Knowledge that Transforms

[A one-way expected utility representation has the expected utility of one probability measure greater than the expected utility of another probability measure whenever the first is preferred to the second. It requires preferences to be acyclic but not necessarily transitive, and does not require indifference to be transitive. Preference axioms which are sufficient for one-way expected utility for sets of simple probability measures have been presented before (see [8]). This paper uses additional axioms to extend the one-way representation to sets of discrete and more general probability measures.]

The relationship between Pareto optimal (0s) and revenue maximizing (Or) tolls is examined for queuing models that permit balking. When customers have the same value for waiting time, Q, =Or provided the entrepreneur can impose a simple two-part tariff. With heterogeneous values for waiting time, Or can be greater than, equal to, or less than H,. Expanding the number of servers and charging multi-part tariffs are shown to be alternative methods for segmenting the market, and the welfare implications of these two strategies are explored.

This paper obtains Edgeworth or Gram-Charlier expansions for the t ratio of instrumental variable and k-class estimators, and uses them to give approximations to the confidence intervals obtained from these t ratios. These confidence intervals for large sample size are more accurate than the usual asymptotic confidence interval. Charlier expansions is applied to the t ratio of 2SLS and non-stochastic k-class estimators. Previous general theorems in this field, with the exception of those given by Chambers [2], such as those in [3] have assumed that the statistic has moments of appropriate orders. The theorem proved here assumes only that it can be expressed as a function of other variables with moments of all orders with appropriate properties in some neighborhood of the origin. It can be applied to a wide range of

THE WALRAS CORRESPONDENCE associates the set equilibrium price vectors with an economy. The purpose of this paper is to study some topological properties of the graph of the Walras correspondence such as connectedness and contractibility. This is done once the graph is given the structure of a bundle. The mathematical notations used in this paper are given in Section 2. The bundle structure of the graph is proved in Section 3. The contractibility of the graph is then a straightforward result proved in Section 4. Finally, variable demand functions are introduced in Section 5 and connectivity is then proved.

Many policies use two categories of instruments: a financial incentive (most often a tax) for polluters, and direct undertakings or financing of some restorations or maintenances or improvements of environmental qualities. The financial consequences of such policies, when optimum, are important for considerations of public finance, decentralization (financial autonomy), and equity (must polluters pay?). They turn out essentially to depend upon the mathematical structure of, first, the environment function, i.e., the way in which qualities depend upon both deteriorating and improving activities, and, second, the various constraints of the problem. Constraints which can be expressed by functions homogeneous of any degree are shown to have no direct financial effect. Apart from the constraints' effects, budgetary equilibrium, surplus or deficit are respectively given by functions which present constant, decreasing, or increasing qualitative returns to scale, i.e., weighted homogeneity of degree zero, positive or negative. The opposite polar cases of cleaning and dilution types of improvement technology are presented, with some other mixed simple cases and a few examples of application of the results.

[This paper considers the impact of certain types of policy related voting patterns on the existence and location of equilibrium strategies in the spatial model of two-candidate competition. In contrast to much of the previous literature, this paper makes a distinction between the aggregate level patterns of voting and the individual level variables which bring them about. By so doing the assumptions can focus on objects which have a more direct empirical referent, namely, the aggregate level support function and the distribution of ideal points. Using this approach, sufficient conditions are found for the existence of equilibrium which, although themselves strong, make considerably weaker demands on individuals than have been generally assumed in the literature. Thus, it is not necessary that each voter vote strictly with regard to policy but, rather, it is sufficient that in the electorate as a whole there is a moderate amount of policy related voting. Other results of the analysis are that policy related voting of any type seems to encourage candidates to converge towards the center, with support from extremists only accentuating this tendency. It is the candidate's most loyal supporters who seem to have the least influence over his policy position.]

FIML is shown to be an instrumental variables estimator where the instruments embody all the over-identifying a priori restrictions. FIML is compared to the two alternative estimators 3SLS and full information instrumental variables. 3SLS differs from FIML in not using all a priori restrictions in forming the instruments. The full information instrumental variables estimator when iterated to convergence yields the FIML estimate. For the case of nonlinearity in the parameters a nonlinear 3SLS and a nonlinear full information instrumental variables estimator are proposed. Both estimators are asymptotically efficient. THIS PAPER UNDERTAKES an investigation of asymptotically efficient estimators for linear and nonlinear simultaneous equation econometric models. By using an instrumental variable approach the equivalence of previously proposed linear estimators to full information maximum likelihood (FIML) follows in a straightforward manner, and a class of new estimators which includes a nonlinear three stage least squares estimator (NL3SLS) and nonlinear full information instrumental variables estimator are proposed and shown to be asymptotically equivalent to FIML. First, an instrumental variable interpretation of FIML is developed by investigating the first order conditions for the maximum of the likelihood function without first concentrating the likelihood function. The essential difference between 3SLS and FIML then becomes evident. The difference between the two estimators is first that FIML uses all over-identifying restrictions in forming the instruments while 3SLS ignores some of these restrictions. Also, FIML uses an estimate of the covariance matrix in forming the instruments which is consistent in the sample with the parameter estimates. Thus the instruments used by FIML are mutually consistent with the parameter estimates in the given sample, while for other estimators the instruments are consistent with the parameter estimates only asymptotically. While this difference in forming the instruments is of no importance asymptotically as is known by the earlier results of Sargan [10] and Rothenberg and Leenders [9], in finite samples there seems to be no reason for not using all known prior information. The use of the a priori restrictions gives a more useful criterion than Dhrymes' [3] recent interpretations of a difference in purging the endogenous variables since all other proposed estimators can be shown to be equivalent by simply proving asymptotic equivalence of the instruments used to those instruments used by the FIML estimator. Then using the instrumental variable interpretation, a relation between FIML and the class of estimators recently proposed by Dhrymes [2], Lyttkens [5, 6], and Brundy and Jorgenson [1] is established. The full information instrumental