economics letters ELSEVIER Economics Letters 50 (1996) 91-97 Population monotonicity in a general model with indivisible goods Carmen Bevifi Departamento de Fundamentos del Analisis Economico, Universidad de Alicante, Alicante E-03071, Spain Received 19 January 1995; accepted 26 April 1995 Abstract We show that, in a model with indivisible goods where each agent can receive more than one indivisible good, there are no population monotonic selections from the Pareto solution. However, if substitutability is imposed on preferences, the Shapley solution satisfies population monotonicity. Keywords: Population monotonicity; Indivisible goods JEL classification: D63 I. Introduction Population monotonicity is a property related to population variation, and can be understood as a solidarity property. This property requires that, if the resources are kept fixed, no agent originally present in the economy should benefit from the entrance of new agents. Population monotonicity has been studied in different models (see Thomson, 1995, for a survey) and can be considered as a strong property which is frequently incompatible with efficiency and fairness criteria. For example, in economies with indivisible goods where each agent receives at most one object, no-envy is incompatible with population monotonicity (Alkan, 1994; Moulin, 1990; Tadenuma and Thomson, 1993). However, if no-envy is replaced by the Identical Preferences Lower Bound solution, solutions that satisfy both population monotonicity and this criterion of fairness exist (Moulin, 1990, 1992; Bevifi, 1994a). In economies with divisible goods, monetary transfers, and quasi-linear preferences, this property is even harder to obtain. Moulin (1992) showed that there is no selection from the Pareto solution satisfying population monotonicity. However, positive results are possible if goods are substitutes. In this paper we present a model with indivisible goods where monetary transfers are 0165-1765/96/$12.00 ~ 1996 Elsevier Science S.A. All rights reserved SSDI 0165-1765(95)00722-9