Question

In a perfectly competitive market, industry demand is: P = 850 – 2Q, and industry supply is: P = 250 + 4Q (Supply is the sum of the marginal cost curves of the firms in the industry).
(a) Determine price and output under perfect competition.

(b) Now suppose that all the firms collude to form a single monopoly cartel. Given that there is no change in the demand or cost conditions of the industry, what price and total output would the cartel set? Compare the monopoly outcome with the competitive outcome calculated earlier.

Answer 1

Answer : a) Here the supply curve is the MC curve. In perfectly competitive market at equilibrium Demand = Supply occur. So,

850 - 2Q = 250 + 4Q

=> 850 - 250 = 4Q + 2Q

=> 600 = 6Q

=> Q = 600 / 6

=> Q = 100

From demand function we get,

P = 850 - (2 * 100)

=> P = 850 - 200

=> P = 650

Therefore, in perfect competition the price is $650 and quantity is 100 units.

b) Now,

TR (Total Revenue) = P * Q = (850 - 2Q) * Q

=> TR = 850Q - 2Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 850 - 4Q

Here the supply curve is the MC curve.

In case of single monopoly cartel at equilibrium MR = MC occur. So,

850 - 4Q = 250 + 4Q

=> 850 - 250 = 4Q + 4Q

=> 600 = 8Q

=> Q = 600 / 8

=> Q = 75

From demand function we get,

P = 850 - (2 * 75)

=> P = 700

Therefore, here the price is $700 and quantity is 75 units.

Now by comparing the monopoly outcome with competitive outcome we get that the price in monopoly is higher than the competitive price but the quantity in monopoly is lower than the competitive quantity.