Suppose a competitive firm has as its total cost function: TC 21 +3q Suppose the

Question

Suppose a competitive firm has as its total cost function: TC 21 +3q Suppose the fim's output can be sold (in integer units) at $71 per unit. Using calculus and formulas (but no tables or spreadsheets) to find a solution, what is the total profit at the optimal integer output level? 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 functiorn)

Explanation / Answer

TC = 21 + 3q2

MC = 6q

P = 71

The profit maximizing level of output is where:

MC = P

6q = 71

q = 71 / 6 = 12    (11.8 is rounded as 12)

Profit = TR - TC

TR = P * q = 71 * 12 = $852

TC = 21 + 3q2 = 21 + 3(12)2 = 21 + 432 = $453

Profit = 852 - 453 = $399

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