Economy & Business Journal of International Scientific Publications www.scientific-publications.net THE OPTIMAL SUPPLY OF CONGESTED PUBLIC GOODS Tchai Tavor 1 , Uriel Spiegel 2 1 Department of Economics, Yisrael Valley College, Israel 2 Department of Management, Bar-Ilan University, and Visiting Professor, Department of Economics, University of Pennsylvania Abstract Impure public goods resulting from the congestion effect are discussed in the literature solely for the case of homogenous populations where consumers have identical demands. We extend this to include heterogeneous populations, where demands are rectangularly distributed. We compare the optimal values of the control variables (quantity of the public good and the number of users) for both homogeneous and heterogeneous populations, as well as the social optimum values for both cases. Key words: Congested Public Good, Lindhal, Rectangulary Distributed Demand, Homogeneous and Heterogeneous Customers 1. INTRODUCTION The issue of congested public goods that maintain on the one hand the non-exclusion principle and on the other hand also maintain some degree of rivalry has been discussed in the economic literature over the last few decades. Sandler (2002) mentions some impure public goods that include ocean fisheries, pest-control, curbing organized crime, and eliminating acid rain. All these items display rivalry but remain non-excludable. The congested public goods case can be thought of as an extension of the Club theory developed by Buchanan (1965) in his seminal paper that attempted to bridge the gap between a pure private good, which is excludable and rivalrous in consumption, and a pure public good, that holds for goods whose consumption is non- rivalrous and non-excludable. The club goods are excludable and subject to some rivalry in the form of congestion, while the congested public good can either be excludable or not, although rivalry definitely exists due to congestion or crowding effects. The original model of Buchanan assumes a club good being consumed by a homogeneous population whose individuals possess the same tastes and endowments. In the following years more extended models were developed and scenarios of heterogeneous populations were also discussed. For example, Sandler (1977) used the assumption of a distribution of net willingness to pay, while Fraser and Hollander (1992) assume homogeneous populations in tastes but with different individual incomes. Many more theoretical and empirical papers dealing with congestion (or crowding) effects for club and public goods can be found in a survey named "Club Theory: Thirty Years Later" of Sandler and Tschirhart "(1997). Still, the congested public good is a topic that continues to interest economists up till this very day. For example, the recent paper of Birulin (2006) also discusses the issue of public goods with congestion where the capacity (termed G) is given, while the number of consumers (users), N, is determined (which means that some other consumers are excluded for the sake of ex-post efficient allocation). It turns out, some what surprisingly, that the goods of larger capacity, i.e. those which exhibit less exclusion, may be easier to finance than goods of smaller capacity (see pp. 290 third paragraph) Page 977 ISSN 1314-7242, Volume 8, 2014