Suppose a competitive firm has as its total cost function: TC=25+3q2 Suppose the

Question

Suppose a competitive firm has as its total cost function: TC=25+3q2 Suppose the firm's output can be sold (in integer units) at $54 per unit. Using calculus and formulas (but no tables or spreadsheets) to find a solution, how many integer units should the firm produce to maximize profit? Please specify your answer as an integer. In the case of equal profit from rounding up and down for a non-integer initial solution quantity, proceed with the higher quantity. Hint: When computing the total cost component of total profit for a candidate quantity, use the total cost function provided in the exercise statement (rather than summing the marginal costs using the marginal cost function).

Explanation / Answer

Profit=Total revenue- total cost

Total revenue =Price *Quantity =54q

Total cost=25+3q2

Profit=TR-TC=54q-25-3q2

Profit is maximised when dProfit/dq=0

Thus dProfit/dq=54-6q=0

Thus q=54/6=9

Profit is maximised when quantity=9

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