This paper introduces the classical Public Finance concept of taxation according to ability to pay in the set-up of standard optimal income tax models. The fundamental concept used is the specification of an individual revenue requirement function, a mapping from abilities to taxes. The discussion is centered on the derivation of a tax function on income such that agents of a given ability pay exactly the amount specified by the revenue requirement function. The construction of the tax function is achieved by using the differentiable approach to the revelation principle. A basic differential equation is generated from which the tax function is found. A discussion of the necessary and sufficient conditions for the validity of this technique and an interpretation of the results in graphs are provided. A welfare ranking of the solutions is used to select the best tax function that implements the individual revenue requirements
