[A generalization of the St. Petersburg paradox has led Menger to observe that utility functions must be bounded to insure existence of expected utility when probability distributions are unrestricted. It is clear that the admissible set of utility functions can be expanded as restrictions are imposed on the distribution functions under consideration. This paper provides a schema for determining the admissible utility functions for each probability distribution set defined by a minimum order requirement on the moments of the distribution.]

Charles Blackorby, Richard Boyce, R. Robert Russell, Estimation of Demand Systems Generated by the Gorman Polar Form; A Generalization of the S-Branch Utility Tree, Econometrica, Vol. 46, No. 2 (Mar., 1978), pp. 345-363

We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare, and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality, or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines. We also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another. The sampling distribution of convenient dual estimators for the measurement of poverty is also established. The statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes. Our results are briefly illustrated using data for four countries drawn from the Luxembourg Income Study data bases.

We establish the asymptotic sampling distribution of general functions of quantile-based estimators computed from samples that are not necessarily independent. The results provide the statistical framework within which to assess the progressivity of taxes and benefits, their horizontal inequity, and the change in the inequality of income which they cause. By the same token, these findings characterise the sampling distribution of a number of popular indices of progressivity, horizontal inequity, and redistribution. They can also be used to assess welfare and inequality changes using panel data, and to assess poverty when it depends on estimated population quantiles. We illustrate these results using micro data on the incidence of taxes and benefits in Canada.

Decentralized decision making is consistent if it is executed without cost (i.e., without a loss of output or utility). Consistency requires that the objective function be appropriately structured. In this paper, a hierarchical decision making structure is rationalized by an objective function which combines some of the properties of homothetic separability and asymmetric separability. THIS PAPER EXAMINES consistent decentralized decision making in a hierarchical structure. The decision making process is rationalized by a class of objective functions which combines some of the properties of homothetic separability [1, 3] and recursive, or asymmetric, separability [5,8]. We refer to these functions as homothetically recursive. After introducing our basic notation and definitions, we prove a representation theorem for homothetically recursive functions in Section 1. In Section 2 we prove two duality theorems for homothetically recursive structures. A recursively decentralized decision making process, described in Section 3, is made manifest in the structure of the associated cost function. The analysis is carried out in the context of the theory of the firm but other applications are discussed briefly in Section 4.

[In this study, a dynamic initial investment-borrowing model involving nonconvex investment effects and borrowing limitations is formulated as a discrete-time control problem. In the model, the firm's objective is to maximize, subject to constraints, the net worth of the firm over a finite decision-making period. Initial investment and borrowing are control parameters; and the scale of capacity use is the control variable. Investment costs, which reflect the "six-tenths" rule in particular, are nonconvex. Special considerations are thus involved in deriving the investment and borrowing rules. It is shown that the optimum must be at one of the following three points: (i) no investment and no borrowing, (ii) investment of just the endowment, and (iii) investment of the maximum amount possible. This result is especially important computationally, because the problem is convex at the points described by (ii) and (iii), and trivial at the origin. Therefore, the optimum may be computed by the use of published algorithms.]

Gorman [2] has derived necessary and sufficient conditions for the existence of category expenditure functions which yield the optimal allocation of a consumer unit's income to each of a number of groups of commodities as functions of total income and group price indices. These conditions take the form of certain restrictions on the structure of the utility function. Gorman, however, did not address the problem of how these functions are derived. In this paper, we construct an algorithm (a budgeting procedure) for deriving the category expenditure functions and show that the necessary and sufficient condition for this procedure to be consistent is that the utility function be separable into homothetic parts. CASUAL OBSERVATION REVEALS that many consumers budget; that is, they first allocate their total expenditure among broad commodity categories and then decide upon the precise allocation of category expenditure to each of the commodities within the group. This type of consumer behavior is especially interesting if it is possible to carry out the broad category allocation with reference only to price indices for each of the budgeting categories, and then decide upon the intracategory allocation with reference only to commodity prices within that group. R. H. Strotz [4, 5] and W. M. Gorman [2] have examined the relationship between this type of consumer behavior and the form of the consumer unit's utility function. More precisely, they have shown that the necessary and sufficient conditions for the existence of group price indices (which depend only upon commodity prices within the group), such that category expenditures are functions only of these price indices and total expenditure, are that the utility function be (a) homothetically separable2 or (b) strongly (additively) separable (with a certain restriction on the polar form of the utility function).3 Strotz and Gorman do not address the issue of how these functions could be derived. This paper discusses a method of deriving the category expenditure functions-a budgeting procedure-which requires stronger constraints on the utility function than does the mere existence of the functions. Price indices are first derived for each budgeting category. Then the

In this study, the authors report the results from laboratory asset markets designed to test the rational expectations hypothesis that markets aggregate and transmit the information of differentially informed traders. After documenting evidence in favor of the rational expectations model, they examine which features of their environment are necessary or sufficient to achieve an rational expectations equilibrium. The authors find that trading experience and common knowledge of dividends are jointly sufficient to achieve a rational expectations equilibrium, but that neither is a sufficient condition by itself. They also present some stylized facts about the convergence process leading to a rational expectations equilibrium.