Tax Rates and Tax Collections: The Basic Analytics of Khaldun-Laffer Curves

Abstract

This article describes the relation between tax rates and tax collections for three different types of taxes: unit excises, ad valorem excises, and general income taxes. The tax rate-tax collections relationship is currently the subject of widespread discussion, but the determinants of the shape of the function have not been clearly specified. This article presents mathematical and graphical expositions of the linkage between supply and demand for taxed commodities and the tax rate-tax collections relationship. The tax collections function will often, but not always, be shaped as it is commonly drawn; its shape is uniquely determined by the underlying supply and demand functions in the taxed market. Whether a tax rate change will increase or reduce tax collections is always an empirical issue which depends on the values of items identified by the theoretical analysis in this article.