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.

Comparing June 2015 to August 2015, using the arc formula for price elasticity of demand: What is the price elasticity of demand? If the business didn’t have to pay the sales tax to the government, what affect would the price increase have had on their revenue? Type your response in the box below.

Answer 1

In June the price is 13.18 and quantity is 310. In August, the price is 13.48 and quantity is 303.1. Hence we find the arc elasticity as Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2]

= (303.1 - 310)/((303.1+310)/2) divided by (13.48-13.18)/((13.48+13.18)/2)

= -1.

This is the price elasticity of demand

Now since |ed| = 1, when price is raised by a given %, quantity demanded is reduced by the same percentage so that there will be no change in the revenue received. Hence, if the business didn’t have to pay the sales tax to the government, the price increase has no effect on their revenue as it remains unchanged (which is $4086)