Question

Suppose you are analyzing a firm operating in a perfectly competitive market. You know the market demand curve is P = 300 - Q and the market supply curve is P = -525 + 2Q. You also know that the cost function of the firm is: C (Q) = -1/6Q^3 - 1/2^2 + 21Q + 100/3.

Using this information find

A. the quantity that will maximize profits.

B. If the firm is making a profit or suffering loss

Answer 1

A. Profit maximising condition of a firm is MR=MC. Now in competitive market P = MR therefore in equilibrium there will be P = MC, the upward portion of above AVC is the supply curve of firm. So market supply curve actually denotes the MC of the firm. Now if we equalise market demand and market supply we get that - P = 300 - Q = P = - 525 + 2Q , or 300 - Q = - 525 +2Q , or 3Q = 825 , or Q = 825/3 = 275. Therefore profit maximising quantity will be Q= 275. P= -525 +2*275 = 25. Total Revenue = 25*275 = 6875.

B. I think C(Q) = -1/6Q^3 - 1/2Q^2 +21Q + 100/3 , ( note: in question - 1/6Q^3 -1/2^2 +21Q+100/3, here Q is missing in 2nd term there should be 1/2Q^2). Now if we put Q =275 , we get C or Cost = -1/6*275^3 -1/2*275^2 +21*275 +100/3 = - 3,498,150. So the firm is making loss because total revenue (6875) is less than total cost (3,498,150).