Coasian equilibrium

We consider a general equilibrium economy with public goods and externalities. Following Boyd and Conley (1997), we treat externality markets directly instead of indirectly through Arrovian commodities. Because such direct externality markets are not subject to the nonconvexities that Starrett [Starrett, D., 1972. Fundamental nonconvexities in the theory of externalities. Journal of Economic Theory 4, 180–199] shows are fundamental to Arrow’s externality markets, this new approach admits the use of largely standard methods to prove welfare and existence theorems in an economy with externalities. We extend the Boyd and Conley model to allow firms to benefit from public goods and be damaged by externalities, and to allow consumers to produce externalities. We state a first welfare theorem and prove the existence of a competitive equilibrium. Taken together, this can be viewed as a type of general equilibrium Coase theorem. Considered as a special case, these theorems also represent a significant generalization of existing results for pure public goods economies.     

Wealth concerns and equilibrium

Most properties of the classical general equilibrium model without externalities fail to extend to the wildest forms of consumption externalities. The recent interest for wealth concerns, a kind of externality associated with herding behavior and other-regarding preferences, motivates a study of the general equilibrium exchange model with those externalities. The diffeomorphism of the equilibrium manifold with a Euclidean space, the smoothness and properness of the natural projection and its non-zero degrees are shown to hold true for endowment spaces with variable total resources. Other properties of the classical exchange model without externalities are fragile in the sense that they do not resist the introduction of wealth concerns even in models where consumers preferences are represented by the simplest forms of utility functions like the log-linear (or Cobb–Douglas) functions. The most notable fragile properties are the uniqueness and regularity of equilibrium at equilibrium allocations and the stability of no-trade equilibria.     

On the robustness of the competitive equilibrium: Utility-improvements and equilibrium points

We show that the set of competitive equilibrium points of a pure exchange economy are the equilibrium points of a broader class of better-response demands than the usual utility-maximizing demand functions. The better-response demands are derived from assigning weights to all commodity bundles with higher utility than the current commodity bundle, with the greatest weights being placed on the commodity bundles with the highest utility gain. The usual utility-maximizing demand functions are then those in which the weight on the utility-maximizing bundle is one. We also show that these better-response demands belong to a large class of response maps that are generated by monotonic transformations of the utility functions and/or monotonic transformations of the weights assigned to the commodity bundles.     

Impatience and equilibrium indeterminacy

This paper extends the neoclassical one-sector optimal growth model by postulating that individual agents’ time preference (impatience) depends on the economy-wide average consumption and average income, which are social factors taken as external by individual agents. The paper shows that with the socially determined individual time preference local equilibrium indeterminacy can arise. Moreover, local indeterminacy can also be associated with global indeterminacy in many cases. The results hold in models with bounded and unbounded growth.     

Piecewise linear exchange equilibrium

It is known that if a pure exchange model in which all consumers have linear utility functions has an equilibrium it has one which is rational in the initial data. Examples show on the other hand that this is no longer true in general if utility functions are merely piecewise linear. In this note we observe that for the case of two traders the rationality result carries over and we sketch a finite procedure for calculating the equilibrium.     

Strategic Ramsey equilibrium dynamics

We study strategic Ramsey equilibria. First, we give necessary and sufficient conditions for a stationary equilibrium point to exist where only the most patient household owns capital. We develop the dynamics of strategic Ramsey equilibrium trajectories when the turnpike property holds and there is a stationary equilibrium with only the most patient household owning capital. We conclude by showing there is a class of economies for which the turnpike property obtains.     

An optimistic search equilibrium

We study a market search equilibrium with aggregate uncertainty, private information and heterogeneous beliefs that are initially optimistic. Despite these biased beliefs, it is shown that all optimistic equilibria converge to perfect competition in the limit as the time between matches tends to 0.     

General equilibrium in CLO markets

We address a two-period equilibrium model with securitization of collateral-backed promises. Borrowers may suffer extra-economic default penalties and debts are pooled into collateralized loans obligations (CLO), allowing different seniority levels among tranches in a same CLO.     

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.     

Risk premia in general equilibrium

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.     

