Question

In: Economics

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 Qd = 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).


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