Optimal Tax System:

Recall that we define an allocation of resources in an economic system to be optimal in terms of Pareto efficiency. A Pareto efficient allocation is obtained with regard to a given distribution of resources or endowments. Since there can be many such Pareto optimal allocations, depending on various configurations of initial distribution of resources, such allocations are not comparable with one another. However, one can rank the allocations in terms of some criteria such as equity or fairness. In similar vein, Pareto efficient tax structure is one where there exists no alternative tax structure, which can make at least one individual better off without making anybody else worse off in the process. There can also be many Pareto efficient tax structures depending on  the initial distribution of income or endowments. However, one can choose an optimal tax system which maximises social welfare by using a social welfare function.

This requires ranking the efficient tax structure in terms of equity criterion. In more sophisticated models, equity and distribution of welfare are also assigned due importance and the social welfare function is formulated to take this into account to choose an  optimal tax system.

However, there is disagreement as to what constitutes a good tax policy to achieve the redistributional goals as per the objective of the government. Presence of a trade-off between efficiency and equity complicates the problem. Generally speaking, achieving greater equity entails higher tax rates. But inefficiency rises with the rise in tax rates.

Optimality can also be defined in terms of other criteria. One can argue that a good tax system is one, which minimises resource  cost of the tax system. One could also evaluate different tax systems in terms of justice and fairness.