Ramsey equilibrium with liberal borrowing

This paper considers a multi-agent one-sector Ramsey equilibrium growth model with borrowing constraints. The extreme borrowing constraint used in the classical version of the model, surveyed in Becker (2006), and the limited form of borrowing constraint examined in Borissov and Dubey (2015) are relaxed to allow more liberal borrowing by the households. A perfect foresight equilibrium is shown to exist in this economy. We describe the steady state equilibria for the liberal borrowing regime and show that as the borrowing regime is progressively liberalized, the steady state wealth inequality increases. Unlike the case of a limited borrowing regime, an equilibrium path need not converge in the case of liberal borrowing regime. We show through an example that a two period cyclic equilibrium exists when agents are allowed to borrow against their two period future wage income. This result is similar to the possibility of non-convergent equilibrium capital stock sequences in the model with no borrowing.     

Inequity-averse preferences in general equilibrium

We study the stability with respect to the introduction of opportunity-based inequity aversion à la Dufwenberg et al. (2011) of three welfare properties satisfied by competitive equilibria in self-regarding economies: (i) Pareto efficiency may not be a stable property; (ii) undomination with respect to income redistribution is a stable property whenever the marginal indirect utility of income has no extreme variations; and (iii) generically (endowment-wise) market-constrained efficiency is a stable property.     

Population equilibrium in primitive societies

The aboriginal distribution of population in North America is found not to be positively related to the richness of the natural environment, contrary to the predictions of the Malthusian model, the dominant one in Anthropology. Great abundance of some resources can encourage nomadism or raise the productivity of women, two determinants of the cost of children, which I find are associated with, lower aboriginal population density among a sample of tribes of North American Indians.     

International monetary equilibrium with default

We present an integrated framework for the study of the international financial economy with trade, fiat money, monetary and fiscal policy, endogenous default and regulation. Money is introduced via a cash-in-advance requirement and real trade is endogenous. The standard international finance pricing results obtain. Market incompleteness and positive default in equilibrium allow for the study of the transmission of default through the international financial markets and imply a positive role for policy. Finally, we present an example where, due to the trade-off between the non-pecuniary cost of default and the resulting allocation, a Pareto improvement occurs following an increase in interest rates.     

Two definitions of correlated equilibrium

Correlated equilibrium constitutes one of the basic solution concepts for static games with complete information. Actually two variants of correlated equilibrium are in circulation and have been used interchangeably in the literature. Besides the original notion due to Aumann (1974), there exists a simplified definition typically called canonical correlated equilibrium or correlated equilibrium distribution. It is known that the original and the canonical version of correlated equilibrium are equivalent from an ex-ante perspective. However, we show that they are actually distinct – both doxastically as well as behaviourally – from an interim perspective. An elucidation of this difference emerges in the reasoning realm: while Aumann’s correlated equilibrium can be epistemically characterized by common belief in rationality and a common prior, canonical correlated equilibrium additionally requires the condition of one-theory-per-choice. Consequently, the application of correlated equilibrium requires a careful choice of the appropriate variant.     

Monotonic matching in search equilibrium

It is well-known from Becker’s [Becker, G., 1973. A theory of marriage, Part I. Journal of Political Economy 81, 813–846] analysis of the neoclassical marriage market that matching is positive assortative if agent-types are complements in household production. Shimer and Smith [Shimer, R., Smith, L., 2000. Assortative matching and search. Econometrica 68, 343–369] have shown that this result does not generally extend to markets with search frictions, and they provide additional conditions on the production function that guarantee assortative matching in these settings. Here, the relationship between the Shimer–Smith restrictions and equilibrium matching pattern is considered, and alternative proofs of their results on assortative matching are provided.     

Multilateral bargaining and Walrasian equilibrium

A class of bargaining games in which agents bargain over prices and maximum trading constraints is considered: It is proved that all the Stationary Subgame Perfect Equilibria of these games implement Walrasian allocations as the bargaining frictions vanish. The result holds for any number of agents and is robust to different specifications of the bargaining process.     

General equilibrium and optimal taxes

It is shown that if subsidies are not excessive, there exists a general competitive equilibrium in the presence of a complex tax structure. Furthermore, under certain continuity assumptions, a tax structure which is optimal from the social point of view can be determined. Procedures maximize quasi-concave after tax profit functions. Consumers have convex budget sets reflect- ing their income from sales and profits minus taxes on fixed income and progressive sales taxes. Their preferences are interdependent, intransitive and incomplete. The government provides public goods and determines the optimal tax regime on the basis of its preferences on the final competitive consumption allocation.