[This paper develops a general, competitive model of commodity differentiation. The structure analyzed is sufficiently rich to admit the basic structures of many of the common models of commodity differentiation as special cases. Thus, the model provides a unifying framework within which alternative formulations of strategic product choice can be compared. It is shown that competitive equilibria exist under only mild restrictions on the underlying economic structure and vary continuously with endowments. Finally, some results relevant to all models of commodity differentiation featuring price taking consumers are presented. The results are shown to point to some potentially important methodological restrictions.]

In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat potential agents that are not born. We show that these concepts are closely related to the notion of Pareto-efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. We discuss two sets of sufficient conditions for noncooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case. Finally, we study examples of equilibrium settings in which fertility decisions are not efficient, and classify them into ones where inefficiencies arise inside the family and ones where they arise across families.