Optimal tax

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Optimal tax theory or the theory of optimal taxation is the study of designing and implementing a tax that maximises a social welfare function subject to economic constraints.^[1] The social welfare function used is typically a function of individuals' utilities, most commonly some form of utilitarian function, so the tax system is chosen to maximise the aggregate of individual utilities. Tax revenue is required to fund the provision of public goods and other government services, as well as for redistribution from rich to poor individuals. However, most taxes distort individual behavior, because the activity that is taxed becomes relatively less desirable; for instance, taxes on labour income reduce the incentive to work.^[2] The optimization problem involves minimizing the distortions caused by taxation, while achieving desired levels of redistribution and revenue.^[3][4] Some taxes are thought to be less distorting, such as lump-sum taxes (where individuals cannot change their behaviour to reduce their tax burden) and Pigouvian taxes, where the market consumption of a good is inefficient, and a tax brings consumption closer to the efficient level.^[5]

In the Wealth of Nations, Adam Smith observed that

“Good taxes meet four major criteria. They are (1) proportionate to incomes or abilities to pay (2) certain rather than arbitrary (3) payable at times and in ways convenient to the taxpayers and (4) cheap to administer and collect.” ^[6]