A Numerical Model of Optimal Differentiated Indirect Taxation

This study examines the structure of optimal commodity tax rates in a many-person many-goods static computational model using segmented LES utility. One of the major findings is that with non-linear Engel curves and linear income tax, optimal commodity tax rates will be progressive and highly dispersed under logarithmic utility specifications. The dispersion of tax rates is reduced if the inequality aversion rate of society is low. With exogenously given non-optimal and non-linear income tax schedules, usually there is still a need for differentiated and progressive indirect taxation. These findings are in marked contrast to the continuing preoccupation of much of the literature with uniform indirect taxation for redistributive purposes. The results also indicate that if tax evasion incurs substantial deadweight costs, it usually reduces optimal tax rates by over a half of the evasion/revenue ratio of the product, with the reduction being larger for necessities and smaller for luxuries. Private compliance costs and government administration costs reduce optimal tax rates by a similar amount to the share of these costs from taxes. In a model with linear income tax, the effect of externalities on optimal tax rates substantially exceeds the corresponding Pigouvian tax rates or subsidies. The main benefit of higher taxes on leisure complements than leisure substitutes appears to be in boosting tax revenue for redistribution, rather than in improving the utility position of those paying the taxes. The effect of complexities such as tax evasion, administrative costs, externalities and leisure complements/substitutes on redistribution is not neutral. Generally, these factors tend to increase the progressivity of optimal commodity tax rates.