A firm in a perfectly competitive market has the following c

A firm in a perfectly competitive market has the following cost curve: TC = 200 + Q + 2Q^2 and The market demand is: Qd = 121 - P. There are 20 identical firms in the market (N =20) in the short-run.

a) What is the firm\'s supply function?

b) What is the market supply function in the short-run?

c) What is the market equilibrium price and quantity in the short-run?

d) What is the quantity that the firm produces in the short-run?

e) At the equilibrium price found in part (c), how much profit is each firm making in the short-run? Will there be entry or exit in this market in the long-run?

f) What is the price of the product in the long-run?

g) How many firms are there in the market in the long-run?

h) How much profit is each firm making in the long-run?

Solution

TC = 200 + Q + 2Q²

Marginal cost (MC) = dTC/dQ = 1 + 4Q

Market demand: Qd = 121 - P

(a) Firm supply function is its MC function, therefore

Firm supply: P = 1 + 4Q

(b) Since N = 20, Market supply (QS) = 20Q, therefore Q = QS/20

P = 1 + 4 x (QS/20) = 1 + (QS/5)

QS/5 = P - 1

QS = 5P - 5 [Industry supply]

(c) In market equilibrium, QD = QS

121 - P = 5P - 5

6P = 126

P = 21

Q = 121 - 21 = 100

(d) Firm output = Market output / N = 100/20 = 5

NOTE: As per Chegg Answering Policy, first 4 parts are answered.