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Optimal Taxation

Vincent A. Hildebrand

Glendon College, York University and SEDAP, McMaster University

Lecture 7

Frank Plumpton Ramsey (February 22, 1903 January 19, 1930) was a British

mathematician, philosopher and economist.

Ramsey's immortal contribution to economic theory was the elegant concept of

Ramsey pricing. This is applicable in situations where a (regulated) monopolistwants to maximize consumer surplus whilst at the same time ensuring that its

costs are adequately covered. This is achieved by setting the price such that

the markup over marginal cost is inversely proportional to the price elasticity of

demand for that good.

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Optimal Commodity Taxation >

I will derive the Ramsey rule using two different

methods.

From the second method, I will derive the well-known inverse elasticity rule of

taxation.

Discussion on optimal income taxation when equity is added to the equation.

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Optimal Taxation

This chapter is really an extension of the material in the previous chapter on

efciency.

This is the question we will attempt to address in this chapter:

If taxes have an excess burden how should taxes be designed so as to

minimize the excess burden (and maximize govt revenue) ?

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Optimal Commodity Taxation

The chapter in the text begins with a result that I already derived : that a tax on

all commodities including leisure would be a tax on the value of a person's time

endowment, and would therefore be lumpsum.

In this case, the inability to impose a lump sum tax is irrelevant.

The government can effectively take away a lump sum amount through equal

taxes on all commodities (including leisure).

No excess burden.

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Optimal Commodity Taxation

Obviously we need to proceed under the more realistic assumption that such a

lumpsum tax is infeasible since taxing leisure is virtually impossible to

implement.

As a result, some excess burden is inevitable. Key question is how to select

rates on "X" and "Y" to minimize excess burden subject to achieving the

government revenue constraint.

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Optimal Commodity Taxation: The Ramsey Rule (1)

To answer this, consider the following, somewhat articial problem : given the

total excess burden, let's try and raise as much revenue as possible.

That is, suppose that we raise the tax on food by one percent, and then lower

the tax on clothing by whatever amount makes the total excess burden

constant.

This policy, by construction, leaves the excess burden constant : it justsubstitutes more excess burden in the food market for less in the clothing

market.

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The Ramsey Rule (2)

It's worth doing if the new policy higher taxes on food, lower taxes on

clothing leads to more tax revenue (TR). Then we've got more revenue for

the same amount of waste. By construction,

EBF = EBC

The move is a good one ifTRF < TRC

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The Ramsey Rule (3)

That is, dividing both sides by the equivalent changes in excess burden, if at the

margin

TRF

EBF