Suppose the market for grass seed can be expressed as: Demand: QD = 1

Suppose the market for grass seed can be expressed as:

Demand: QD = 100 – 2p
Supply: QS = 3p
If government imposes a $5 specific tax to be collected from sellers, what is the price consumers will pay? How much tax revenue is collected? What fraction is paid by sellers?

ANSWER

At equilibrium without the tax, p = 20 and Q = 60. In addition to receiving their price, sellers must also receive $5 per unit. Rearranging the supply curve yields p = Q/3; adding the tax yields p = (Q/3 ) + 5. Substituting this into the demand curve yields Q = 100 – 2[(Q/3 ) + 5] =
90 – (2/3 )Q or (5/3 )Q = 90. Solving yields Q = 54. Substituting into either demand curve or supply curve plus tax yields p = 23. Tax revenue = 5 ∗ 54 = 270. Since price rose $3 on a $5 tax, consumers pay 3/5 of the tax or 162, and sellers pay 2/5 of the tax.