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) Pre-tax Price = $30 - $8 = $22

% Change in price = (Change in price / Pre-tax price) x 100% = ($8 / $22) x 100% = 36.36%

Price 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% (Quantity demanded falls by 25.45%)

(b) Price will decrease by less than full amount of tax when demand and supply curves have their usual shapes following law of demand and law of supply respectively, i.e. when demand curve is downward sloping and supply curve is upward sloping, in which case demand and supply are neither perfectly elastic (i.e. horizontal) nor perfectly inelastic (i.e. vertical).

(c) The more (less) elastic the demand, the higher (lower) the price elasticity of demand and the larger (smaller) is the fall in quantity arising out of a given rise in price (as a result of the tax), and so, the smaller (larger) the tax revenue. Therefore, smaller (larger) tax is imposed in the more elastic (inelastic) market.