[Changes in asset prices are shown to produce only substitution effects in a broad class of portfolio-choice models. Wealth effects are identically zero unless the individual's stocks of assets are subject to unanticipated changes.]

[The problem under consideration is to select the smallest majority size such that at least one social state is not defeated by any other when restrictions on possible voters' preferences are explicitly known, and when populations of arbitrary size are possible. This problem is formulated in mathematical programming terms. The special structure of the formulation is discussed, and some results concerning bounds on the majority sizes are established.]

IN A RECENT ARTICLE in Econometrica [1] Barbara Bergmann argues that improvement over the usual regression procedures can be gained by a combination of a very simple do-it-yourself simulation with regression. She asserts that this approach can provide insights which would not be found using a regression approach, and claims that simulation-regression offers a partial solution for the problems of multicollinearity and choice of functional form while economizing on degrees of freedom. These points are illustrated with an application to a simple model determining the incidence of poverty. In this comment we point out an analytic solution to Bergmann's theoretical model and show her simulation to be inefficient. We explore the general properties of prepared regression, arguing that its usefulness is overstated and that it is not more fruitful for scientific investigation than properly performed regression analysis. Bergmann proposes a model of the effects on the incidence of poverty (p) of the unemployment Tate (u), the weekly gross turnover rate (v), and the weekly wage rate relative to the poverty line. In her model, which assumes homogeneous labor force participants who stochastically become employed or unemployed, the probability that a person will be employed next week depends only on his employment status this week. A participant is poor if he is employed no more than a certain number of weeks in the year (c), which number depends on the poverty threshold and the weekly wage. This model can be criticized on many substantive grounds such as its use of a homogeneous labor force, the assumption that accessions and separations are random, the neglect of the labor force participation decision, and the omission of unearned income. Hall [4] has shown that the probability of separation depends importantly on the length of employment. It may also be important to distinguish between quits and layoffs. Our primary purpose, however, is not to offer substantive criticism of the model. We need only emphasize here that the poor in this model are very different from the poor in the real world.2 Bergmann solves the model by computer simulation, but in fact it has an analytic solution. The model is a two state Markov process in equilibrium, with the states defined as employed this week (state 1) and unemployed this week (state 0). The transition probability matrix is as follows:

[Models of the behavior of populations of self-reproducible natural resources in an economic framework have rarely anticipated the consequences of different forms of production functions. This paper investigates sufficient conditions for extinction in a very general model as well as a model having a specific production function. In the second section additional considerations relating to extinction are deduced as well as the existence of a watershed level of population. These conclusions are exemplified using data from one particular population of red deer.]