Question

“Pot producers heading down bankruptcy path: Insiders predict price slump, oversupply will spell doom for numerous companies” (Subramainiam, V., Vancouver Sun Newspaper, Thursday, January 02, 2020, p. C7).

“Cannabis industry insiders are bracing for a slew of bankruptcies in the coming year as small and medium-sized companies low on cash struggle to raise funds in the downtrodden sector. ‘We have had a busy few years, but next year we’re going to be busy for a different reason – we expect a few million dollars in legal fees from insolvencies and consolidations,’ said Ranjee Dhillon, a partner at McCarthy Tetrault LLP and the firm’s cannabis group lead.

There are currently more than 200 cannabis companies either in the cultivation, processing, or extraction businesses, primarily supplying a domestic market that has yet to cross the $1-billion mark in annual sales. Although cannabis sales have been increasing on a monthly basis since legalization in October 2018, inventory has been growing much more quickly, resulting in oversupply and declining prices.”

Suppose that the Inverse Demand Curve for recreational Cannabis is given as: P = 14.60 – 0.40 [Q_d] per gram.

i.     After determining the NORMAL Demand Curve from the Inverse demand curve above, determine the Quantities Demanded, Q_d in Millions of grams, if the Price, P is reduced from $11.00 per gram to $10.00 per gram AND the value of the Price Elasticity of Demand over the “arc” of this change.

ii.     Carefully explain how each of the “sign” and the “magnitude” of the elasticity determined in part i above would be interpreted?

iii.     Suppose that in response to a reduction in Price, P for Cannabis-based Gummi Bears from $12.00 to $10.00 per package results in a reduction in of 0.75 million grams at every price point from the original Demand Curve. Using this information, determine the elasticity of grams of Cannabis in response to the change in Price of the Gummi Bears.

iv.     Carefully explain how each of the “sign” of the elasticity determined allows us to describe the “type” of relationship between the Cannabis and Gummi Bears AND the interpretation of the “magnitude” of the elasticity?

Answer 1

Given, P = 146 -0.4QD

Add 0.4QD to both sides we get

Subtracting P from both sides

Divide both sides by 0.4, we get

Above equation represents the normal demand function.

Price elasticity of demand can be determined as follows

Applying the arc elasticity or mid point method to determine the elasticity

Simplifying above equation we get

When P1 = $ 11,

Q1 = 9 million grams

When P2 = $ 10

Q2 = 11.5 million grams

Plug in these values in the elasticity equation

Elasticity of demand = - 2.56 (Elastic)

ii. The elasticity of demand is negative this means that with the increase in price the quantity demanded will decrease or, price is indirectly proportional to quantity demanded.

Further, the absolute value of elasticity of demand is greater than 1. Hence the elasticity of demand is relatively elastic.

iii. Gummi beers price has been reduced from $ 12 to $ 10 due to which the quantity demanded of Cannabis has reduced by 0.75 million grams at every price. Let us assume initially the price of cannabis was $ 11 then the quantity demanded was 9 million grams

Initial demand, Q1 = 9 million grams

Change in demand = 0.75 million grams

Therefore, Q2 = 9 - 0.75 = 8.25 million grams

Now calculating the % ∆ Price of Gummi beers

The cross elasticity of demand can be determined using the following formula

Cross elasticity of demand = 0.4785 (Substitute, since positive)

iv. The cross elasticity of demand is positive therefore the two goods are substitute to each other.

By magnitude we mean, if there will be 1% change in price of gummi beers the quantity demanded of cannabis will change by 0.4785%. Both will move into the same direction. If the price increases by 1% quantity demanded will increase by 0.4785% and vice-versa.

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