A Note on the Musgravian Transformation

Abstract

It has been long recognized that an ad valorem tax rate on revenues (demand) has its counterpart in costs (supply). Such a one to one correspondence is referred to as the Musgravian transformation. The transformation is monotonic and nonlinear. However, the property of concavity of the tax revenue curve is not preserved under the transformation. Even if the tax revenue curve of the demand ad valorem tax is strictly concave everywhere, the tax revenue curve of the supply ad valorem tax is guaranteed to be concave only before its own revenue-maximizing tax rate.