SFB 303 Discussion Paper No. A - 169
Author: Ebert, Udo
Title: Optimal Income Taxation: On the Case of Two-Dimensional Populations
Abstract: Mirrlees' model for the determination of an optimal nonlinear income tax is an important part of public
finance. But the underlying economic model is interesting in itself. It can be interpreted in different ways.
Basically it is a principal-agent problem. The government - the principal - develops an optimal tax schedule for
its individuals - the agents who maximize their own utility. Similarly we can consider a monopolist who wants to
determine an optimal nonuniform price schedule (cf. Roberts (1979), Goldman/Leland/Sibley (1984)). Guesnerie
and Laffont (1984) investigate an analogous more specific model for designing an optimal control of a self-
managed firm. Further examples could be added. In all cases the principal is not able to observe the agents'
characteristics directly. It must be inferred from the agents' behaviour.Solving this general problem is difficult.
Most of the literature deals with the case where there is only one type of characteristic; i.e. that the agents'
population is one-dimensional. It can be described by one parameter. Even here some difficulties have to be
surmounted. This paper deals with the problem of optimal income taxation for a two-dimensional population.
Some conditions on the preference orderings and the utility functions are provided which allow to transform the
problem and to describe some properties of its solution. The limitations of the method employed are discussed.
Of course these results are also important for other applications of the general principal-agent problem which
underlies our analysis.
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Creation-Date: March 1988
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