Income Tax and Unit Tax

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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:...
View Full Document

## 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.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online