Suppose that Pokhara manages to hire an even better (and still costless) market research team, allowing Pokhara to acquire even finer information about consumers' valuations. It can now tell whether a consumer's valu- ation v belongs to either of Groups 1, 2 or 3 with valuations within the intervals [0,1/3], (1/3,2/3], or (2/3, 1] respectively. As such, Pokhara can respectively charge p₁, P2 and p3 separately to these three groups of con- sumers. h. i. Write down Pokhara's profit maximization problem for each group of consumers. Derive the optimal prices for each group pi", på" and på". (Hint: note that for each group, the firm can at most has a demand of 1/3.) Following [h], write down Pokhara's profit ****, consumer surplus CS*** and total surplus W*** when it can set group-based prices to three groups. 2 j. Compare your results in [c], [f] and [i] and explain the im- pact of Pokhara having more precise consumer information on prof- its, consumer surplus and total welfare. (i.e., does it always in- crease(decrease) profits, consumer surplus and total welfare when the firm has more information about consumer valuations?)
Suppose that Pokhara manages to hire an even better (and still costless) market research team, allowing Pokhara to acquire even finer information about consumers' valuations. It can now tell whether a consumer's valu- ation v belongs to either of Groups 1, 2 or 3 with valuations within the intervals [0,1/3], (1/3,2/3], or (2/3, 1] respectively. As such, Pokhara can respectively charge p₁, P2 and p3 separately to these three groups of con- sumers. h. i. Write down Pokhara's profit maximization problem for each group of consumers. Derive the optimal prices for each group pi", på" and på". (Hint: note that for each group, the firm can at most has a demand of 1/3.) Following [h], write down Pokhara's profit ****, consumer surplus CS*** and total surplus W*** when it can set group-based prices to three groups. 2 j. Compare your results in [c], [f] and [i] and explain the im- pact of Pokhara having more precise consumer information on prof- its, consumer surplus and total welfare. (i.e., does it always in- crease(decrease) profits, consumer surplus and total welfare when the firm has more information about consumer valuations?)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please help me understand part g-j of this questions
![Suppose that Pokhara manages to hire an even better (and still costless)
market research team, allowing Pokhara to acquire even finer information
about consumers' valuations. It can now tell whether a consumer's valu-
ation v belongs to either of Groups 1, 2 or 3 with valuations within the
intervals [0,1/3], (1/3,2/3], or (2/3, 1] respectively. As such, Pokhara can
respectively charge p₁, p2 and p3 separately to these three groups of con-
sumers.
h.
i.
Write down Pokhara's profit maximization problem for each
group of consumers.
Derive the optimal prices for each group pi", p2" and p**.
(Hint: note that for each group, the firm can at most has a demand
of 1/3.)
Following [h], write down Pokhara's profit ***, consumer
surplus CS*** and total surplus W*** when it can set group-based
prices to three groups.
2
j.
Compare your results in [c], [f] and [i] and explain the im-
pact of Pokhara having more precise consumer information on prof-
its, consumer surplus and total welfare. (i.e., does it always in-
crease(decrease) profits, consumer surplus and total welfare when the
firm has more information about consumer valuations?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a4decfa-c86a-4508-ad17-cd6b643e587a%2Fa11a1061-0eed-4e4c-9372-7cad11b59da0%2Fkg56bre_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that Pokhara manages to hire an even better (and still costless)
market research team, allowing Pokhara to acquire even finer information
about consumers' valuations. It can now tell whether a consumer's valu-
ation v belongs to either of Groups 1, 2 or 3 with valuations within the
intervals [0,1/3], (1/3,2/3], or (2/3, 1] respectively. As such, Pokhara can
respectively charge p₁, p2 and p3 separately to these three groups of con-
sumers.
h.
i.
Write down Pokhara's profit maximization problem for each
group of consumers.
Derive the optimal prices for each group pi", p2" and p**.
(Hint: note that for each group, the firm can at most has a demand
of 1/3.)
Following [h], write down Pokhara's profit ***, consumer
surplus CS*** and total surplus W*** when it can set group-based
prices to three groups.
2
j.
Compare your results in [c], [f] and [i] and explain the im-
pact of Pokhara having more precise consumer information on prof-
its, consumer surplus and total welfare. (i.e., does it always in-
crease(decrease) profits, consumer surplus and total welfare when the
firm has more information about consumer valuations?)
![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
v≥p 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.
a.
b.
C.
e.
Write down Pokhara's profit maximization problem.
Use the first-order condition to derive the optimal uniform
price p* of each jacket.
f.
1
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.
Following [b], write down Pokhara's profit *, consumer sur-
plus CS* and total surplus W* when it charges a uniform price to all
consumers.
Write down Pokhara's profit maximization problem for each
group of consumers.
Derive the optimal prices for each group pi* 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a4decfa-c86a-4508-ad17-cd6b643e587a%2Fa11a1061-0eed-4e4c-9372-7cad11b59da0%2Fvl8c8z_processed.png&w=3840&q=75)
Transcribed Image Text: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
v≥p 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.
a.
b.
C.
e.
Write down Pokhara's profit maximization problem.
Use the first-order condition to derive the optimal uniform
price p* of each jacket.
f.
1
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.
Following [b], write down Pokhara's profit *, consumer sur-
plus CS* and total surplus W* when it charges a uniform price to all
consumers.
Write down Pokhara's profit maximization problem for each
group of consumers.
Derive the optimal prices for each group pi* 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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Step 1: Defining price discrimination, consumer suplus and total surplus
VIEWStep 2: Write the profit maximization problem for each group of customers
VIEWStep 3: Find the demand function for group 1, 2, and 3
VIEWStep 4: Find the optimal price for each group
VIEWStep 5: Find the profit, consumer surplus and total surplus
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