Bertrand and Walras equilibria under moral hazard

We consider a simple model of competition under moral hazard with constant return technologies. We consider preferences that are not separable in effort: marginal utility of income is assumed to increase with leisure, especially for high income levels. We show that, in this context, Bertrand competition may result in positive equilibrium profit. This result holds for purely idiosyncratic shocks when only deterministic contracts are considered, and extends to unrestricted contract spaces in the presence of aggregate uncertainty. Finally, these findings have important consequences upon the definition of an equilibrium. We show that, in this context, a Walrasian general equilibrium a la Prescott-Townsend may fail to exist: any 'equilibrium' must involve rationing.

Collective labor supply with children

We extend the collective model of household behavior to allow for the existence of public consumption. We show how this model allows the analysis of welfare consequences of policies aimed at changing the distribution of power within the household. Our setting provides a conceptual framework for addressing issues linked to the "targeting" of specific benefits or taxes. We also show that the observation of the labor supplies and the household demand for the public good allow one to identify individual welfare and the decision process. This requires either a separability assumption or the presence of a distribution factor

Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

Hedonic pricing with quasi-linear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition (also known as a twist condition) the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match

Non-unitary Models of Household Behavior: A Survey of the Literature

This article considers non-unitary models of household behavior. These models suppose explicitly that households consist of a number of different members with preferences that are different from each other. They can be split up into two principal categories: cooperative (or collective) models, in which the allocations are supposed to be Pareto efficient; and non-cooperative (or strategic) models which are based on the concept of Cournot-Nash equilibrium. The demand functions that describe household behavior in these models are subject to constraints that differ from the traditional Slutsky conditions. In addition, in a certain number of specific cases, the preferences of the different household members can be identified from observable behavior.households, collective model, strategic model, testability, identification

Learning from a Piece of Pie: the Empirical Content of Nash Bargaining

Consider a model of bargaining, in which two players, 1 and 2, share a pie of size y. The bargaining environment is described by a set of parameters ? that may affect agents' preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither the agents' utilities nor their threat points. Assuming that the agents adopt a Nash bargaining solution, we investigate the empirical content of this assumption. We first show that in the most general framework, any outcome can be rationalized as a Nash solution. However, if (i) the size of the pie y does not influence the players' threat points and (ii) there exist (at least) two parameters ?1 and ?2 that are player-specific, in the sense that ?i does not influence the utility or the threat point of player j ? i, then Nash bargaining generates strong testable restrictions. Moreover, the underlying structure of the bargaining, i.e., the players' utility and threat point functions, can be recovered under slightly more demanding conditions.Bargaining game, Nash solution, Testability, Identifiability, Cardinal utility

Testing Contract Theory: A Survey of Some Recent Work

While the theoretical literature on contracts has been enormous since the seventies, empirical tests of the theory have long remained scarce. However, new empirical work has been developed in the last ten years that sheds light on the empirical validation of the theory. This paper aims at surveying the recent empirical work on contracts. The focus throughout is on the need to properly account for unobserved heterogeneity.

Relative Risk Aversion Is Constant: Evidence from Panel Data

Most classical tests of constant relative risk aversion (CRRA) based on individual portfolio composition use cross sectional data. Such tests must assume that the distributions of wealth and preferences are independent. We use panel data to analyze how individuals’ portfolio allocation between risky and riskless assets varies in response to changes in total financial wealth. We find the elasticity of the risky asset share to wealth to be small and statistically insignificant, supporting the CRRA assumption; this finding is robust when the sample is restricted to households experiencing ‘large’ income variations. Various extensions are discussed.-

Collective labour supply with children

We extend the collective model of household behavior to allow for the existence of public consumption. We show how this model allows to analyze welfare consequences of policies aimed at changing the distribution of power within the household. In particular, we claim that our setting provides an adequate conceptual framework for addressing issues linked to the ’targetting’ of specific benefits or taxes. We also show that the observation of the labor supplies and the household demand for the public good allow to identify individual welfare and the decision process. This requires either a separability assumption, or the presence of a distribution factor