Question

Assume you have to find the optimal commodity tax rate for all the goods in an economy featuring only 17 goods. How many first order conditions would you have to find in your DWL minimisation problem?

Answer 1

This paper uses a three-tax linear model to study numerically the optimal tax mix. The

three aggregate taxes relate to labour, capital and commodities respectively. The most striking

result is that with a linear expenditure system (LES) based on econometric estimates, indirect

(i.e. commodity) taxation dominates the optimal tax mix, with over 80% of tax revenue coming

from indirect taxes. Although some analytical justification is presented for this surprising result,

it should be tested numerically using other econometrically estimated utility-demand systems.

Comprehensive computational modelling of the optimal tax mix has been so far missing from

the literature. Considering the results presented here, there seems to be considerable scope for

further research in this area. From a theoretical perspective, a major innovation in this paper is

the introduction of capital taxation into a static tax mix model. The analytical part of the paper

provides approximate predictions for optimal linear tax rates (including capital tax) called the

modified inverse elasticity rules. Using these formulas, it is possible to provide some

explanations for the dominance of indirect taxation in the optimal tax mix.

The three-tax model studied here is a fairly comprehensive one, incorporating labour,

capital and indirect taxes. It is assumed that there is only one linear labour income tax rate,

denoted and a single capital income tax rate, denoted Labour income is denoted  zi =

wiLi, where wi is the fixed wage rate for household i and Li is the corresponding labour supply.

Capital income is capital (k) multiplied by a fixed average pre-tax real rate of return (r), that is

kr. r and wi are assumed to be fixed. The net after-tax rate of return is r (1-T_k). r is measured after taking away depreciation and the remuneration of self-employed.