Question

Suppose the Ontario cannabis market of a particular specie consists of the following supply and demand curves:

QD = 150 - 20p

QS = 40p

where Q is the number of packs of cannabis per year (in millions!), and p is the price per pack.

a. Calculate the price elasticities of each curve at the equilibrium price/quantity.

b. Demand for cannabiss is generally more elastic over longer periods of time as consumers have more time to kick the habit. What does this imply about the tax incidence in the long run as compared to the short run?

Answer 1

Answer : a) Given,

Demand : Q = 150 - 20p

=> 20p = 150 - Q

=> p = (150 - Q) / 20

=> p = 7.5 - 0.05Q

Supply : Q = 40p

=> p = Q / 40

=> p = 0.025Q

At equilibrium, demand = supply.

=> 7.5 - 0.05Q = 0.025Q

=> 7.5 = 0.025Q + 0.05Q

=> 7.5 = 0.075Q

=> Q = 7.5 / 0.075

=> Q = 100

Now, from demand function we get,

p = 7.5 - (0.05 * 100)

=> p = 2.5

Price elasticity of demand (Ed) = (QD / p) * (p / Q)

=> Ed = - 20 * (2.5 / 100)

=> Ed = - 0.5

Price elasticity of supply (Es) = (QS / p) * (p / Q)

=> Es = 40 * (2.5 / 100)

=> Es = 1

Therefore, here the price elasticity of demand is - 0.5 and price elasticity of supply is 1.

b) If the demand is more elastic than before then consumers bear less tax incidence than before. Here the long-run demand curve is more elastic in compared to short-run. This means that consumers bears less tax incidence in long-run in compared to short-run.