Question

A perfectly competitive market is described by the Aggregate demand curve Q = 60 – 2P and the aggregate supply curve Q = -10 + 5P. A typical firm (and all firms are identical to each other) in the market has a cost function = 16 + 2Q + Q2

(a) Calculate the equilibrium price and quantity
(b) Show that the price you derive in part (a) is commensurate with the long run equilibrium of this market. Explain
(c) In the long run, how many firms will be in the market?

Answer 1

Step-by-step explanation:

a )

At equilibrium price , total demand = total supply

60 – 2P = -10 + 5P

7P = 70

P = 10 .

quantity produced Q = 60 - 2P = 60 - 2 x 10 = 40 .

b )

cost function C = 16 + 2Q + Q²

marginal cost MC = dC / dQ = 2 + 2Q

In the long run , no profit , or

marginal cost = Average cost = Price

2 + 2 Q = 16 + 2Q + Q² / Q

2 Q + 2 Q² = 16 + 2Q + Q²

Q² = 16

Q = 4

Marginal cost = price

Price = 2 + 2 Q

= 2 + 2 x 4

= 10

Same as that in part ( a )

c ) No of firms

Production by one firm = 4

Total production = 40

no of firm = 40 /4 = 10 .