Question

QUESTION 5: THIRD DEGREE PRICE DISCRIMINATION (20pt) A monopolist engages in third degree price discrimination.There are 2 types of consumers, and the monopolist wants to sell to both groups. The monopolist is allowed to charge different prices and hence engages in third degree price discrimination. The demand curve for each group (the entire group) is as follows 01 500 10P Q2 200-5P2 The total cost function is TC 2000+10Q (a) What price does this firm charge to each group? (b) If the government forces this firm to charge the same price to all customers, what would that price be?

Answer 1

a)

Q1=500-10P1
Q2=200-5P2
TC = 2000+10Q

Step 1. Find marginal revenues curve
P1 = (500-Q1)/10 = 50-0.1*Q1
P2 = 100-0.2Q2
TR1(Q1) = p1Q1 = (50-0.1Q1)*Q1 = 50Q1-0.1Q1^2
TR2(Q2) = p2Q2 = (100-0.2Q2)*Q2 = 100Q2-0.2Q2^2
MR1(Q1) = 50-0.2Q1
MR2(Q2) = 100-0.4Q2

Step 2 Find optimal sales for Q1 and Q2 group
MC (Q1+Q2) = 10
MR1Q1= MC
50-0.2Q1 = 10
200 = Q1
MR2(Q2) = MC
100-0.4Q2=10
Q2=225

Step 3 Find prices by replacing quantities
P1 = 50-0.1*200= 50-20=30
P2 = 100-0.2*225 = 55

b) He needs to charge P1= 30 as it would still be under profit

Q P TR TC Profit

425 30 12750 6250 6500