Question

For the monopolistic competition model, a firm's average cost is given by AC=2+2x, where x is the number of firms in the industry. The relationship between a firm's price and the number of firms is p=2+ 32/x. What is the equilibrium of firms?

A)2

B)4

C)6

D)8

E)10

Answer 1

The correct answer is (B) 4

Monopolistic competitive like a competitive firm earns 0 profit in the long run because when they started earning positive profits new firm enters and this shifted Supply curve to the right resulted in decrease in price and this will continue till profit becomes 0 for each firm.

Profit = Total Revenue - Total Cost

Total Revenue(TR) = pq

Total Cost(TC) = AC*Q

As in the long run each firms earn 0 profit => In order to find equilibrium number of firms we have to find that x at which TR - TC = 0 => TR = TC

=> pq = AC*q => p = AC

Hence, we should have p = AC

=> 2+ 32/x = 2 + 2x

=> 2x+ 32 = 2x² + 2x

=> 32 = 2x²

=> x = 4

Hence, the equilibrium of firms = 4

Hence, the correct answer is (B) 4