Chapter 14 Efficient and Equitable Taxation

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Chapter 14 Efficient and Equitable Taxation

• In this chapter we analyze the efficiency and
  equity implied by a tax side by side.
• A. Optimal Commodity Taxation
• When financing the goods and services provided
  publicly, how should the government tax various
  goods? Our first aim is showing the efficiency
  side of the argument Tax goods in such a way
  that excess burden is minimal.
• Consider Stella who consumes two goods, X and Y,
  as well as leisure, l. Given her time endowment
  of T, Stellas budget then is given by
• Now suppose that all goods, including leisure,
  was taxed at a rate of t, resulting in an
  after-tax budget constraint of
• Note that from the last equation, this tax is
  indeed a lump sum tax, since the value of time
  endowment has been reduced by 1/(1t) no matter
  how Stella acts!
• But there is a problem Putting a tax on leisure
  time available is impossible. The government
  cannot decrease the amount of hours available to
  work.
• The closest option is taxing all goods X and Y at
  the same rate t, without, of course, taxing
  leisure. (Neutral tax) But such a tax is, in
  general, not efficient.

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• Ramsey Rule Let us ask a more general question
  How should the taxes on X and Y be? How can one
  minimize excess burden?
• The answer lies in marginal analysis The
  marginal excess burden per additional dollar
  revenue from each commodity should be the same.
  (Why? What happens if the two marginal excess
  burdens are not equivalent?)

• For example, for good X, the marginal excess
  burden for the last dollar of tax, up from the
  previous unit tax of ux is the area of the
  trapezoid, fbea. (What is this area?)
• With a little bit of algebra one can show that
  this area is approximately ?X.

• Then, the marginal tax revenue is given by X1 -
  ?X. The Ramsey rule, then, dictates that the
  marginal excess burden per additional dollar of
  tax revenue for two goods must be the same, or
  that