Knowledge that Transforms

[This paper presents a general framework for the analysis of programs over an infinite horizon in continuous time. Sufficient conditions for the existence of an optimal program are derived and are shown to reduce to the condition that the underlying preference ordering exhibit impatience in a topology determined by the underlying technology.]

[A simple scheme for making governmental decisions about the production and financing of public goods is presented. The "competitive" equilibria under the scheme are Pareto optimal; more importantly, they are Lindahl equilibria. Thus, it is never in any individual's interest to refuse to participate (no one will be worse off at the equilibrium than at his initial holding); moreover, the existence of equilibria is assured in the usual classical public-goods economies.]

[Cournot-Nash models of free entry into industries with large fixed costs yields equilibria with only a few operating firms, and each firm has some monopoly power. I consider a model where each firm's strategy is a function q(P) which specifies how much it will supply at each price. Unlike in Cournot models, the competitive equilibrium (where it exists) is always a Nash equilibrium in supply function strategies, and under weak assumptions it is the only equilibrium. This permits a Nash equilibrium model of the threat of entry as a deterrent to the exercise of monopoly power by operating firms.]

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In this paper the concept of approximate slope, introduced by R. R. Bahadur, is used to make asymptotic global power comparisons of econometric tests. The approximate slope of a test is the rate at which the logarithm of the asymptotic marginal significance level of the test decreases as sample size increases, under a given alternative. A test with greater approximate slope may therefore be expected to reject the null hypothesis more frequently under that alternative than one with smaller approximate slope. Two theorems, which facilitate the computation and interpretation of the approximate slopes of most econometric tests, are established. These results are used to undertake some illustrative comparisons. Sampling experiments and an empirical illustration suggest that the comparison of approximate slopes may provide an adequate basis for evaluating the actual performance of alternative tests of the same hypothesis.