# SFB 303 Discussion Paper No. A - 054

**Author**: Tillmann, Georg

**Title**: Taxation and Observability

**Abstract**: One of the most fundamental issues in welfare economics is the problem of redistribution. "Poor people"
are favoured and "rich ones" taxed by certain ethical reasons. There may be many tools to change the income
distribution but one of the most fundamental ones is an income tax or more generally, taxes. Normally, a special
social welfare function (SWF) which represents the redistributive aims of the government is maximized. In most
of these models we have a continuum of consumers. In every tax-problem there is a two-step maximisation: First
agents maximize their utility - given a special tax function T; second, the government seeks the optimal tax
according to its aims. This is normally done using calculus and especially first order conditions. But it is well
known that these conditions characterize only a local solution - apart from the fact that it is not even known if
they determine a maximum at all. The discrete approach avoids these difficulties and provides us with a different
perspective on how the problem works. Additionally, it makes more explicit the interaction between the
government which is the planner and the agents who are the consumers. Therefore we have a special principal-
agent problem, where incentives play an important role.

In our paper we will do the following: As the weakness of SWF's is well known we use the Pareto-criterion only and ask ourselves: Which optima can be implemented
if the planner observes *l* (number of hours worked), *y* (income) or
*(y,l) * together? Which "signal" *s* is "better"?
Here better means that the set of implementable optima with respect to *si
* contains the set of optima with respect
to *sj*. At first this will be done in finite economies. We then go over to "large economies" with a continuum of
agents. Which optima do "survive" in this case? This is examined in a second part. All proofs are given in part
three.

**Keywords**:

**JEL-Classification-Number**:

**Creation-Date**: 1986

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