Equity and Efficiency in Public Sector Pricing: A Case for Stochastic Rationing

Abstract

A VIEW STILL WIDELY HELD among economists is that given the objective of maximizing a Paretian social welfare function-rationing of private goods is inferior to transfers and subsidies. Hence, existing rationing, e.g. in housing programs involving rent regulation, subsidized medical treatment to needy individuals, distribution of day care for children according to need, etc., is often interpreted as a reflection of paternalistic objectives on the part of the government or simply as bad policy; see Tobin (1970). The purpose of this paper is to challenge the general validity of this conventional wisdom in the context of a traditional model of public sector pricing supplemented by an anonymous rationing scheme which affects individuals' consumption patterns significantly. As is often the case, a government cannot achieve distributional equity (i.e., situations where the social value of marginal utility of income is equal for all individuals) by means of taxes and transfers because the use of these instruments is subject to various constraints. This is a common feature of many taxation models; cf. Atkinson and Stiglitz (1980). From a purely technical point of view, there is scope for improving on social welfare in such situations by means of other measures such as rationing. But, since the use of rationing as well as taxes and transfers is likely to be restricted by the same underlying factors, e.g. information about consumers' preferences and endowments or administrative costs, it may be questioned whether rationing qualifies as an efficient policy instrument. The type of rationing considered in this paper is stochastic rationing; when prices are set at levels which generate excess demand, some of the potential consumers are randomly barred from the markets entirely so that demand equals supply. From the point of view of implementation, such a rationing scheme has the desirable property of not requiring the government to have information about preferences and endowments at the individual consumer level; nor is extensive administration required. Another interesting aspect of such a scheme is that, in a sense, it represents a lower bound on rationing schemes since, in most cases, actual rationing can be based on some information about consumers. Therefore, if there are cases where a market-clearing equilibrium can be improved upon by reducing prices below market-clearing levels combined with elimination of excess demand by means of stochastic rationing, the argument for rationing as a potentially efficient policy tool is in fact fairly strong. In this paper we show that such cases do exist. We also indicate that stochastic rationing may still be efficient even in situations where prices can be highly differentiated among different groups of individuals, e.g. income groups. We conclude that the absence of costless redistribution of income, which indeed seems to be consistent with real-world situations, is crucial for the results. Two kinds of policy changes are considered. The first involves eliminating a marginal excess demand by means of rationing. In the model in this paper, there is a continuum of consumers. Therefore, while such a marginal rationing affects some consumers in a nonmarginal fashion, it only affects an infinitesimal group of consumers. Hence, it only