Question

Competition
Consider an industry in pure and perfect competition. You have the
following information:
• Market demand: QD = 5,200 - 100P.
• Market offer: QO = 1,200P.
• All firms are identical and have the function of
cost: C (q) = 450 + q2 / 200.
This cost function is the same in the short run and in the long run.
a) Determine the market equilibrium.
b) What is the marginal cost of firms? Deduct the number of firms present on the
market.
c) What is the quantity produced by each firm and what is its profit?
d) Do you expect the entry of new firms or the exit of firms already
present? Why ?
e) In the short term, what is the lowest price at which a firm decides to continue to
produce? What is his profit at this price?
f) In the long term, what is the lowest price at which a firm decides to stay on the market?
market ? Explain your reasoning.
g) In the long term, how many companies will be in the market?

Answer 1

For pure and perfect competition, we have:

Market demand: QD = 5,200 - 100P.

Market offer: QO = 1,200P, All firms are identical and have the function of
cost: C (q) = 450 + q2 / 200.

cost function is the same in the short run and in the long run

a) Marginal equilibrium = (Market demand = Market offer)

since, QD = QO

5,200 - 100P. = 1,200P

P = 4

So, Market equilibrium will be 4.

b) marginal cost of firms = 450 + q2 / 200.

c) quantity produced = (450*100)/2 = 22500 and the profit will be Revenue minus cost

profit = 89000 - 450 = 88550

d) There will be  entry of new firms because there is huge profit in the market.

e)  In the short term, lowest price at which a firm decides to continue to
produce will be 4 because of market equilibrium. His profit at this price will be 88550.

f) In the long term,  the lowest price at which a firm decides to stay on the market will be same as short term because the market is in equilibrium. there will be no effect on long term and short term.

g) In long term, there is will be large number of comapnies which will want to entry in the market since the revenue generate will be huge.