Some Equity in Tax Collections of the Government in a Commodity Market

Abstract

The Laffer effect has been discussed before in context of macroeconomic endogenous growth models or in labor market. Discussion have been mainly about whether a tax cut on wages would induce workers to spend more time on work rather than leisure and at the same time leading to an increase in income tax revenues of the government. In this paper, we are interested in providing a general formula for the revenue-maximizing government using an ad valorem tax rate in a single (micro) commodity market such as automobiles, liquor or cigarettes in the case of non-linear demand and supply curves. It turns out that the optimal commodity tax rate depends on the after-tax demand elasticity. Therefore, in practice the government officials should try to project the after-tax elasticity and not rely on the before-tax elasticity, which is commonly assumed in the economics literature. More importantly, if the government imposes an ad valorem tax on a product in a micro market, then the consumers’ share of burden of tax does not change no matter what the tax rate is. Hence, in that sense, we find some equity in taxing. Some additional important theoretical results are derived when the demand and supply curves have different positions.