Question

. Suppose that the Vermont government needs to collect $10 from each adult who lives in Vermont and

     there are two alternative ways to collect the $10 from each adult: (a) $10 of income tax from each

     adult and (b) a 2% sales tax on food for the first $500 spent on food (2% of $500 is equal to $10 and  

     we assume each adult spends at least $500 on food per year in Vermont).

1. Clearly explain the lump-sum principle and why the income tax is expected to have smaller impact on individual’s welfare (utility).

2. Ask 10 of your friends who live in Vermont about their preferences for the two alternative ways: (a) prefers the income tax, (b) prefers the sales tax, or (c) indifferent between the two. Report the result (the number of friends who selected (a), (b) and (c), respectively). Make sure you clearly present the two alternative ways to each of them.

3) Is the response from your friends consistent with the lump-sum principle? If any of them selected

      (b) or (c), explain the possible reasons for the inconsistency with the principle.

Answer 1

Considering both the scenarios of an income tax and a quantity tax on the food we can analyse the budget constraints in the two cases as follows:

For income tax-

P₁X₁+P₂X₂=M

after the tax is imposed, tax=t

P₁X₁+P₂X₂=M-t

For Quantity tax-

P₁X₁+P₂X₂=M

After the tax of r=0.02P₁ is imposed

(P₁+r)X₁+P₂X₂=M

P₁X₁+P₂X₂=M-rX₁

Note that in both the cases the value of the tax remains the same therefore we can say that, M-t=M-rX₁

Equating the 2 budget constraints we find the constrains to hold the same value of tax but a difference in their slopes. Considering this difference in the slopes we draw the curve of both the budget lines to analyse further.

AB depicts the original budget line. AC is the budget line depicting the quantity tax and ED is the budget line depicting the income tax. The consumer is first at optimum point 1 on IC1. After the imposition of tax the consumer moves to IC2 at point 2 which is the insection point of both the new budget lines. At this point the IC is tangent to the line AC but not to the line ED therefore, there is scope for the consumer to move along the same line ED but to a higher indifference curve on that line IC3 and point 3. Due to this the consumer feels better off when income tax is imposed even though the value of the tax remains the same throughout.

However this analysis cannot be 100% certain and therefore different consumers may have difference preferences.

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