Question

A monopolist, faces a demand curve given by: P+105-3Q, marginal cost of production is $15, no fixed cost, what is deadweight loss

Answer 1

Answer : Given,

P = 105 - 3Q

TR (Total Revenue) = P*Q = (105 - 3Q) * Q

=> TR = 105Q - 3Q^2

MR (Marginal Revenue) = $\dpi{50} \Delta$TR / $\dpi{50} \Delta$Q

=> MR = 105 - 6Q

MC (Marginal Cost) = $15

For monopoly the profit maximizing condition is MR = MC. So,

105 - 6Q = 15

=> 105 - 15 = 6Q

=> 6Q = 90

=> Q = 90 / 6

=> Q = 15

From demand function we get,

P = 105 - (3 * 15)

=> P = $60

For perfectly competitive firm the profit-maximizing condition is P = MC. So,

105 - 3Q = 15

=> 105 - 15 = 3Q

=> 3Q = 90

=> Q = 90 / 3

=> Q = 30

From demand function we get,

P = 105 - (3 * 30)

=> P = $15

Deadweight loss for monopolist = 0.5 * (Pm - Pc) * (Qc - Qm)

Here

Pm = monopoly price

Pc = competitive price

Qc = competitive quantity

Qm = monopoly quantity

So,

Deadweight loss = 0.5 * (60 - 15) * (30 - 15) = 0.5 * 45 * 15

=> Deadweight loss = $337.5

Therefore, here the deadweight loss for monopolist is $337.5 .