Question

(a) Using an appropriate diagram Illustrate and explain the welfare effects of a unit tax on a commodity within the framework of indifference curves analysis

(b) Illustrate on the same diagram, the welfare effects of a lump-sum tax that generates the same amount of tax revenue as in (a). (1.5 marks)

(c). Are the welfare effects the same? Is any of the taxes efficient? Explain why or why not. (1.5 marks)

Answer 1

Let, Initially the consumer is in equilibrium at point Q1, where his budget line PL intersects the indifference curve IC1.

(a) Now suppose that a unit tax is imposed on the good X, this increases the price of good X and hence the consumer can consume less of this good. So his budget line shifts from PL to PL1 and the consumer is in equilibrium at point Q2 where the new budget line is tangent to the indifference curve IC2, hence there is a loss in welfare of consumer because he comes at a lower IC, here tax revenue is KQ2.

(b) Now suppose a lump-sum tax is imposed, the price line will shift below but will be parallel to PL, since this tax also generates same tax revenue, so the new price line AB will pass through Q2. So we can see that the indifference curve IC3 is tangent to the new price line AB at Q3 and hence this is equilibrium for consumer. Here also there is a welfare loss because IC3 is below IC1.

(c) No, the welfare effects in both the situations are different even with the same tax revenue. As it can be seen from the graph that in the case of per unit tax the equilibrium is at IC2, but in case of lump sum tax, equilibrium is at IC3. We can see that IC3 is above IC2, so we can say that the welfare loss is more in per unit tax and less in lump sum tax. The lump sum tax is more efficient as it decreases the welfare less.