# Math Help - Profit Maximization Problem

1. ## Profit Maximization Problem

Need help ASAP on this homework assignment. I am stuck.

(i) A competitive firm’s total cost function is given by

TC = .25Q2 + 25
(with MC = .5Q).

The firm faces a market price of $15. Algebraically calculate the profit maximizing output and the level of optimal profit for the firm. (ii) Suppose that fixed costs increase by$50 but the prevailing market price remains unchanged. Using algebra determine the effects of this change in cost on the profit maximizing output and the optimal profit. Do you see any change from your answer to (i) above? Explain why or why not.

2. $Profit = PQ - TC = PQ - 0.25Q^2 - 25$.. Simply find $dProfit/dQ = 0$ and confirm $d^2Profit/dQ^2 < 0$.

Solution: $Q=30 units$