This paper contains a generalization of the General Possibility Theorem to situations where choice over two-element (more generally, “small”) sets is not possible. The analysis is developed in terms of the social choice function formulation rather than the social welfare function approach. In this formulation, assumptions concerning the size of sets of feasible alternatives are explicit, allowing the role of these assumptions in inducing impossibility results to be explored.

The notion that the cost of increasing family size depends upon the level of expenditures or investment per child (child quality), formalized in Becker and Lewis (1973) and Willis (1973), provides a rationale for the contemporaneous inter-country negative correlation between the schooling attainment of young persons and birth rates as well as the trends in these variables over time in developed countries during their demographic transition.A sufficient condition for fertility to fall and, say, schooling to rise as development proceeds in this framework is that the shadow-price constant income effect on quality per child 1 exceed that on numbers of children.Such an explanation, however, would appear :..o be of little value for those who hold that population growth itself impedes economic development (e.g., Coale and Hoover (1958)).From this perspective, the compensated substitution.implications of the theory are of concern, whereby price interventions which impinge on family size decisions can be used to accelerate pe~-capita income.The chief focus of policies aimed at reducing fertility in the absence of income growth appears to be on altering the "own" price of children through lowering information costs associated with contraceptive methdos in order to take advantage of recent innovations in birth control technolo~y.In this paper, we examine both theoretically and empirically the natalist impact of two alternative potential policies--reductions in the price of schooling and tech~ological innovation in the agricltural context--based on a rural household model in which (school) investments per child influence the cost of children as in the Becker-Lewis framework and in which the returns to schooling rise in a dynamic environment as a consequence of the allocative effect of education (Welch, 1970;Schultz, 1975).I show that, as a consequence of the "quantity-quality" interaction, reductions in the direct costs of schooling may raise fertility levels even if child schooling and the quantity of children are substitutes as conventionally defined and even if (observed) income effects are not positive.2,:. w

The study explores the incremental explanatory power of replacement cost earnings variables (derived from ASR 190 data) with respect to explaining cross sectional differences in security returns. As such, the study is a natural extension of previous research, including analyses of the effect of security returns of ASR 190 data at the time of disclosure, investigations of cross sectional relationships between security returns and historical cost earnings, and studies of multiple signals. The basic finding is that pre-holding gain net income provides no incremental explanatory powerm given knowledge of historical cost earnings. However, the converse does not hold. Taken together, the findings are consistent with the contention that pre-holding gain net income is a garbled version of historical cost earnings. The basic finding is robust under several extensions of the initial research design. The research design incorporates a two-stage approach which permits a determination of the incremental explanatory power of collinear variables. The findings are in contrast to those of a previous study by Easman et al. (1979). The nature of the difference in research design inducing the difference is identified. Potential reasons for the difference in findings are provided.