A Note on the Long-Run Effect of a Tax-Rebate Program

We consider the following dynamic tax-rebate program. In each period, a (fixed) quantity tax is imposed on each unit of the good consumed and the tax revenue is rebated back to the consumer in the next period. The program lasts for infinite number of periods. We consider consumer's dynamic consumption behavior, the consumption behavior in the long-run steady state, and the welfare effects of the program. Under the standard continuity and strict convexity assumption on consumer preference, we show that the tax will strictly reduce the consumption of the good being taxed in each period as well as in the steady state, and consumer is strictly worse off. We also provide analytical solutions when consumer has quasilinear or Cobb-Douglas utility function