A monopolist sells to two groups of people and practices price discrimination by

Question

A monopolist sells to two groups of people and practices price discrimination by charging separate prices for each group; students and non-students. This monopolist produces at constant marginal cost MC = 10. Demand function of the students is Q1 = 100 2p1. The non-student demand is Q2 = 100 p2.

(a) What is the price for each group if he can successully price discriminate and charge a seperate price in each market? How much proÖt does he make?

(b) What is the price if he cannot price discriminate and has to set the same price for everyone? What is his profit?

(c) How much profit he would make if he can perfectly price discriminate?

(d) Which one of the above is the best outcome for the monopolist (single price, segmented markets(third degre price discrimation) or first degree(perfect) price discrimination?

(e) What is the best outcome for the society? Why?

Explanation / Answer

Given student demand function:

                                      Q1=100-2P1

Total Revenue (TR) function = P*Q

= (100-2P1)*P1

=100P1-2P12

Marginal Revenue (MR) = d (TR) = 100-4P1

MR =MC

100-4P1 = 10

P1 = $22.5

Therefore, Price P1 = $22.5.

Given non student demand function:

                                      Q2=100-P2

Total Revenue (TR) function = P*Q

= (100-P2)*P2

=100P2-P22

Marginal Revenue (MR) = d (TR) = 100-2P2

MR =MC

100-2P2 = 10

P2 = $45

Therefore, Price P2 = $45.

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