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Finding out the profit maximizing output, price and profit for a perfectly competitive firm.

The market supply and demand curves in a perfectly competitive market are, respectively:
Qs = 400 + 25P
Qd = 700 - 50P
The representative firm, in this market, has the following cost function:
TC= Q³- 7Q² + 12Q + 5
a)Find the profit maximizing output of the firm.
b)Find the total profit earned at this level of output.
c)How many firms are in the market?

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