The cheese business in Lake Fon-du-lac, Wisconsin, is a competitive industry. All cheese manufacturers have the...

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

Solutions

Expert Solution

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).

Rahul Sunny answered 2 years ago

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