Question

Demand for good X is X = 100 – 4P, where P is the market price of X. A monopolist supplies this market and has a cost function 5X.

When the monopolist produces his optimal level of X, what is the resulting deadweight loss in the economy?

Could you draw the graph with curves?

(a.) $180
(b.) $200
(c.) $222
(d.) $285

Answer 1

Answer : The answer is option b.

For monopoly :

Demand : X = 100 - 4P

=> 4P = 100 - X

=> P = (100 - X) / 4

=> P = 25 - 0.25X

TR (Total Revenue) = P * X = (25 - 0.25X) * X

=> TR = 25X - 0.25X^2

MR (Marginal Revenue) = TR / X

=> MR = 25 - 0.5X

Total Cost (TC) = 5X (Given)

MC (Marginal Cost) = TC / X

=> MC = 5

At monopoly equilibrium, MR = MC.

=> 25 - 0.5X = 5

=> 25 - 5 = 0.5X

=> 20 = 0.5X

=> X = 20/ 0.5

=> X = 40

Now, P = 25 - (0.25 * 40)

=> P = 15

For competitive firm :

At equilibrium condition of competitive firm, P = MC.

=> 25 - 0.25X = 5

=> 25 - 5 = 0.25X

=> 20 = 0.25X

=> X = 20 / 0.25

=> X = 80

Now, P = 25 - (0.25 * 80)

=> P = 5

Deadweight loss = 0.5 * (Pm - Pc) * (Xc - Xm)

Here, Pm = Monopoly price

Pc = Competitive price

Xm = Monopoly output

Xc = Competitive output

=> Deadweight loss = 0.5 * (15 - 5) * (80 - 40)

=> Deadweight loss = 0.5 * 10 * 40 = 200

So, here the deadweight loss is $200.

Therefore, option b is correct.

The deadweight loss of the economy is shown by the following picture's diagram. In the following diagram the shaded area is the deadweight loss area of the economy.