THE EFFECTS OF COMMODITY PRICE STABILIZATION on an individual consumer's welfare has been controversial ever since the issue was first analyzed by Waugh [15]. The early approach of Waugh, which was based explicitly on expected consumer's surplus and ignored the production side of the economy, has since been generalized in several respects. For instance, Turnovsky, Shalit, and Schmitz (hereafter T-S-S) [14] have suggested an approach that utilizes the indirect utility function of a single individual. By focusing on a single consumer and comparing risk-no risk situations where prices are random variables, they derive interesting and useful results that express conditions for the desirability of price stabilization in terms of the familiar Arrow-Pratt measure of relative risk aversion, price and income elasticities, and budget shares. Although the approach of T-S-S provides useful information about an individual's preference for or against price stability, it does not provide information about a group of heterogeneous consumers' preference for price stability. The approach of T-S-S also assumes that perfect price stabilization is possible; indeed, in many cases government policy may serve to partially stabilize prices, but not perfectly stabilize prices.2 Thus the analysis of T-S-S does not address comparisons of risk-risk situations (the comparisons of unstable versus partially stabilized prices) nor comparisons when there are heterogeneous individuals. Recently, Newbery and Stiglitz [9, 10] have used stochastic dominance rules to analyze mean preserving partial price stabilization schemes. The purpose of the present note is to extend the T-S-S and Newbery-Stiglitz analysis by providing comparisons of partial price stabilization policies that affect multiple prices in non-mean preserving ways. Since an excellent survey of the stabilization literature appears in Newbery and Stiglitz [10], we proceed with the results of our analysis.

Let S denote a set of consumers who have identical, nondecreasing, ordinal, quasiconcave utility functions u: XS(t) -* u[X (t)], where XX(t) is the vector of n goods consumed by individual s at time t. Consumers shop at different stores and hence may pay different prices for commodities.4 Let PS(t) and yS(t) denote exogenous vectors of commodity prices and income, respectively, faced by individual s at time t. This does not preclude the existence of a subset, 5, of consumers who all face the same prices, i.e., P5(t) = pS (t) for all s, s'c S. At each instant in time consumers attempt to

This paper emphasizes the roles played by personal taxation and pension wealth in portfolio choice and composition. A theoretical discussion of the impacts of taxation and participation in social security and private pension systems on individual wealth allocation is followed by empirical evidence based on U.S. cross-section data. Both effects prove to be significant. Anticipated social security and private pension benefits exert a measurable influence on household portfolio allocation. Their omission from an asset demand model may lead to a misinterpretation of the impact of taxation on portfolio composition.

