Question

The cheese business in Lake Fon-du-lac, Wisconsin, is a competitive industry. All cheese manufacturers have the cost function C = Q² + 16, while demand for cheese in the town is given by Q_d = 120 - P. The long-run equilibrium numbe of firms in this industry is:

a. 14

b. 28

c. 22

d. 120

e. 29

 

Answer 1

To find a long run competitive equilibrium in a constant cost industry we need to

• find the minimizer of the LAC, which is the output of each firm in a long run competitive equilibrium
• find the minimum of the LAC, which is the long run equilibrium price
• add together the consumers' demand functions to get the aggregate demand
• divide the the aggregate demand at the equilibrium price by the output of each firm to get the number of firms

LAC(Q) = Q + 16/Q , This is minimized when its derivative is 0, 1 - 16/q^2 = 0 or Q = 4 Hence output = 4

The min of LAC = LAC(4) = 8 Thus the long run equilibrium price is 8

Aggregate demand at the price 8 is 120-p=120-8 = 112, so the number of firms is 112/4 = 28 ANSWER (B).