Optimal labour income tax is a sub-area of optimal tax theory which refers to the study of designing a tax on individual labour income such that a given economic criterion like social welfare is optimized.
Efficiency-equity tradeoff The modern literature on optimal labour income taxation largely follows from James Mirrlees' "Exploration in the Theory of Optimum Income Taxation". The approach is based on asymmetric information, as the government is assumed to be unable to observe the number of hours people work or how productive they are, but can observe individuals' incomes. This imposes incentive compatibility constraints that limit the taxes which the government is able to levy, and prevents it from taxing high-productivity people at higher rates than low-productivity people. The government seeks to maximise a utilitarian social welfare function subject to these constraints. It faces a tradeoff between efficiency and equity:
Higher levels of taxation on the rich create revenue that can be used to redistribute to the poor, which raises social welfare because the marginal utility of income is (assumed to be) higher for the poor than the rich; However, taxation reduces the incentive to work, and so leads to labour supply below the optimal level.
Mechanical, behavioral and welfare effects Emmanuel Saez in his article titled "Using Elasticities to Derive Optimal Income Tax Rates" derives a formula for optimal level of income tax using both the compensated and uncompensated elasticities. Saez writes that the tradeoff between equity and efficiency is a central consideration of optimal taxation, and implementing a progressive tax allows the government to reallocate their resources where they are needed most. However, this deters those of higher income levels to work at their optimal level. Saez decomposes the marginal effects of a tax change into mechanical, behavioural and welfare effects, as follows:
The mechanical effect is the effect that the tax change would have on government revenue, if no individuals changed their behaviour in response. For a tax increase, this is positive. The behavioural effect is the effect that the behavioural change induced by the tax change would have on government revenue, at the initial tax rates. Raising taxes will discourage labour supply, and this will lead to lower tax revenue as a result; so for a tax increase, this is negative. The welfare effect is the effect that the tax change has on the social welfare function by changing individual's utilities. For a tax increase, this is negative. The sum of these effects should be zero at the optimum. Stipulating this condition results in the following formula for the optimal top tax rate, if incomes are Pareto distributed:
τ = 1 − g ¯ 1 − g ¯ + ζ ¯ u + ζ ¯ c ( α − 1 ) {\displaystyle \tau ={\frac {1-{\bar {g}}}{1-{\bar {g}}+{\bar {\zeta }}^{u}+{\bar {\zeta }}^{c}(\alpha -1)}}}
where:
τ {\displaystyle \tau } is the tax rate
g ¯ {\displaystyle {\bar {g}}} is the ratio of social marginal utility for the top bracket taxpayers to the marginal value of public funds for the government, which depends on the social welfare function. The case g ¯ = 0 {\displaystyle {\bar {g}}=0} corresponds to one where the government does not care about the welfare of top bracket taxpayers, and wants to raise as much revenue as possible from them, so setting g ¯ = 0 {\displaystyle {\bar {g}}=0} gives a formula for the revenue-maximising top tax rate.
ζ ¯ u {\displaystyle {\bar {\zeta }}^{u}} and ζ ¯ c {\displaystyle {\bar {\zeta }}^{c}} are respectively the uncompensated and compensated elasticity of labour supply; higher elasticities imply that labour supply will fall more in response to an increase in taxes.
α {\displaystyle \alpha } is the shape parameter in the Pareto distribution of income. Empirical estimation of the parameters of this equation suggests that the revenue-maximising top tax rate is between approximately 50% and 80%, although this estimate neglects long-run behavioural responses, which would imply higher elasticities and a lower optimal tax rate. Saez's analysis can also be generalised to tax rates other than the top rate.
Arithmetic vs. economic effects In the late 1970s, Arthur Laffer developed the Laffer curve, which demonstrates that there are two effects of changing tax rates:
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