The paper focuses on the benefits derived from public elementary and secondary education; monetary values of households' perceived benefits from operating expenditures are estimated. Information concerning the preference mappings of citizens is obtained using a random utility model to analyze micro voting data. The estimated model in turn provides information concerning the efficiency and distributional consequences of public education expenditures. The conclusion is that operating expenditures exceed the estimated efficient level. Furthermore, it may be difficult to justify the inefficiently large expenditures on equity grounds since the estimated distribution of households' perceived benefits, net of local taxes, is pro-rich. G~ OVERNMENT provision of goods and I J~ services has the potential of greatly affecting the welfare of citizens. This paper focuses on the benefits derived from one such service, public elementary and secondary education; monetary values of households' perceived benefits from public education expenditures are estimated. Information concerning the preference mappings of citizens is obtained using a multinomial probit, random utility model to analyze micro voting data. The estimated model in turn provides information concerning the efficiency and distributional consequences of public education expenditures. The conclusion is that operating expenditures exceed the estimated efficient level. Furthermore, it may be difficult to justify the inefficiently large expenditures on equity grounds since the estimated distribution of households' perceived benefits, net of local taxes, is pro-rich. In contrast to this study, a number of studies employ ad hoc rules to measure citizens' benefits from public elementary and secondary education. Initially total benefits are assumed to equal the cost of educational services; this input cost measure of benefits is then allocated to households using some unproven rule of thumb.' When an ad hoc rule is used to allocate a questionable measure of total benefits, the results are even more suspect. Conceptually, it is quite odd to determine (assume) total benefits and then allocate the total to individuals or households. The correct method is first to obtain estimates of individuals' or households' benefits. These estimates can then be used to determine the magnitude of total benefits and analyze how the benefits are distributed across the population. Aaron and McGuire (1970) criticize ad hoc benefit measures and propose the income value measure. For X' units of the politically allocated good X this measure is IV = MRSj X' where MRSj is the marginal rate of substitution of X for a composite commodity evaluated at X' and one's aftertax income. This measure is comparable to measures of the income values of goods purchased in private markets. While Aaron and McGuire argue for preferencebased benefit measures, the lack of information concerning preference mappings necessitates that they assume the shape of the utility function. Even though the results by Maital (1973), based on a similar method, are slightly less restrictive, a number of restrictive assumptions are common to both studies. Not only are households assumed to have identical, separable utility functions, but the existing levels of politically allocated goods are assumed to be efficient, implying the total income value equals the input cost. Also, the allocation of benefits from mixed goods (e.g., public education) between public and private components is based on ad hoc rules. The major contribution of the current study is that the benefit estimates are based on information concerning the preference mappings of individuals as revealed through referenda voting.2 The estiReceived for publication March 9, 1983. Revision accepted for publication June 4, 1984. *State University of New York-Albany. This paper was improved as a result of the advice and encouragement of Kenneth Wertz, John Akin, David Guilkey and James Wilde, as well as the helpful comments of two referees. Financial support for this research was, in part, provided by a Dissertation Research Fellowship from the Brookings Institution. 1 An example is the 1967 Tax Foundation Study. 2NMicro voting data are also used by Rubinfeld (1977) to obtain information about citizens' preferences for public school expenditures; he uniquely estimates the parameters of a demand function up to an unknown multiplicative constant. A micro demand function for education is uniquely estimated by Bergstrom, Rubinfeld, and Shapiro (1982), using a different type of survey data. While the method used here is to directly estimate preference mappings, the information concerning such mappings embedded in such a demand function provides an

We present some examples of Nash equilibria that are independent of the distribution of some parameter across the economic agents and describe a general theorem that characterizes this phenomenon.

A Cournot model of oligopoly in which otherwise identical firms have private differential information about the common cost of production and a shared (but unknown) demand curve is examined. A Bayesian equilibrium of the corresponding game of incomplete information is solved for explicitly and analysed. In the symmetric equilibrium, different firms produce at different output levels because they have different information. Because the information individual firms have is random, total output and hence market price is also random for any finite number of firms. The main result of the paper relates to the asymptotic properties of the equilibrium, when the number of firms becomes large. Under fairly general conditions on the joint distribution of demand and individual firms' information about demand, the random equilibrium price converges almost surely to a constant in the limit. More importantly, this price equals the perfectly competitive price. In other words, in large markets, even if no firm knows the true market demand curve and firms are not price-takers and do not use price as a signal to improve their information, the competitive price will prevail with certainty. In the limit, aggregate outcomes are as if all firms shared their private information with each other.

This study employs an alternative stochastic model which offers important advantages over those proposed by Cohen and Pekelman, and Biddle and Martin. Rather than optimizing with respect to a single order-up-to level determined at the start of each year, the model permits a second order at year-end. This achieves greater descriptive validity by allowing intrayear (as well as interyear) cost changes and additional purchases after demand has been assessed. More important, there is a greater sensitivity to the effects of tax incentives on year-end procurement decisions and a smaller likelihood of year-end stockouts (which unrealistically affect tax incentives by drastically altering inventory cost structures). As a result, the model is uniquely suited for an examination of optimal choices among alternative inventory costing methods and the optimal ordering policies under each. In this study we extend the model to include not only LIFO and FIFO but also AC, a method not previously considered in order quantity models.

Barry R. Marks, Krishnamurthy K. Raman, The Importance of Pension Data for Municipal and State Creditor Decisions: Replication and Extensions, Journal of Accounting Research, Vol. 23, No. 2 (Autumn, 1985), pp. 878-886

The unique characteristics of options enable investors to create nonnormal portfolio return distributions that cannot be replicated with other assets. This analysis explores the power of various investment selection criteria to identify efficient portfolios from investment strategies involving call options and treasury bills, stocks, and covered option writing. The preference structure for strategies incorporating options is compared to traditional stock-fixed income investments, and the importance of options to investor utility maximization is illustrated. This study reveals that rules of stochastic dominance that place few restrictions on investor preference functions and asset return distribution are appropriate criteria by which to rank portfolios containing options and other assets.