In a seminal paper, Becker (1968) showed that the most efficient way to deter crime is to impose the severest possible penalty (to maintain adequate deterrence) with the lowest possible probability (to economize on costs of enforcement). We shall call this the Becker proposition (BP). The BP is...

With nondistortionary user charges, the first best and second best of a single-club-exogenous-income economy with identical individuals coincide. They differ if incomes differ. Overprovision of a superior club good then occurs in the Second Best.

We show that preference-homogeneity and loss-aversion are necessary and sufficient for the value function to have the power form with identical powers for gains and losses and for the probability weighting functions for gains and losses to be identical.