Question

Practice Sales Tax Problems

a. Suppose the government puts a sales tax on textbooks and tells publishers they are responsible for paying a $20 tax on every book sold. Without any more information, what would you predict is likely to happen?

b. Now suppose that the price elasticity of demand for textbooks is -.3 and the price elasticity of supply is 1.2 . Make specific predictions about how much the price paid by consumers will rise, the price received by publishers will fall and how much of the tax is paid by each group.

c. Suppose a sales tax is placed on a product with perfectly inelastic demand. Sketch out a supply – demand diagram and shift the supply curve. Use the graph to explain what happens.

d. If the elasticity of demand is -2 and the elasticity of supply is .5, then explain how a $10 per unit tax will affect prices. How much of this tax do consumers pay? Producers?

Answer 1

a. Sales tax of $20 is likely to increase the price paid by consumers and decrease the price received by sellers.

b. Consumer share=Pes/(Ped+Pes)= 1.2/(0.3+1.2)= 0.8 or 80%

Producers share of tax= Ped/(Ped+Pes)= 0.3/(0.3+1.2)= 0.2 or 20%

Out of the $20 tax, 80% or $16 is paid by consumers and 20% or $4 is paid producers.

c. Sales tax will raise the supply curve by the amount of tax. Complete tax will be paid the consumers and producer will not pay any tax at all.

d.

Ped= -2

Pes= 0.5

Consumer share=Pes/(Ped+Pes)= 0.5/(0.5+2)= 0.2 or 20%

Producers share of tax= Ped/(Ped+Pes)= 2/(0.5+2)= 0.8 or 80%

Out of the $10 tax, 80% or $8 is paid by producers and 20% or $2 is paid by consumers.