(Perfect Competition and consumer Surplus) Suppose the demand function for widgets is Q(p) = 60 –...

(Perfect Competition and consumer Surplus) Suppose the demand function for widgets is Q(p) = 60 – p, and all firms that produce widgets have total cost function C(q) = 16 + q^3 .

a) Suppose that the market is perfectly competitive and there is free entry and exit. All firms that enter use the same technology. A firm that decides to stay out of the market can avoid paying the fixed cost and has a profit of zero. Solve for the long-run competitive equilibrium. What is the long-run equilibrium price? What is the quantity produced by each firm? How many firms will produce in this market?

b) What is the consumer surplus under the perfectly competitive model? (Hint: If a right-angle triangle has legs of length a and b, then it has area A= ½ ab.)

Expert Solution

A) Average cost is minimised when dAC/dQ=0

thus dAC/dQ

AC=16/Q+Q²

dAC/dQ=-16/Q²+2Q=0

Thus Q=2 and AC=16/2+4=12

Thus in long run price=12 and market demand=48 and no of firms=48/2=24 each produces 2units

b) Conusmer surplus=1/2*48*48=1158

Rahul Sunny answered 2 years ago

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