Optimal redistribution with unobservable preferences for an observable merit good

This paper considers a government that seeks both to redistribute income and to encourage or discourage the consumption of a certain good. This good is assumed to be either a merit or demerit good. Individuals differ in their exogenous income and in their preferences for the merit good. The government can perfectly observe the level of consumption of the merit good. However, it cannot observe neither income nor preferences. The only observable variable is thus each individual's consumption of the merit good. In order to account for merit good considerations, we consider a modification of the utilitarian social welfare function in which the government imposes uniform preferences, despite the heterogeneous individual preferences, at a level which will depend on the merit or demerit nature of the observable good. We derive the optimal nonlinear redistributive policy and compare our results to the ones that would be obtained under a utilitarian social welfare function that respects the own preferences of individual.