Suppose we have a duopoly in the production of mineral spring water. Each firm h

Question

Suppose we have a duopoly in the production of mineral spring water. Each firm has the same
cost structure where MC(Q) = 10. The market demand for mineral spring water is given by:
P = 70 - Q/50

Suppose that for the 2 firms, Firm 1 can choose its output first, and then Firm
2 chooses its output level. How much will each firm produce? What is the total industry output?
How much profit do each of the firms earn? Is there an advantage to choosing your
output first?

Please ignore all "A" symbols. I dont know how to take them off. Thank you.

Explanation / Answer

firm 1 tries to make max profit,

total revenue=P*Q=70Q-Q^2/50

MR=70-Q/25

fo requilibrium MC=MR

=>10=70- Q/25

=>Q=1500

firm 2 also produces same 1500

total output=3000

profit of each=1500(70-1500/50 - 10)=45,000

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