Question

     Use an appropriate diagram to show that an income tax leaves a consumer better off than does an excise tax that raises the same amount of revenue for the Government. Explain your diagram fully.

Answer 1

An excise tax is like a quantity tax, which is a tax on the quantity of good produced. On the other hand, income tax is a tax on income of the consumer. Suppose the original budget line is following

p1x + p2y = m

In the above p1 is the price of x and p2 is the price of y, and m is the income of the consumer. Now, assume the government imposes an excise tax at a rate of t on good x. From the viewpoint of the consumer it is just as if the price of good x has increased by an amount t. Thus, the new budget constraint is following

(p1 + t)x + p2y = m

The budget will rotate around the x axis from AB to AC.

So, the excise tax on good x increases the price perceived by the consumer. The revenue raised by this tax is R = tx.

Let us now consider an income tax that raises the same amount of revenue. The form of this budget constraint would be

p1x + p2y = m – R

or, substituting for R

p1x + p2y = m – tx

The budget line will shift from AB to DF

Now, let us see the impact of the two taxes on the budget line and optimal choice of the consumer.

One can see that the slope of the budget line after the imposition of the income tax is the same as the slope of the original budget line (– p1/p2). However, we need to determine the location of this new budget line with income tax. One can see from the diagram that the budget line with income tax must pass through the optimal point with excise tax (E). So, point E lies on the budget line with income tax, and it is an affordable choice for the consumer.

However, with income tax point E is not an optimal choice. This is because at point E, the marginal rate of substitution (MRS) is – (p1 + t)/p2. But the income tax allows us to trade at a rate of exchange of (– p1/p2). Thus, the budget line cuts the indifference curve at E which implies that there will be some point on the budget line that will be preferred to E.

So, one can say that income tax is superior to the excise tax in the sense that one can raise the same amount of revenue from a consumer and still leave the consumer better off under the income tax than under the excise tax.