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lecture7 - Lecture Note 7 Redistribution Optimal Taxation...

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Lecture Note 7: Redistribution, Optimal Taxation and Tax Reform Part 2B: Paper 1. Dr. T.S. Aidt ° University of Cambridge Michaelmas 2010 1 Introduction The discussion of optimal policy so far has emphasized that taxes should be levied e¢ ciently and that governments should aim at raising the revenues they need in such a way that the deadweight cost per unit of revenue is the least possible. However, this totally ignores another important consideration: equity. In this lecture, we shall discuss two issues in optimal taxation related to whether and how equity considerations should be build into the tax structure. The main themes can be captured by the following three questions: 1. How can optimal commodity taxes be used to take equity considerations into account? 2. Should optimal commodity taxation be used as a means to redistribute income or is that better left to the income tax system? 3. Is there a need for a separate income tax system and if so how should it look like? In addition, we shall look at a recent example of commodity tax reform in Ireland to illustrate how the theory can be put to very e/ective practical use. 2 Equity and the design of Ramsey Taxes The Ramsey Tax rule considered in the previous lecture is purely based on e¢ ciency considerations and, in fact, it is derived in a world with only one ° Disclaimer: This note may contain mistakes. If you spot any, please bring them to my attention. 1
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individual (or many identical individuals), so equity considerations and redis- tribution is ruled out from the very beginning. To think about the possible equity-e¢ ciency trade-o/ involved in designing optimal Ramsey taxes, we must consider a many-person version of the Ramsey model considered in the previous lecture and introduce a social welfare function to allow for comparisons between individuals. We consider the same two-goods-one-factor-of production model as in the previous lecture. The new feature is that we assume that there are two (types) of consumers (individuals) instead of just one. Let us call them the rich ( R ) and poor ( P ), i.e., h 2 f R; P g The indirect utility functions of the two types are given by V R ( q; m R ) (1) V P ( q; m P ) (2) The social welfare function is assumed to be utilitarian so that we simply add up the indirect utilities of the two (types of) consumers: SWF = ° R V R ( q; m R ) + ° P V P ( q; m P ) (3) where ° R and ° P are the (welfare) weights given to the welfare of the two types of consumers and m R and m P are the incomes of the two types. If society wants to help the poor, we would expect ° P > ° R . The optimal tax problem is to select (ad valorem) taxes on good x 1 and x 2 to maximize social welfare subject to the revenue requirement that e R = ( q 1 ° p 1 ) x 1 + ( q 2 ° p 2 ) x 2 ; (4) where x i = x R i + x P i is aggregate consumption of commodity i . We can derive the optimal tax structure by going through the same steps as in the single consumer case, but we shall not repeat this here. Instead, let us make the assumption of independent demands (i.e., that the compensated cross price e/ects between
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