Can the Laffer curve for consumption tax be hump-shaped?

This paper characterizes the shape of the Laffer curve for consumption tax analytically, considering (i) the functional form of utility and (ii) the use of tax revenue in a neoclassical general equilibrium model. The tax revenue curve for consumption tax cannot be hump-shaped if the utility function is King–Plosser–Rebelo utility with constant labor supply elasticity. Conversely, the curve can be hump-shaped if the utility function is additively separable in consumption and labor supply or if the utility function is Greenwood–Hercowitz–Huffman, both of which are popular in the literature. The use of tax revenue also has significant effects on the tax revenue curve for consumption tax. If the tax revenue is mainly used as a lump-sum transfer to households, then the tax revenue is likely to be unbounded, whereas it is likely to be bounded and the tax revenue curve is likely to be hump-shaped if the tax revenue is mainly used as government consumption