**"Implicaciones de la manipulaciónde la correspondencia de Lindahl: un ejemplo"**, joint with J.V.LLinares, V.Romero andT.Rubio, *Revista Española de Economía*, 7,2,(1990)

Abstract

In this paper we examine the consequencesof the manipulation of Lindahl equilibrium by means of an example.It will be proven that it is likely that some agent has incentiveto be sincere. Moreover, this equilibrium favors the agent withless initial endowments, which implies that manipulation has aredistributing effect.

**"On the Generic Impossibility ofTruthful Behavior: a Simple Approach"**,joint with L. Corchón,* Economic Theory*, 6,2, 365-371(1995).

Abstract

We provide an elementary proofshowing how in economies with an arbitrary number of public goodsan utility functions quasi-linear in money, any efficient andindividually rational mechanism is not strategy-proof for anyeconomy satisfying a mild regularity requirement.

**"Identical Preferences Lower BoundSolution and Consistency in Economies with Indivisible Goods"**, *Social Choice and Welfare*, 13,1,113-126 (1996).

Abstract

We consider the problem of allocatinga finite set of indivisible good among a group of agents, andwe study a solution, called the Identical Preferences Lower Boundsolution, in the presence of consistency properties. This solutionis not consistent. we prove that its maximal consistent subsolutionis the No-envy solution. Our main result is that the minimal consistentextension of the intersection of the Identical Preferences Lowerbound solution with the Pareto solution is the Pareto solution.This result remains true in the restricted domain when all theindivisible goods are identical, but not when there is a uniqueindivisible good.

**"Population Monotonicity in a GeneralModel with Indivisible Goods"**,*Economic Letters*, 50, 91-97 (1996)

Abstract

We show that, in a model withindivisible goods where each agent can receive more than one indivisiblegood, there are no population monotonic selections from the Paretosolution. However, if substitutability is imposed on preferences,the Shapley solution satisfies population monotonicity.

**"Population Monotonicity in Economieswith one Indivisible Good"**,*Mathematical Social Sciences*, 32,2, 125-138 (1996)

Abstract

In this paper we present a Pareto-efficientsubsolution of the Identical Preferences Lower Bound solutionsatisfying population monotonicity in economies with one indivisiblegood and where preferences are not necessarily quasi-linear. Sucha solution is a generalization of the Shapley solution, whichsatisfies the above properties in quasi-linear economies.

**"Fair Allocation in a General Modelwith Indivisible Goods"**,*Review of Economic Design*, 3, 195-213 (1998).

Abstract

In this paper we study the problemof fair allocation in economies with indivisible goods, droppingthe usual restriction that one agent receives at most one indivisiblegood. We show that most of the results obtained in the literaturedo not hold when the aforementioned restriction is dropped.

"**Buying Several IndivisibleGoods"**, joint withM. Quinzii and J.A. Silva, *Mathematical Social Sciences*,37, 1-23 (1999).

Abstract

This paper studies economies inwhich agents exchange indivisible good and money. The indivisiblegoods are differentiated and agents have potential use for allof them. we assume that agents have quasi-linear utilities inmoney, have sufficient money endowments to afford any group ofobjects priced below their reservation values, have reservationvalues which are submodular and satisfy the Cardinality Condition.This Cardinality Condition requires that for each agent the marginalutility of an object depends only on the number of objects towhich it is added, not on their characteristics. Under these assumptions,we show that the set of competitive equilibrium prices is a nonempty lattice and that, in any equilibrium, the price of an objectis between the social value of the object and its value in itssecond best use.

**"Manipulation Games in Economieswith Indivisible Goods"**,mimeo (1997).

Abstract

In the first part of the paperwe study the strategic aspects of the Non-Envy solution for theproblem of allocating a finite set of indivisible goods amonga group of agents when monetary compensations are possible and,each agent, receives, at most, one indivisible good. In this contextwe prove that the set of equilibrium allocations of any directrevelation game associated with a subsolution of the No-Envy solutioncoincides with the set of envy-free allocations. That is, undermanipulation all the subsolutions of the No-Envy solution areequivalent. In the second part of the paper, the same problemis addressed, but now, we allow each agent to receive more thanone indivisible good. In this situation the result is sightlydifferent from the above. We prove that any equal income walrasianallocation can be supported by an equilibrium of any direct revelationgame associated with subsolutions of the No-envy solution.

**"Taxation, Altruism and Subsidiesfro Higher Education"**,joint with Iñigo Iturbe-Ormaetxe, mimeo (1998).

Abstract

The financing of higher educationthrough public spending imposes a transfer of resources from taxpayers(being or not users of the education services) to students andtheir parents. Moreover, most of the students come from the middleand upper income groups and then they are the chief recipientsof that transfer of purchasing power. We provide a simple explanationof this phenomenon. We know that those individuals who attendhigher education will earn a higher level of income in the futureand thus they will pay more taxes. Then people whose childrendo not attend higher education will agree to help pay the costof education provided taxes are high enough to imply that in thefuture there will be enough redistribution in favor of their ownchildren.