Question

For a monopolist’s output: Demand: P= 90 – 4Q    Cost: TC = 10Q. For the profit maximizing monopolist that charges the same price to all buyers:

Compute P and Q.

Compute the Lerner Index (Price Cost Markup). Use the Lerner Index formula.

Compute price elasticity of demand at the price in answer (a).

Explain the relationship between your answers to b and c.

Compute the deadweight loss from monopoly?

Compute the deadweight loss from monopoly that Gordon Tullock would calculate? Explain.

Answer 1

For a monopolist’s output: Demand: P= 90 – 4Q. Revenue function is TR = PQ = 90Q - 4Q^2 and MR = 90 - 8Q

Cost: TC = 10Q. Which implies MC = 10.

For the profit maximizing monopolist that charges the same price to all buyers, use MR = MC

90 - 8Q = 10

8Q = 80

Q = 10 units

P = 90 - 4*10 = $50 per unit

Compute the Lerner Index (Price Cost Markup).

Use the Lerner Index formula = (P - MC)/P = (50 - 10)/50 = 40/50 = 0.80

Compute price elasticity of demand at the price in answer (a).

This is given by P = MC*(ed/ed + 1)

50 = 10*(ed/ed + 1)

5ed + 5 = ed

ed = -5/4 = -1.25

Also elasticity = -1/Lerner index = -1/0.8 = -1.25

This is relationship between Lerner index and price elasticity: elasticity = -1/Lerner index

Compute the deadweight loss from monopoly?

DWL = 0.5*(price - marginal cost)*(competitive quantity - monopoly quantity) = 0.5*(50 - 10)*(20 - 10) = $200

deadweight loss from monopoly that Gordon Tullock would calculate includes rent of the monopoly which is worth (P - MC)*Q = (50 - 10)*10 = $400. Total DWL = $600.