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A perfectly competitive firm faces a market price of $100 and has total cost of TC...

A perfectly competitive firm faces a market price of $100 and has total cost of TC = 100 + 0.25q + 0.01q2. How much output (q) should this firm produce to maximize profits?

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Answer #1

A competitive firm maximizes profit according to the rule that price (P) equals Marginal cost (MC).
P = $100
MC = d(TC)/dq = 0.25 + 2(0.01q) = 0.25 + 0.02q
So, P = MC gives,
100 = 0.25 + 0.02q
So, 0.02q = 100 - 0.25 = 99.75
So, q = 99.75/0.02 = 4,987.5

Thus, q = 4,987.5

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