A monopolist discriminates the price of its product among two groups as follows: Q1 = 100 - p1 (demand of customers in group 1) Q2 = 120 - 0.5p2 (demand of customers in group 2) TC = 2000 + ( Q1 + Q2)2 (total cost of production) a) Find the optimal sales to the first, Q1 * , and to the second, Q2 * , group.b) Find prices to be charged to the first, p1 * , and to the second, p2 * , group.c) Find the profit of this firm. d) Show that the group with more elastic demand gets lower price.

Q1 = 100 - p1 Q2 = 120 - 0.5p2 TC = 2000 + ( Q1 + Q2)2

Answered: A monopolist discriminates the price of…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A monopolist discriminates the price of its product among two groups as follows:

Q₁ = 100 - p₁ (demand of customers in group 1)

Q₂ = 120 - 0.5p₂ (demand of customers in group 2)

TC = 2000 + ( Q₁ + Q₂)² (total cost of production)

a) Find the optimal sales to the first, Q₁ * , and to the second, Q₂ * , group.
b) Find prices to be charged to the first, p₁ * , and to the second, p₂ * , group.
c) Find the profit of this firm.

d) Show that the group with more elastic demand gets lower price.

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