Optimal tax

Optimal tax theory or the theory of optimal taxation is the study of designing and implementing a tax that reduces inefficiency and distortion in the market under given economic constraints. Generally, this criterion consists of individuals' utility and the optimization problem involves minimizing the distortions caused by taxation. A neutral tax is a theoretical tax which avoids distortion and inefficiency completely. Other things being equal, if a tax-payer must choose between two mutually exclusive economic projects (say investments) that have the same pre-tax risk and returns, the one with the lower tax or with a tax exemption would be chosen by a rational actor. Thus economists argue that taxes generally distort behavior.

In the Wealth of Nations, Adam Smith observed that

Generating a sufficient amount of revenue to finance government is arguably the most important purpose of the tax system. Optimal taxation, which is the theory of designing and implementing taxes that reduce inefficiency and distortion in the market through Pareto optimal moves under given constraints, is constantly debated. Though inequality will always exist within even the most efficient markets, the goal of taxation is to eliminate as much inefficiency as possible and to raise revenue to fund government expenditures. With any tax, there will be an excess burden, or additional cost, to the consumer and the producer. Whenever the consumer purchases the taxed good or service, and the higher elasticity, or responsiveness, of the demanded product, the greater the excess burden is on either the consumer or producer. Those individuals or corporations who have the most inelastic demand curve pay the brunt of the excess burden curve. However, the tradeoff of placing larger taxes on inelastic goods is that the higher tax will lead to lower quantity exchanged and thus a smaller deadweight loss of reduced revenue.

When discussing what a fair and optimal tax level would be, the principle of equity, both horizontal and vertical, is important. Equity is determined by first assessing an individual’s ability-to-pay. The idea of the ability-to-pay principle considers whether or not it is fair to tax someone higher just because that person has the ability and resources to pay. If it is decided that they should be required to pay more, the question of how much more arises. These questions can be analyzed through horizontal and vertical equity which are subsets of the ability-to-pay principle. Horizontal equity suggests it is fair if people who have equal ability-to-pay actually do pay the same amount in taxes. Vertical equity is the idea that people who have a higher ability-to-pay should actually pay more than those who have a lower ability-to-pay, as long as the increase in tax level is considered to be reasonable.

...
Wikipedia