(i) Assuming that each company tries to maximise profits separately, find the equilibrium prices PA and PB. (ii) Find the quantities sold by each company, and the profits for each company.

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Chapter14: Monopoly
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2. Bertrand (price) competition. Company A and B both produce widgets,
at price PA and PB respectively. We suppose that the quantities q4 and qв
sold are given by
QA = 80-2PA + PB, B = 60 +3PA - PB -
The production and distribution costs are 20 for company A and 10 for com-
pany B. Then we have profits
profitA=qA(PA-cost A)
profitBqB(PB- cost B)
(i) Assuming that each company tries to maximise profits separately,
find the equilibrium prices PA and PB.
(ii) Find the quantities sold by each company, and the profits for each
company.
Transcribed Image Text:2. Bertrand (price) competition. Company A and B both produce widgets, at price PA and PB respectively. We suppose that the quantities q4 and qв sold are given by QA = 80-2PA + PB, B = 60 +3PA - PB - The production and distribution costs are 20 for company A and 10 for com- pany B. Then we have profits profitA=qA(PA-cost A) profitBqB(PB- cost B) (i) Assuming that each company tries to maximise profits separately, find the equilibrium prices PA and PB. (ii) Find the quantities sold by each company, and the profits for each company.
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