The Ramsey Rule Revisited

Abstract

In pursuit of an optimum tax scheme in terms of minimizing welfare loss, economists have been searching for a better solution since the seminal contribution of Ramsey [17]. The literature is voluminous: they include the works by Hotelling [9], Hicks [8], Harberger [7], Dimond and Mirrlees [2], Dixit [3; 4], and Sandmo [19]. The Ramsey optimum tax rule, that is, the percentage reduction in quantity demanded of each commodity be the same was interpreted by Kahn [11] as the inverse elasticity rule. The inverse elasticity rule states that the optimum tax rates and price elasticities of demand should be inversely related. The merit of the inverse elasticity rule is that the optimum tax rate does not require the explicit knowledge on prices and quantities of the taxed commodities. To evaluate policy implications, one needs only to examine the published price elasticities of demand to arrive at optimum tax rates. However, the inverse elasticity rule normally applies only to a constant cost case in which average cost (hence marginal cost) is horizontal [10; 18]. In a competitive market, while the constant cost case is plausible, it assumes away the producer's surplus. In this paper, we prove that the inverse elasticity rule with the ad valorem tax on the gross demand price is equivalent to that with the supply ad valorem tax developed by Ramsey.' However, the inverse elasticity formula with the unit tax as shown in this paper is different. Furthermore, we propose a sufficient condition for optimum tax ratio with a positively sloped supply schedule. In addition, we explore a sufficient condition for an optimum equiproportional tax across all commodities. Last, we employ some empirical estimates of price elasticities of both demand and supply to calculate the optimum tax ratios.