We define a new mathematical function that is an adaptation of a welfare function consistent with the premises of classical welfare. This function is innovative in that it enables us to specifically identify income tax functions that optimally balance the objectives of justice and efficiency in an economy. The new welfare function combines gross national product as an expression of economic performance with the Gini coefficient as a measure of its distributive justice. Afterwards we concentrate on the application of the new welfare function to the design of tax regimes and discuss the question of how to optimize income taxes. On the basis of our data, we discover interesting solutions. To find these, we compute optimal values of the welfare function under constraints of negative tax incentives; in the present case, tax avoidance.