Question

Gazprom is a monopoly that faces P = 600 -2 Q and has MC = 50+1.5Q. Find the competitive and monopoly equilibrium P, Q, and the deadweight loss due to monopoly

Answer 1

In order to maximize profit a monopolist produces that quantity at which MR = MC

MR = d(TR)/dQ where TR = Total revenue = P*Q = ( 600 - 2Q)*Q and MR = Marginal Revenue

=> MR = 600 - 2*2Q = 600 - 4Q

Thus MR = MC => 600 - 4Q = 50 + 1.5Q

=> Q = 100.

Hence P = 600 - 2*100 = 400.

Hence Monopoly Price = 400 and Monopolist quantity = 100

In order to maximize profit a competitive firm produces that quantity at which P = MC

P = MC => 600 - 2Q = 50 + 1.5Q

=> Q = 157.14.

Hence P = 600 - 2*157.14 = 285.72.

Hence perfect competitive equilibrium Price = 285.72 and perfect competitive equilibrium quantity = 157.14

Deadweight loss is the loss in surplus that occurs due to monopoly and is the are above MC curve and below demand curve where quantity ranges from monopoly quantity to competitive equilibrium quantity.

when Q = 100 , MC = 50 + 1.5*100 = 200.

Hence Deadweight loss = (1/2)*(400 - 200)*(157.14 - 100), Note that Area of a triangle = (1/2)* base *triangle

=> Deadweight loss = 5714