Question

Suppose the demand for the good is P = 10 - Q. A monopolist's total cost is TC = 2 + 4Q. What's the optimal price and quantity of the monopolist?

calculate the deadweight loss from the monopoly.

Answer 1

Demand : P= 10–Q

Total Revenue: PQ= 10Q–Q²

Marginal Revenue= 10–2Q

TC= 2+4Q

Marginal Cost= 4

For Profit maximisation, Marginal Revenue= Marginal Cost

10–2Q= 4

Q= 3

P= 10–3= 7

Optimal Price of the Monopolist= 7

Optimal Quantity of the Monopolist= 3

Now, Equate Marginal Cost and Demand for calculating Dead Weight Loss

10–Q= 4

Q= 6. This is the Quantity that would have prevailed if the market was perfectly Competitive.

Dead Weight Loss from Monopoly= 0.5×(7–4)×(6–3)= 4.5

Dead Weight Loss from Monopoly = 4.5