Question

A firm in monopolistic competition has the firm demand curve: P = 60 - 2Q. The Total Cost equation is TC = 40 + Q2 How much deadweight loss is created by the firm? Enter as a value.

Answer 1

Answer : For monopolistically competitive firm :

P = 60 - 2Q

TR (Total Revenue) = P * Q = (60 - 2Q) * Q

=> TR = 60Q - 2Q^2

MR (Marginal Revenue) = TR / Q

=> MR = 60 - 4Q

Given, TC = 40 + Q^2

MC (Marginal Cost) = TC / Q

=> MC = 2Q

At monopoly equilibrium, MR = MC.

=> 60 - 4Q = 2Q

=> 60 = 2Q + 4Q

=> 60 = 6Q

=> Q = 60 / 6

=> Q = 10

Now, P = 60 - (2 * 10)

=> P = 40

Therefore, the monopolistically competitive firm's price is $40 and quantity is 10 units.

For perfectly competitive firm :

At equilibrium for perfectly competitive firm, P = MC.

=> 60 - 2Q = 2Q

=> 60 = 2Q + 2Q

=> 60 = 4Q

=> Q = 60 / 4

=> Q = 15

Now, P = 60 - (2 * 15)

=> P = 30

Therefore, the perfectly competitive firm's price level is $30 and quantity is 15 units.

Deadweight loss for monopolistically competitive firm = 0.5 * (Pm - PC) * (Qc - Qm)

Here Pm = monopoly price, Pc = competitive price, Qc = competitive quantity, Qm = monopoly quantity.

=> Deadweight loss = 0.5 * (40 - 30) * (15 - 10) = 0.5 * 10 * 5

=> Deadweight loss = 25

Therefore, the deadweight loss of monopolistically competitive firm is $25.