Question

Recreational marijuana was legalized in the state of Washington in July of 2014 creating a new source of revenue for the government. July 1, 2015, the state government raised excise taxes paid by marijuana retailers on final sales leading to the following effects on prices and quantity sold:

Date	Quantity Sold (average grams per day)	Price (per gram)
June 2015 (pre tax change)	310.0	13.18
July 2015	307.0	13.48
August 2015	303.1	13.48

The above example is adapted from a recent study into the effects of an increase in taxes on the marijuana market in Washington (Hansen, Miller, & Weber, 2017). The authors can estimate the price elasticity of demand from these data points because the sudden tax change created a ceteris paribus situation, where all other supply and demand conditions were held fixed, similar to the way our models assume in the textbook.

In that spirit, interpret the excise tax increases as an increase in input costs for marijuana dispensaries holding all other supply and demand characteristics fixed.

All else equal, what would you expect to happen to the price elasticity of demand if there were an additional increase in taxes? Why?

Answer 1

We can calculate the price elasticity of demand using the mid-point formula.

Price elasticity of demand = (Q2 – Q1) / [(Q2 + Q1) / 2] / (P2 – P1) / [(P2 + P1) / 2]

Case 1

Between June 2015 and July 2015, the values are as follows -

Q1 = 310; Q2 = 307 ; P1 = 13.18 ; P2 = 13.48

Price elasticity of demand = (307 – 310) / [(307 + 310) / 2] / (13.48 – 13.18) / [(13.48 + 13.18) / 2]

Price elasticity of Demand = 0.432

Case 2

Between June 2015 and August 2015, the values are as follows -

Q1 = 310; Q2 = 303.1 ; P1 = 13.18 ; P2 = 13.48

Price elasticity of demand = (303.1 – 310) / [(303.1 + 310) / 2] / (13.48 – 13.18) / [(13.48 + 13.18) / 2]

Price Elasticity of Demand = 0.435

Observation

It is clear that even without further change in price from July 2015 to August 2015, the quantity demanded (all other factors being equal) for marijuana declines and the price elasticity of demand increases marginally. The reason is that relatively higher prices are having a gradual impact on the quantity demand, which was more inelastic in July 2015 as compared to August 2015.

Therefore, if there is an additional increase in taxes, the price elasticity of demand will increase further. More taxes will make consumption of marijuana relatively less affordable. Further, the quantity consumed will gradually decline as has been the case witnessed from July 2015 to August 2015.