lp spaces

AbstractLet λ¯ be any atomless and countably additive probability measure on the product space {0,1}N with the usual σ-algebra. Then there is a purely finitely additive probability measure λ on the power set of a countable subset T⊂T¯ such that Lp(λ¯) can be isometrically isomorphically embedded as a closed subspace of Lp(λ). The embedding is strict. It is also ‘canonical,’ in the sense that it maps simple and continuous functions on T¯ to their restrictions to T

A Theory of Continuum Economies with Independent Shocks and Matchings

Numerous economic models employ a continuum of negligible agents with a sequence of idiosyncratic shocks and random matchings. Several attempts have been made to build a rigorous mathematical justification for such models, but these attempts have left many questions unanswered. In this paper, we develop a discrete time framework in which the major, desirable properties of idiosyncratic shocks and random matchings hold. The agents live on a probability space, and the probability distribution for each agent is naturally replaced by the population distribution. The novelty of this approach is in the assumption of unknown identity. Each agent believes that initially he was randomly and uniformly placed on the agent space, i.e., the agent's identity (the exact location on the agent space) is unknown to the agent.random matching, idiosyncratic shocks, the Law of Large Numbers, aggregate uncertainty, mixing

A Theory of Continuum Economies with Idiosyncratic Shocks and Random Matchings

Many economic models use a continuum of negligible agents to avoid considering one person's effect on aggregate characteristics of the economy. Along with a continuum of agents, these models often incorporate a sequence of independent shocks and random matchings. Despite frequent use of such models, there are still unsolved questions about their mathematical justification. In this paper we construct a discrete time framework, in which major desirable properties of idiosyncratic shocks and random matchings hold. In this framework the agent space constitutes a probability space, and the probability distribution for each agent is replaced by the population distribution. Unlike previous authors, we question the assumption of known identity - the location on the agent space. We assume that the agents only know their previous history - what had happened to them before, - but not their identity. The construction justifies the use of numerous dynamic models of idiosyncratic shocks and random matchings.random matching; idiosyncratic shocks; the Law of Large Numbers; aggregate uncertainty; mixing

Informative Voting and the Samuelson Rule

We study the classical free-rider problem in public goods provision in a large economy with uncertainty about the average valuation of the public good. Individual preferences over public goods are shaped by a skill and a taste parameter. We use a mechanism design approach to solve for the optimal utilitarian provision rule. The relevant incentive constraints for information aggregation ensure that individuals behave as if they were engaging in informative voting over the level of public good provision. It is shown that the use of information by an optimal provision rule is inversely related to the polarization of preferences which results from the properties of the skill distribution.information aggregation; informative voting; public goods; two-dimensional heterogeneity

Optimal Income Taxation and Public Good Provision in a Two-Class Economy

This paper combines the problem of optimal income taxation with the free-rider problem in public good provision. There are two groups of individuals with private information on their earning ability and their valuation of a public good. Adjustments of the transfer system are needed to discourage the more productive from exaggerating the desirability of public good provision. Similarly, the less productive need to be prevented from understating their valuation. Relative to an optimal income tax, which focuses solely on earning ability, income transfers are increased whenever a public good is installed and are decreased otherwise

What Goods Do Countries Trade? New Ricardian Predictions

Though one of the pillars of the theory of international trade, the extreme predictions of the Ricardian model have made it unsuitable for empirical purposes. A seminal contribution of Eaton and Kortum (2002) is to demonstrate that random productivity shocks are sufficient to make the Ricardian model empirically relevant. While successful at explaining trade volumes, their model remains silent with regards to one important question: What goods do countries trade? Our main contribution is to generalize their approach and provide an empirically meaningful answer to this question.

Collectively Incentive Compatible Tax Systems

This paper assumes that individuals possess private information both about their abilities and about their valuation of a public good. Individuals can undertake collective actions on order to manipulate the tax system and the decision on public good provision. Consequently, an implementable scheme of taxation has to be collectively incentive compatible. If preferences are additively separable, then an implementable tax systems has the following properties: (i) tax payments do not depend on public goods preferences and (ii) there is no scope for a collective manipulation of public goods preferences. For a quasilinear economy, the optimal tax system is explicitly characterized.Optimal Taxation, Public Good Provision, Revelation of Preferences, Information Aggregation

Optimal Democratic Mechanisms for Taxation and Public Good Provision

We study the interdependence of optimal tax and expenditure policies. An optimal policy requires that information on preferences is made available. We first study this problem from a general mechanism design perspective and show that efficiency is possible only if the individuals who decide on public good provision face an own incentive scheme that differs from the tax system. We then study democratic mechanisms with the property that tax payers vote over public goods. Under such a mechanism, efficiency cannot be reached and welfare from public good provision declines as the inequality between rich and poor individuals increases.Public goods, optimal taxation, two-dimensional heterogeneity, asymmetric information