GoPro holds a monopoly in two countries where it sells video cameras, USA and Ca

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

MC in both countries is 20

A) Pu = 105 - Qu so revenueRu = P*Q = 105Qu - Qu^2 so MRu = dRu/dQu = 105-2Qu

to maximize profit MC = MR so 20 = 105-2Qu so Qu = 42.5 so i.e either 42 or 43

at Qu=42 and 43 Pu = 63 ad 62

Pc = 42.5/.5 - Qu/.5 so revenueRu = P*Q = 42.5Qu/.5 - Qc^2/.5 so MRu = dRc/dQc = 85-4Qu

to maximize profit MC = MR so 20 = 85-4Qc so Qc = 16.25 so i.e 16

at Qc=16 Pc = 53

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