# maximize profit of competitive firm in short-run

Consider a competitive firm with the short-run cost function $C(q) = 20 + 6q +5q^2$. The firm faces a market price of $p$ for its output.

(1) Find the firm's Profit Maximization problem.

(2) Find F.O.C and S.O.C.

I'm uncertain how to write the maximization problem up. As I understand competitive firm in short-run, we simple need to maximize profits minus cost by choosing the optimal quantity $q$.

So my guess is that the answer is:

$\max_{q} p-C(q)$.

Assuming that is correct, I am then uncertain how to make sense of the S.O.C.

• Are you asking what a SOC is? Apr 16, 2018 at 20:36
• I'm asking if I understood the first part of the exercise correctly, and assuming I am, I follow up with the question regarding S.O.C. Do I simple find the F.O.C first and then differentiate the F.O.C? which should be either greater or less than 0. Apr 16, 2018 at 20:42
• Also regarding (1). Should I not minimize as it is a cost-function? Apr 16, 2018 at 20:42

Is the cost given the marginal or cumulative cost? If it's the cumulative cost, then the profit is pq-C(q): your price is money per item, so you have to multiply by the number of items to find the total gross revenue. The problem is then to maximize the profit, i.e. find $\max_{q} pq-C(q)$.