This paper explores the workings of stratified societies in which there is primogeniture and where the nobility practice monogamous marriage with a double standard of sexual fidelity. We model a simple stratified society and define the reproductive values of the male and female nobility relative to that of commoners. We then explore implications of the hypothesis that preferences have evolved to favor maximization of reproductive value. The hypothesis is tested against fragmentary data from ancient civilizations and quite detailed information about the British aristocracy in the seventeenth and eighteenth centuries.

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## Scholarly Works (131 results)

William Hamilton developed the biological theory of kin selection before game theory became familiar to biologists. Thus he implicitly confined his analysis to a rather special subclass of games, with linear structure. This paper shows that while Hamilton's rule does not apply to a more general class of games, there is a useful generalization that does apply. This paper also generalizes results in my 1995 AER paper on sibling interaction from symmetric two-player games to multiplayer games that may be asymmetric.

This paper was my attempt to build a theory of "public factors of production" such as scientific knowledge and to see whether there is any way that Arrow-Debreu general equilibrium theory can cope with the nonconvexities that arise. I propose that the economy might be partitioned into provision of "social overhead goods" and ordinary goods in such a way that given the quantities of social overhead goods, the remaining activities satisfy the assumptions needed for the existence of competitive equilibrium. I proposed and examined a notion of "Lindahl-Hotelling equilibrium" in which individuals were assigned Lindahl prices for the social overhead goods. These Lindahl prices depend on the effects of the social overhead goods on competitive prices for ordinary goods. This allows a nice application of duality and indirect utility functions.

Cournot's classic oligopoly model has two mineral water sellers whose products are perfect substitutes. Cournot studies equilibrium when each duopolist believes the other's quantity choice is invariant to his own action. Cournot also studied the case of dupolists producing perfect complements, copper and zinc, which are used in fixed proportions to produce brass. In this case Cournot studies equilibrium where each duopolist believes the others price is invariant to his own action. This paper unifies Cournot's two theories of duopoly as special cases of a more general technology and discusses the existence of Cournot equilibrium in price and quantity in general. There is seen to be a neat duality between equilibrium in price and in quantity (generalizing an observation of Hugo Sonnenschein).

Gary Becker's ``Rotten Kid Theorem'' asserts that if all family members receive gifts of money income from a benevolent household member, then even if the household head does not precommit to an incentive plan for family members, it will be in the interest of selfish family members to maximize total family income. We show by examples that the Rotten Kid theorem is not true without assuming transferable utility. We find a simple condition on utility functions that is necessary and sufficient for there to be the kind of transferable utility needed for a Rotten Kid Theorem. While restrictive, these conditions still allow one to apply the strong conclusions of the Rotten Kid Theorem in an interesting class of examples.

This paper argues that since the supply of oil in the ground is inelastic, the incidence of a sales tax on oil, maintained forever at a fixed rate, would fall entirely on the oil-suppliers. In the world economy, however, the elasticity of supply of oil to a single country depends on that country’s imports as a share of world output and on the elasticity of demand for that country. The paper calculates optimal tax rates for a country as a function of these variables and estimates optimal oil tax rates for the U.S., for some OECD countries separately, and for the U.S. plus the OECD collectively. Current U.S. tax rates are shown to be far below optimal values.

This paper generalizes results of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive binary relations. It proves a generalization of Nash's theorem on the existence of non-cooperative equilibrium. It also shows that existence of competitive equilibrium can be proved as a consequence of the existence of a maximal element for an appropriately chosen binary relation.

This note was inspired by a 1970 JPE paper by Robin Barlow, who claimed that if the ratio of income elasticity to price elasticity of a public good exceeded the elasticity of tax rate with respect to income, then too little public goods would be supplied under majority voting. This note shows that Barlow's claim is not true in general, but also shows that with some fairly plausible additional assumptions it is true.