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

Given P1 = 13.18

Q1 = 310

P2 = 13.48

Q2 = 317

The price elasticity of demand using the midpoint method can be determined using the following formula

$\LARGE e =\frac{ \frac{Q_2-Q_1}{\frac{Q_1+Q_2}{2}}}{\frac{P_2-P_1}{\frac{P_2+P_1}{2}}}$

Plug in and solve

$\LARGE e =\frac{ \frac{307-310}{\frac{307+310}{2}}}{\frac{13.48-13.18}{\frac{13.48+13.18}{2}}}$

$\LARGE e =\frac{ \frac{-3}{\frac{617}{2}}}{\frac{0.3}{\frac{26.66}{2}}}$

$\LARGE e =\frac{-3*26.66}{617*0.3}$

$\LARGE e = - 0.4322$

Price Elasticity of marijuana is inelastic as we know in case of inelastic product higher the price higher the revenue, lower the price lower the revenue.

Thus, the increase in price will increase the Total Revenue.

Revenue in June 2015 = P1*Q1 = 310*13.18 = $ 4,085.80

Revenue of July 2015 = P2*Q2 = 307*13.48 = $ 4,138.36

From above it is clear that total revenue increased from $ 4085.8 to $4,138.36.

Thus, we can conclude in case of inelastic demand with the increase in price Total Revenue will INCREASE.

When company is not required to pay any tax then due to increase in price the total revenue will increase.

Now between June and August

$\LARGE e =\frac{ \frac{303.1-310}{\frac{303.1+310}{2}}}{\frac{13.48-13.18}{\frac{13.48+13.18}{2}}}$

$\LARGE e =\frac{ \frac{-6.9}{\frac{613.1}{2}}}{\frac{0.3}{\frac{26.66}{2}}}$

$\LARGE e =\frac{-6.9*26.66}{613.1*0.3}$

$\LARGE Elasticity, e = -1 (Unitary Elastic)$

Between June and August the elasticity of demand = 1(Unitary elastic).

So, no impact of price change on Total Revenue.

When no tax is charged then the TR in both months would be same in June as well as August.

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