Suppose that Pokhara acquires customer-specific information through (costless) market research and, thereby, a more accurate estimate of how much each consumer values its jackets. More specifically, the information allows Pokhara to identify and split the consumers into two groups. Group 1 has a v within the subinterval [0,1/2] while Group 2 has a v within the subinterval (1/2, 1]. This allows Pokhara to charge different prices to different groups of consumers, p₁ and p2. Further assume that consumers cannot move between groups nor resell the jacket between themselves. d. e. f. group Write down Pokhara's profit maximization problem for each of consumers. Derive the optimal prices for each group p** and p**. (Hint: note that for each group, the firm can at most has a demand of 1/2. If Pokhara can already sell to all consumers in the group, it has no reason to further decrease its price for that group.) Following [e], write down Pokhara's profit **, consumer surplus CS** and total surplus W** when it sets those group-based prices.

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Chapter1: Making Economics Decisions
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Q1. Personalized pricing
Pokhara, a monopolist in the market for winterised jackets, faces a unit
mass of consumers with unit demand for their jackets. A consumer's valu-
ation (i.e., her reservation price) for a jacket, denoted by v, is drawn from
the uniform distribution over the interval [0, 1]. At price p, consumers with
vp each purchase one jacket while the other consumers do not buy.
Then, the market demand is given as follows:
Q(p) = 1-p
Suppose for simplicity that Pokhara's marginal cost is equal to zero.
At the beginning, Pokhara has no information regarding consumers'
valuations at the individual level and only knows that v is uniformly dis-
tributed on [0, 1]. As such, Pokhara can only charge a single price to all
consumers.
Transcribed Image Text:Q1. Personalized pricing Pokhara, a monopolist in the market for winterised jackets, faces a unit mass of consumers with unit demand for their jackets. A consumer's valu- ation (i.e., her reservation price) for a jacket, denoted by v, is drawn from the uniform distribution over the interval [0, 1]. At price p, consumers with vp each purchase one jacket while the other consumers do not buy. Then, the market demand is given as follows: Q(p) = 1-p Suppose for simplicity that Pokhara's marginal cost is equal to zero. At the beginning, Pokhara has no information regarding consumers' valuations at the individual level and only knows that v is uniformly dis- tributed on [0, 1]. As such, Pokhara can only charge a single price to all consumers.
Suppose that Pokhara acquires customer-specific information through
(costless) market research and, thereby, a more accurate estimate of how
much each consumer values its jackets. More specifically, the information
allows Pokhara to identify and split the consumers into two groups. Group
1 has a v within the subinterval [0, 1/2] while Group 2 has a v within
the subinterval (1/2, 1]. This allows Pokhara to charge different prices to
different groups of consumers, P₁ and p2. Further assume that consumers
cannot move between groups nor resell the jacket between themselves.
d.
e.
f.
Write down Pokhara's profit maximization problem for each
group of consumers.
Derive the optimal prices for each group p** and p**. (Hint:
note that for each group, the firm can at most has a demand of 1/2.
If Pokhara can already sell to all consumers in the group, it has no
reason to further decrease its price for that group.)
Following [e], write down Pokhara's profit **, consumer
surplus CS** and total surplus W** when it sets those group-based
prices.
Transcribed Image Text:Suppose that Pokhara acquires customer-specific information through (costless) market research and, thereby, a more accurate estimate of how much each consumer values its jackets. More specifically, the information allows Pokhara to identify and split the consumers into two groups. Group 1 has a v within the subinterval [0, 1/2] while Group 2 has a v within the subinterval (1/2, 1]. This allows Pokhara to charge different prices to different groups of consumers, P₁ and p2. Further assume that consumers cannot move between groups nor resell the jacket between themselves. d. e. f. Write down Pokhara's profit maximization problem for each group of consumers. Derive the optimal prices for each group p** and p**. (Hint: note that for each group, the firm can at most has a demand of 1/2. If Pokhara can already sell to all consumers in the group, it has no reason to further decrease its price for that group.) Following [e], write down Pokhara's profit **, consumer surplus CS** and total surplus W** when it sets those group-based prices.
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