GoPro holds a monopoly in two countries where it sells video cameras, USA and Ca
ID: 1196115 • 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
The marginal cost(MC) of producing video camera is $20.
(a) The firm produces where MR = MC and charges price where this quantity cuts the demand curve.
USA:
Q = 105-P
P=105-Q
TR = PQ = 105Q-Q2
MR = 105-2Q
MC = 20
MR = MC
105-2Q =20
85 = 2Q
Q = 42.5
P= 105 - 42.5 = $57.5
In USA, quantity produced would be 42.5 units at price $57.5 each.
CANADA:
Q= 42.5-0.5P
P = 85 - 2Q
TR = PQ= 85Q-2Q2
MR = 85-4Q
MC = 20
MR = MC
85-4Q = 20
65 = 4Q
Q = 16.25
P = 85-2Q
P= 85- 2x16..25
P = $52.5
In canada 16.25 units is sold at $52.5 each.
(B) Elasticity refers to the sensitivity of demand to change in price. The coeeficient with P in demand function denotes the elasticity.
Elasticity = (dQ/dP) x(P/Q)
USA elasticity = -1 x 57.5/42.5
USA elasticity = -1.3529
Canada elasticity = -0.5 x 52.5/16.25
Cananda = -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 elasticty is higher in Canada, the price is lower.
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