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Optimal Commodity Taxation
Demand for some commodity equals P = 90 - 3Q, while the supply is perfectly elastic at the price P = 30.
a) Before the tax is implemented, what is the equilibrium quantity Q??
b) What is the tax revenue from a tax of $t per unit? What is the deadweight loss of an excise tax of $t per unit? Write these as a function of the tax t. It may be helpful to draw a picture.
c) What is the marginal deadweight loss (MDWL) of an increase in the tax? What is the marginal revenue (MR) of an increase in the tax?
d) If the value of government revenue is λ = 41 , use the Ramsey rule to find the optimal per unit tax t.
e) Now, suppose that there is a negative externality created by the production of this commodity. The marginal damage is MD = 15 per unit. What is the new optimal commodity tax?
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