Question

12. Government pays attention to the elasticity of demand when selecting foods and services upon which to levy excise taxes. Assume a $1.00 tax is levied on some good and 10,000 units are sold.

1. What is the tax revenue collected?

Now, assume the government raises the tax to $1.50. This causes sales to decline to 5,000 units.

2. Calculate the price (tax) elasticity of demand.
3. Is it elastic, inelastic, or unit elastic?
4. What happens to total tax revenue?
5. Based on your elasticity coefficient, is the change in total tax revenue consistent with what you would expect to happen? Explain why or why not.

Answer 1

Tax = $1

Units sold = 10,000

New Tax = $1.5

New Units sold = 5,000

a) Tax revenue = Tax imposed * Units sold

= 1 * 10,000 = $10,000

b) Price elasticity of demand = %change in quantity demanded / %change in price

%change in quantity demanded = [(5,000 - 10,000) / 10,000] * 100 = -50%

%change in price = [(1.5 - 1) / 1] * 100 = 50%

Price elasticity of demand = -50% / 50% = -1

We can ignore negative sign here due to negative relationship between price and quantity demanded. Thus price elasticity of demand = 1

c) As price elasticity of demand or %change in quantity demanded = %change in price, elasticity is unitary.

d) New Tax revenue = 5,000 * 1.5 = 7,500

e) As elasticity of demand is unitary, new tax revenue should be equal to initial revenue collected by government which is $10,000 but is have reduced to $7,500. As per their government revenue collected, consumers have some substitute of food which makes it elastic good for them which cause revenue to fall when price rises due to tax.