GoPro holds a monopoly in two countries where it sells video cameras, USA and Ca
ID: 1196873 • Letter: G
Question
GoPro holds a monopoly in two countries where it sells video cameras, USA and Canada. The demand functions for the two regions are,
Q(USA)=105-P(USA)
Q(CANADA)=42.5-.5P(CANADA)
GoPro has a unique manufacturing process where it can produce each video camera for $20. Assume there are very strict laws that prevent the resale of the product across borders
. A. What is the price and quantity produced in both markets?
B. Show that the relationship from part A also holds when evaluated with elasticities.
Explanation / Answer
USA
Demand curve: P(U) = 105-Q(U)
Marginal revenue: MR = 105-2Q(U)
Marginal cost = 20
CANADA
Demand curve: P(C) = 85-2Q(C)
Marginal revenue: MR = 85-4Q(C)
Marginal cost = 20
a)
A monopolist produces output till the point MR=MC
USA:
MR = MC
105-2Q(U) = 20
Q(U) = 42.5 units
P(U) = $62.50
CANADA:
MR = MC
85-4Q(C) = 20
Q(C) = 16.25
P(C) = $52.50
b)
Elasticity refers to the responsiveness of demand with respect to change in price. The coefficient with P in demand function denotes the elasticity.
Elasticity = (dQ/dP).(P/Q)
USA elasticity = -1 x 57.5/42.5 = -1.3529
Canada elasticity = -0.5 x 52.5/16.25 = -1.615
The greater the elasticity the lower is the price. Since elasticity is lower in USA, the price is higher in USA. Similarly the relative elasticity is higher in Canada, the price is lower.
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