Question

A monopolist is considering third degree price discrimination. It estimates that the inverse demand curves of its two potential market segments are:

Segment A: P ( Q A ) = 300 − 10 Q A

Segment B: P ( Q B ) = 150 − 5 Q B

The firm operates a single plant. Assuming fixed costs are negligible, its costs are such that:

A T C = M C = 10.

If the monopolist is able to price discriminate, what will be the equilibrium price and quantity for each market segment? What is the deadweight loss for each market segment?

Segment A Price:

Segment A Quantity:

Segment A Deadweight Loss:

Segment B Price:

Segment B Quantity:

Segment B Deadweight Loss

Answer 1

Monopolist maximizes profit according to the rule MR = MC.

Segment A:
Total revenue, TRA = P*QA = (300-10QA)*QA = 300QA - 10QA2
Marginal revenue, MRA = d(TRA)/dQA = 300 - 2(10QA) = 300 - 20QA
So, MRA = MC gives,
300 - 20QA = 10
So, 20QA = 300 - 10 = 290
So, QA = 290/20
So, QA = 14.5

PA = 300-10QA = 300-10(14.5) = 300 - 145
So, PA = 155

Perfectly competitiv output is that where P = MC.
So, 300-10QA = 10
So, 10QA = 300 - 10 = 290
So, QA' = 290/10 = 29

DWL = (1/2)*(PA-MC)*(QA'-QA) = (1/2)*(155-10)*(29-14.5) = (1/2)*(145)*(14.5)
So, DWLA = 1,051.25

Segment B:
Total revenue, TRB = P*QB = (150-5QB)*QB = 150QB - 5QB2
Marginal revenue, MRB = d(TRB)/dQB = 150 - 2(5QB) = 150 - 10QB
So, MRB = MC gives,
150 - 10QB = 10
So, 10QB = 150 - 10 = 140
So, QB = 140/10
So, QB = 14

PB = 150-5QB = 150-5(14) = 150 - 70
So, PB = 180

Perfectly competitiv output is that where P = MC.
So, 150-5QB = 10
So, 5QB = 150 - 10 = 140
So, QB' = 140/5 = 28

DWL = (1/2)*(PB-MC)*(QB'-QB) = (1/2)*(180-10)*(28-14) = (1/2)*(170)*(14)
So, DWLB = 1,190