Aloisio Araujo

Collateral avoids ponzi schemes in incomplete markets

Without introducing neither debt constraints nor transversality conditions to avoid the possibility of Ponzi schemes, we show existence of equilibrium in an incomplete markets economy with a collateral structure.

Equilibrium without uniform conditions

Abstract We prove two general equilibrium existence theorems. In the first, we suppose pointwise properness of the preference on the Pareto optimal allocations. For example, to support a Pareto optimal allocation, we need to suppose properness only at the allocation itself. Our second theorem deals with the separable utilities case. With this assumption we prove the existence of equilibrium supposing properness only at the initial endownments.

The non-existence of smooth demand in general banach spaces

We study the questions of existence and smoothness of demand functions with an infinite number of commodities. The main result obtained, under some hypothesis, is: if a C1 demand exists in a commodity space B, then B can be given an inner product structure. For example, if B is Lp, 1≦p≦∞, and if there exists a C1 demand function defined on B then p must be 2. Another result is: if a demand function exists, defined for all prices p and income, then the commodity space must be reflexive. For example, if B is Lp and a demand function exists on B, defined for all prices and incomes then 1<p<∞. We also study the cases L∞ and L1 with weaker assumptions. We finish the paper proving that the demand function is always defined for a dense set of prices and convenient incomes.

Maximum principle and transversality condition for concave infinite horizon economic models

Abstract Necessary conditions for optimality in infinite horizon concave maximization problems, which include a generalized “Euler equation” and a transversality condition at infinity, are established. The formulation admits implicit state constraints and utility functions with infinite steepness at the boundary. For these reasons support prices present discontinuities and a theorem characterizing such discontinuities is presented.

Regulating collateral-requirements when markets are incomplete☆

In this paper we examine the effects of default and collateral on risk sharing. We assume that there is a large set of assets which all promise a risk less payoff but which distinguish themselves by their collateral requirements. In equilibrium agents default, the assets have different payoffs, and there are as many linearly independent assets available for trade as there are states of the world. We derive necessary and sufficient conditions for equilibria to be Pareto-efficient in the presence of uncertainty. We explore some examples for which the collateral equilibrium allocation is identical to the Arrow–Debreu allocation, either when agents have a high preference for the durable good, or when the endowment distribution of the durable good is relatively homogeneous. We examine a series of examples to understand which collateral-levels prevail in equilibrium and under which conditions there is scope for regulating margin-requirements, that is, restricting the sets of tradable assets through government intervention. In these examples equilibrium is always sub-optimal but regulation never leads to a Pareto-improvement. While the competitive equilibria are constrained efficient, there do exist regulations which make large groups of agents in the economy better off. These regulations typically restrict all trades to take place in the low-collateral loans and benefit the poor and the rich agents in the economy through their effects on the equilibrium interest rate and the equilibrium prices of the durable goods.

Adverse selection problems without the Spence–Mirrlees condition

This paper studies a class of one-dimensional screening problems where the agents utility function does not satisfy the Spence-Mirrlees condition (SMC). The strength of the SMC for hidden information problems is to provide a full characterization of implementable contracts using only the local incentive compatibility (IC) constraints. These constraints are equivalent to the monotonicity of the decision variable with respect to the agents unobservable one-dimensional parameter. When the SMC is violated the local IC constraints are no longer sufficient for implementability and additional (global) IC constraints have to be taken into account. In particular, implementable decisions may not be monotonic and discretely pooled types must have the same marginal utility of the decision (or equivalently, get the same marginal tariff). Moreover, at the optimal decision, the principal must preserve the same trade-off between rent extraction and allocative distortion measured in the agents marginal rent unit. In a specific setting where non-monotone contracts may be optimal we fully characterize the solution.

Equilibrium with Default and Endogenous Collateral

We study a two-period general equilibrium model with incomplete asset markets and default. We make collateral endogenous by allowing each seller of assets to fix the level of collateral. Sellers are required to provide collateral whose first-period value, per unit of asset, exceeds the asset price by an arbitrarily small amount. Moreover, borrowers are also required to be fully covered by the purchase, in the first period, of state-by-state default insurance. These insurance contracts are offered by lenders. The insurance cost or revenue is a linear charge and plays the role of a spread penalizing borrowers who will incur in default and benefiting lenders who will suffer default. Under these assumptions, equilibrium always exists. Copyright Blackwell Publishers, Inc. 2000.

Notes on the smoothing of aggregate demand

The problem of smoothing (of excess demand) by aggregation was posed by Debreu (1972) and Hildenbrand (1974). It can be informally described as: ‘find natural frameworks in which even if preferences are not convex, one can reasonably expect that if there are a continuum of consumers and their characteristics are disperse, in some appropriated sense, then aggregate demand will be a continuous, or C I, function.’ Contributions have been made by Sondermann (1975a,b), Chichilnisky (1974), Ichiishi (1976), Araujo (1974), Mas-Cole11 (1973), Mas-Cole11 and Neuefeind f1977). Sondermann’s work is especially important for these notes. An economy with a continuum of traders is formalized as follows: there is given a metric space d of consumer characteristics; d will consist, for example, of preferences-endowments pairs or utility functions~ndowments pairs; by using, for example, utility functions we are free to assume when necessary that &’ possess a C’ type metric or even a c’ linear structure. There is given a space E c R” of parameters (or ‘names’) and a (Borel) probability measure v on R” with compact support contained in E and, for definiteness, absolutely continuous with respect to Lebesgue measure on R”. A (continuum) economy will then be specified by E, v, and suitably restricted function f :E--+&, i.e., an assignment of characteristics to parameters. Two approaches have been proposed for the definition and topologization of a space of economies. The first we will call the distribution ~~~~~~c~ and is due to Aumann (1964) and Hildenbrand (1974); since for the purposes of equilibrium theory only the distribution induced by f on d is relevant, two triples (E, v,f), (E’, v’, f’) are viewed as close if mean endowments are close and if the measures induced in & are close in the weak convergence for

Bankruptcy Law in Latin America: Past and Future

This paper studies bankruptcy law in Latin America, focusing on the Brazilian reform. We start with a review of the international literature on this subject. Next we examine the economic incentives associated with several aspects of bankruptcy laws and insolvency procedures in general, as well as the trade-offs involved. We follow this theoretical discussion with an empirical evaluation of the quality of current insolvency procedures in Latin America. We find that the region is governed by a set of laws that is inefficient even when compared with regions of lower per capita income. This inefficiency has severe consequences for credit markets and the cost of capital. Next we focus on the recent Brazilian bankruptcy reform, analyzing its main components and possible effects. The appendix describes difficulties of the reform process in Brazil and lessons other Latin American countries can learn from it.

On the central limit theorem in Banach spaces

It is shown, with the use of a concentration inequality of LeCam, that associated with an infinitely divisible random variable with values in a separable Banach space there is a Levy-Khintchine formula. A partial converse of this fact is also proved. Relations between the continuity of the compound Poisson and the Gaussian variables associated with a Levy measure are studied. A central limit theorem is obtained and examples are given.