Question

Suppose that the Inverse Demand Curve for recreational Cannabis is given as: P = 14.60 – 0.40 [Qd] per gram. i. After determining the NORMAL Demand Curve from the Inverse demand curve above, determine the Quantities Demanded, Qd 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,

When P2 = $ 10

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. Humko bears 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.

Initial demand = 11.5 million grams

Change in demand = 0.75 million grams

Now calculating the % ∆ Price of Humko bears

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

Cross elasticity of demand = 0.4785

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 bears 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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