This paper shows that if workers have identical wealths, abilities, and preferences then a draft lottery is Pareto superior to a voluntary army. It also shows that if being a civilian is a "normal good", then the optimal pay schedule will be such that people prefer not being chosen for the army. The paper shows how this idea extends to occupational choice in general and shows that pure gambles taken prior to occupational choice can substitute for lotteries that determine one's occupation. This paper repairs what I think is a major flaw in standard general equilibrium theory, which assumes away the nonconvexity of preferences that follows from the discreteness of occupational choice.

This paper incorporates medical insurance, life insurance, annuities, and the value of risks to human life in a single theory.

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.