The Long-Run Effect of a Tax-Rebate Program

In each period of a dynamic tax-rebate program, a (fixed) quantity tax is imposed on each unit of a given good, and the tax revenue is rebated back to the consumer in the next period. The program lasts for infinite number of periods. The author considers a representative consumer’s dynamic consumption behavior, the long-run steady-state consumption, and the consumer’s welfare. Under the standard continuity and strict convexity assumptions on the consumer’s preferences, he shows that the tax strictly reduces the consumption of the good in each period as well as in the steady state, and the consumer is strictly worse off. He also provides numerical analysis when the consumer has the quasilinear or the Cobb-Douglas utility functions.