Question

Colorado legalized the recreational use of marijuana in 2014 to raise revenues through sales and excise taxes. In Denver, 1/8 ounce of marijuana costing $30 had about $8 in various taxes added on. Assuming the elasticity of demand for marijuana of -0.7, determine the percentage change in quantity that would result from a price increase of $8. Under what circumstances would prices rise by less than the full amount of a tax? How does the price elasticity of demand affect tax revenues?

Answer 1

(a) Price before tax = $30 - $8 = $22

% Change in price = $(30 - 22) / $22 = 0.3636 = 36.36%

Elasticity of demand = % Change in quantity demanded / % Change in price

- 0.7 = % Change in quantity demanded / 36.36%

% Change in quantity demanded = (-0.7) x 36.36% = - 25.45% (Decrease by 25.45%)

(b) Price will rise by less than full amount of tax when demand curve is downward sloping and supply curve is upward rising, that is, both demand and supply are neither perfectly elastic (horizontal) nor perfectly inelastic (vertical).

(c) The higher (lower) the price elasticity of demand, the more (less) is the decrease in quantity from a given increase in price caused by tax, and therefore, the lower (higher) the tax revenue. Therefore, higher (lower) tax is imposed in the more inelastic (elastic) market.