Barry Haworth
University of Louisville
Department of Economics
Economics 201

### Who pays the tax?

In this handout, we look at how taxes contribute to changes in the price paid by consumers and the price received by sellers. If a per unit tax (e.g. excise taxes) is placed on a good that is sold in different markets, how are these markets affected when the only difference between them is the elasticity of their respective demand curves.

A. Demand and supply curves for gas in the suburbs:

 Demand: P = 3 - 0.5Qd Supply: P = 1 + 0.5Qs

The equilibrium price is \$2 (per gallon) and equilibrium quantity is 2 gallons (Not sure how we get those numbers? Then click here for a quick refresher). Suppose the government decides to put a tax of 50¢ per gallon on suppliers.

1) What is the effect on the market?

a. We can demonstrate this as a decrease in supply - which means that there is a decrease in supply (i.e. shift left).

b. After this, we get a new Supply curve: P = 1.5 + 0.5Qs

c. Our new equilibrium becomes: P = \$2.25 and Q = 1.5 gallons

B. Demand and supply curves for gas in rural areas is:

 Demand: P = 5 - 1.5Qd Supply: P = 1 + 0.5Qs

The equilibrium price and quantity are the same as above: \$2 (per gallon) and 2 gallons.

1) What is the effect of the 50¢ per gallon tax now?

a. Supply decreases, and our new Supply curve is: P = 1.5 + 0.5Qs
b. Our new equilibrium is P = \$2.375 and Q = 1.75 gallons

C. Who bears more of the "tax burden"?

1) Since the new equilibrium prices in each market never changed by more than 50¢ per gallon, we know that the consumers and producers in each market will "suffer".

a. Consumers in the suburbs pay 25¢ extra for each gallon of gas, while consumers in rural areas pay 37.5¢ extra for each gallon of gas.

b. The "burden" of the tax is greater on consumers in rural areas than in the suburbs (i.e. the increase in gas prices, because of the tax, is higher in rural areas).

c. Demand for gas is more inelastic in rural areas than small towns - as demand gets more inelastic (more vertical), those respective consumers pay a higher share of the tax. If demand were perfectly inelastic (i.e. if the demand curve was completely vertical), they'd pay all of it.