Question

Suppose the total cost function for a firm is given by C (Q) = 100 + Q2. If the firm sells its output in a perfectly competitive market at a price of $10, what level output should the firm produce to maximize profits or minimize losses? What will be the level of profits or losses if the firm makes the optimal decision?

Answer 1

In a perfectly competitive market at a price of $10,  the firm should produce to maximize profits or minimize losses where P = MC

10 =MC

MC = d( C(Q))/dQ = 2Q

10 =2Q

Q = 5

the firm should produce 5 units to maximize profits or minimize losses.

Level of profit or loss :

Profit = TR - TC

TR = P*Q = 10*5 = $50

TC= 100 + 5² = 125

Profit = 50 - 125 = -$75

So the  firm makes loss of $75 at the optimal decision