Answer to Question #89332 in Microeconomics for Talha sheikh

Question #89332
The demand equation for a firm operating in a monopolistically competitive market is given by P=4.75-0.2Q. Average cost for a firm is given by AC= 5-0.3Q+0.01Q^2. The firm is in long run equlibrium. Find profit maximizing price and quantity
1
Expert's answer
2019-05-09T10:44:08-0400

If the firm is in long run equilibrium, then it's profit-maximizing price equals its average total cost, so:

P = AC,



"4.75 - 0.2Q = 5 - 0.3Q + 0.01Q^{2} ,"

"0.01Q^{2} - 0.1Q + 0.25 = 0,"


"Q^2 - 10Q + 25 = 0,"


"(Q - 5)^2 = 0,"

Q1 = 0, Q2 = 5 units.

If Q = 5, then P = 4.75 - 0.2×5 = 3.75.

If Q = 0, then P = 4.75 - 0.2×0 = 4.75.


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