Income Taxation when Markets are Incomplete

We investigate the welfare effects of proportional income taxation in a standard general equilibrium model with incomplete markets (GEI). Formally, our analysis is on the allocative effects of state-contingent income tax reforms. Tax reforms are restricted to be anonymous, publicly and truthfully announced before markets open, and they are required to result in an ex-post constrained efficient allocation. Our main result is to show that there do typically exist contingent tax reforms that are Pareto improving. These reforms, acting directly on the asset span, modify private risk sharing opportunities. Thus, unlike most of the GEI literature, the type of policy transmission mechanism considered does not rely on, second order, relative spot prices effects. Yet, the key welfare effects of our tax reforms are substantially equivalent to those induced through changes in relative spot prices, as for example in Geanakoplos-Polemarchakis (1986), Geanakoplos- Magill-Quinzii-Drèze (1990), or in Citanna-Polemarchakis-Tirelli (2001).Incomplete Markets; Efficiency; Tax Reforms; Personal and Capital Income Taxes

Constrained inefficiency in GEI: a geometric argument

In this paper we use global analysis to study the welfare properties of general equilibrium economies with incomplete markets (GEI). Our main result is to show that constrained Pareto optimal equilibria are contained in a submanifold of the equilibrium set. This result is explicitly derived for economies with real assets and xed aggregate resources, of which real numeraire assets are a special case. As a by product of our analysis, we propose an original global parametrization of the equilibrium set that generalizes to incomplete markets the classical one, rst, proposed by Lange (1942).General equilibrium; incomplete markets; optimality; global analysis

Quantifying Inefficiency in Incomplete Asset Markets

It is known that the incompleteness of asset markets causes inefficiency in almost every equilibrium. Yet unexplored is the "size" of this inefficiency. The size of a Pareto improvement is the total willingness to pay for it, out of current consumption. Inefficiency is the maximum size of any Pareto improving reallocation. Inefficiency of US consumption in middle age is computed to be 10-11% of total consumption in youth, for CRRA parameters 1.5-3.25, in calibrated economy. The inefficiency of a general economy is approximated. A natural approximation, based on marginal rates of substitution (MRS), is preposterously crude in the calibrated economy, owing to a law of diminishing willingness to pay. Alternative approximations end up being functions of a classical notion, weighted social welfare maximized subject to resource constraints. They are simple, sharper in general and accurate in the calibrated economy.

A social welfare function characterizing competitive equilibria of incomplete financial markets

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies with missing financial markets. We give such a characterization for economies with missing financial markets, by an amended social welfare function. Its parameters capture both the relative importance of households’ welfare–the classic weights–as well as the disagreements among them as to the value of the missing markets. As a by-product, we identify the dimension of the set of interior equilibrium allocations.incomplete markets, social welfare function, manifold

A social welfare function characterizing competitive equilibria of incomplete financial markets

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies with missing ? nancial markets. We give such a characterization for economies with missing ?nancial markets, by an amended social welfare function. Its parameters capture both the relative importance of households?welfare?the classic weights?as well as the disagreements among them as to the value of the missing markets. As a by-product, we identify the dimension of the set of interior equilibrium allocations.incomplete markets; social welfare function; manifold

Constrained inefficiency in GEI: A geometric argument

In this paper we use global analysis to study the welfare properties of general equilibrium economies with incomplete markets (GEI). Our main result is to show that constrained Pareto optimal equilibria are contained in a linear submanifold of the equilibrium set. This result is explicitly derived for economies with real assets, of which real num´eraire assets are a special case

Indeterminacy of competitive equilibrium with risk of default

We prove indeterminacy of competitive equilibrium in sequential economies, where limited commitment requires the endogenous determination of solvency constraints preventing debt repudiation (Alvarez and Jermann [3]). In particular, we show that, for any arbitrary value of social welfare in between autarchy and (constrained) optimality, there exists an equilibrium attaining that value. Our method consists in restoring Welfare Theorems for a weak notion of (constrained) optimality. The latter, inspired by Malinvaud [15], corresponds to the absence of Pareto improving feasible redistributions over nite (though inde nite) horizons.imited commitment; solvency constraints; Malinvaud efficiency Welfare Theorems; indeterminacy; Welfare Theorems; indeterminacy; Welfare Theorems indeterminacy;financial fragility; market collapse

A social welfare function characterizing competitive equilibria of incomplete financial markets

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies with missing financial markets. We give such a characterization for economies with missing financial markets, by an amended social welfare function. Its parameters capture both the relative importance of households' welfare-the classic weights-as well as the disagreements among them as to the value of the missing markets. As a by-product, we identify the dimension of the set of interior equilibrium allocations