Suppose we have two types of consumers, each buying exactly one unit of the product a monopolist is selling so long as their consumer surplus is non-negative. If the consumer has a choice, she or he will buy the product that gives them the highest consumer surplus. the monopolist has estimated the indirect utility (CS) of each type of consumer as V,= -p,+9 z,-45 V2= -P2+4 z2-12 where z is the quality chosen by the monopolist i.e. vertical differentiation. The monopolist does not know each consumer's type. There are 189 type one consumers and 174 type two consumers. Finally suppose the marginal cost for all quantities is zero. The firm can choose any quality between 0 and 15 What is the lowest quality type 1 consumers will demand What is the lowest quality type 2 consumers will demand What is the participation constraint for type 1 What is the participation constraint for type 2 What is the Incentive compatibility constraint for type 1 What is the Incentive compatibility constraint for type 2 In terms of prices (p,,p2)and number of consumers, what is the profit function of the monopolist In terms of choice of quality (z,,z,) and number of consumers, what is the profit function of the monopolist What is the optimal value for z, What is the optimal value for z, What is the price charged to consumers of type 1 What is the price charged to consumers of type 2 What are the profits of the monopolist How much consumer surplus do consumers of type 1 have How much consumer surplus do consumers of type 1 have

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose we have two types of consumers, each buying exactly one unit of the product a monopolist is selling so long as their consumer surplus
is non-negative. If the consumer has a choice, she or he will buy the product that gives them the highest consumer surplus.
the monopolist has estimated the indirect utility (CS) of each type of consumer as
V,= -p,+9 z,-45
V2= -P2+4 z2-12
where z is the quality chosen by the monopolist i.e. vertical differentiation. The monopolist does not know each consumer's type. There are
189 type one consumers and 174 type two consumers. Finally suppose the marginal cost for all quantities is zero. The firm can choose any
quality between 0 and 15
What is the lowest quality type 1 consumers will demand
What is the lowest quality type 2 consumers will demand
What is the participation constraint for type 1
What is the participation constraint for type 2
What is the Incentive compatibility constraint for type 1
What is the Incentive compatibility constraint for type 2
In terms of prices (p,,p2)and number of consumers, what is the profit function of the monopolist
In terms of choice of quality (z,,z,) and number of consumers, what is the profit function of the monopolist
What is the optimal value for z,
What is the optimal value for z,
What is the price charged to consumers of type 1
What is the price charged to consumers of type 2
What are the profits of the monopolist
How much consumer surplus do consumers of type 1 have
How much consumer surplus do consumers of type 1 have

Expert Solution

Step 1

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Consumer of type 1 requires his consumer surplus to be positive.

For that to be true,

$V_{1} = - p_{1} + 9 z_{1} - 45 > 0 \Rightarrow 9 z_{1} > 45 + p_{1} \Rightarrow z_{1} > 5 + \frac{p_{1}}{9} S i n c e p_{1} > 0, z_{1} > 5$

Hence, consumer of type 1 requires the quality to be greater than 5.

Similarly for consumer of type 2,

$V_{2} = - p_{2} + 4 z_{2} - 12 > 0 \Rightarrow z_{2} > 3 + \frac{p_{2}}{4} S i n c e p_{2} > 0, z_{2} > 3$

So the minimum quality required by the consumer is 3.

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