[This paper investigates the distribution of the least squares estimator of the coefficient α in the model @c"t = @a@c"t -"1 + @?"t where the @?"t where the @?"t are independently distributed N (O, @s extasciicircum2). The exact finite sample and limiting distributions are calculated when α ≥ 1 and finite sample distributions when α extless 1. These distributions are used to compute the power functions of tests of the random walk hypothesis α = 1 as well as the hypotheses.]

Two theorems are derived about social choice functions, which are defined on comprehensive convex subsets of utility allocation space. Theorem 1 asserts that a linearity condition, together with Pareto optimality, implies that a social choice function must be utilitarian. Theorem 2 asserts that a concavity condition, together with Pareto optimality and independence of irrelevant alternatives, implies that a social choice function must be either utilitarian or egalitarian. These linearity and concavity conditions have natural interpretations in terms of the timing of social welfare analysis (before or after the resolution of uncertainties) and its impact on social choices.

[This paper is concerned with characterizing the probability distributions that describe the (stochastic) stationary state of a neoclassical model of optimal growth. In particular, using both theoretical analysis and numerical simulation, we search for systematic relationships between savings (and investment) rates and variability of the economy's aggregates.]