Income Tax and Unit Tax

Income Tax and Unit Tax - Economics 21 Intermediate...

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Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory - Income and Unit Taxes 1 Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory Income and Unit Taxes Reference: Varian, p. 87 Outline: I. Introduction II. Choosing Taxes I. Introduction We show that a consumer would always prefer an income tax to a unit (i.e. quantity) tax designed to raise the same revenues. II. Choosing Taxes Consider the budget constraint: p 1 x 1 + p 2 x 2 = m (1) And first consider a quantity tax: p 1 + t ( ) x 1 + p 2 x 2 = m (2) Even though we do not know whether the tax has increased or reduced the demand for good 1, we do know that the optimal choice x ! = x 1 ! , x 2 ! ( ) must satisfy the constraint: p 1 + t ( ) x 1 ! + p 2 x 2 ! = m (3) The revenue from this tax is: R ! = tx 1 ! (4) Now consider an income tax that is designed to raise the same amount of revenue as the quantity tax. The budget constraint is now: p 1 x 1 + p 2 x 2 = m ! R " # p 1 x 1 + p 2 x 2 = m ! tx 1 " (5) Note that the budget line (5) has same slope as the original budget line (1). Moreover, it must
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Unformatted text preview: Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory - Income and Unit Taxes 2 pass through the point x ! = x 1 ! , x 2 ! ( ) . To see this, simply rearrange equation (3): p 1 + t ( ) x 1 ! + p 2 x 2 ! = m " p 1 x 1 ! + tx 1 ! + p 2 x 2 ! = m " p 1 x 1 ! + p 2 x 2 ! = m # tx 1 ! (6) Thus the optimal choice under the quantity tax , x ! = x 1 ! , x 2 ! ( ) , lies on the income tax budget line and as such is an affordable choice. It is not, however, an optimal choice. At x ! = x 1 ! , x 2 ! ( ) , the MRS is ! p 1 + t ( ) p 2 but the income tax allows the consumer to trade at an ERS of ! p 1 p 2 . Thus MRS > ERS at x ! = x 1 ! , x 2 ! ( ) ; the consumer is wiling to give up more good 2 then the market (under the income tax scheme) demands. Thus, he can move to a higher indifference curve by increasing his consumption of good 1 - see Figure 1: Figure 1: Comparing Income Taxes and Unit Taxes:...
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This note was uploaded on 07/16/2010 for the course ECON 21 taught by Professor Johng.sessions during the Summer '09 term at Dartmouth.

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Income Tax and Unit Tax - Economics 21 Intermediate...

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