Question

We have two goods A and B and the government plans to collect X by imposing tax rate t on these two goods. The marginal costs of both goods are 10. The demand curves of two goods are

pA = 20 - QA
pB = 50 - 2QB

(a) Given tax rate tA and tB, calculate the tax revenues of two goods.
(b) Given tax rate tA and tB, calculate the excess burdens of tax of two goods.
(c) Calculate the relationship between two tax rates tA and tB which minimizes the excess
burdens to collect the same tax revenue.
(d) Good B is mostly consumed by the poor, and the government cares about them. Gov-
ernment treats the half of the tax revenue collected from the market for B as social
loss. That is, the government tries to minimize the sum of excess burden and half of the
revenue from good B while collecting the targeted revenue X. Calculate the relationship
between two tax rates to do that. (Hint: social loss from the tax on good B is not just
a excess burden, but sum of excess burden and half of the tax revenue of good B.

Answer 1

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