Econ 353 Taxation and Income Distribution (ch.15)
Iryna Nekhayevska
#1. In the province of Alberta (which does not have any provincial sales tax), the provincial
tax on hotel rooms is 4%. Supporters of this tax argue that the tax benefits the province because its payers are largely out-of-province tourists. Use the theory of tax incidence to analyze this claim. Solution: Tax theory tells us that the statutory incidence and the actual incidence are usually different. Hotel owners and employees may bear the tax burden if they have to lower their before-tax prices to compensate for the tax. This depends on the elasticities of S and D for hotel accommodation. If local residents travel (say, to Jasper and Banff), they also bear the tax. #2. Assume that the capital-labour ratios are identical in all sectors of the economy. What determines the incidence of a tax on the output of any single sector? Solution: When all capital-labour ratios are the same, inputs released by any sector may be absorbed by the others without changing the relative prices of capital and labour (that is r / w ). Accordingly, the sources of income are not altered. Incidence is determined solely by the use of income. The consumers who purchase relatively large shares of taxed output will bear more of the tax. #3. Gail has an income Y and spends it only on food (F) and music (M). Let good prices be PF and PM. Show that if ad valorem tax of 25% is imposed on both F and M, it is equivalent to 20% tax on her income. Solution: Her after tax budget is (1 + 0.25)PF × F + (1 + 0.25)PM × M = Y or 1.25 × [PF × F + PM × M] = Y or PF × F + PM × M = Y /1.25 . Since Y /1.25 = 0.8Y = (1 − 0.2)Y , it is an equivalent to 20% tax on her income. #4. The demand function for gasoline is Q = 100 − 2P and its supply function is Q = 80 + P (Q is measured in liters and P is per/liter price). Market for gasoline is competitive. What are equilibrium price and quantity in the market? a) If there is a unit tax on gasoline of $1, what are the new equilibrium price and b) quantity? What is the government revenue? How much of the tax is paid by consumers and how much by producers? If there is an ad valorem tax of 50%, what are the new equilibrium price and c) quantity? What is the government revenue? How much of a tax is paid by consumer and how much by producers? Solution: (a) In the market, quantity demanded will equal quantity supplied, or 100 − 2P = 80 + P and P* = 20 / 3 = 6.66 . Then from either D or S, Q = 80 + 6.66 = 86.66 . (b) Once the per unit tax of $1 is introduced, Pd = Ps + 1 . Since quantity demanded will equal
quantity supplied after tax, 100 − 2Pd = 80 + Ps and 100 − 2(Ps + 1) = 80 + Ps or Ps* = 18 / 3 = 6 .
Then Pd* = 6 + 1 = 7 . And equilibrium quantity is Q* = 80 + 6 = 86 (notice that Pd goes into
demand function and Ps goes into supply function). Revenue R = t × Q* = $1× 86 = $86 . Consumers pay Pd* − P* = 7 − 6.66 = 0.34 or 0.34 /1× 100% = 34% and producers pay P* − Ps* = 6.66 − 6 = 0.66 or 0.66 /1× 100% = 66% . (c) Similarly, after tax Pd = (1 + 0.5)Ps . 100 − 2Pd = 80 + Ps and 100 − 2(1.5)Ps = 80 + Ps or Ps* = 20 / 4 = 5 . Then Pd* = 1.5 × 5 = 7.5 and Q* = 80 + 5 = 85 . R = (Pd* − Ps* )Q* = ((1 + τ)Ps* − Ps* )Q* = τ× Ps* × Q* = 0.5 × 5 × 85 = 212.5 . Consumers pay Pd* − P* = 7.5 − 6.66 = 0.84 or 0.84 / 2.5 × 100% = 33.6% . Producers pay P* − Ps* = 6.66 − 5 = 1.66 or 1.66 / 2.5 × 100% = 66.4% .