Question

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

Answer 1

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.