Duopolistic firms without cost compete on price with product differentiation. Demand for firm i is q₁ = 2 - 2p; + p;, where i is that individual firm and j is the other firm. a. Find the best response functions in the static game. (Be very careful since you'll keep using the best response functions.) b. Prices are nonnegative. Given this, do the first iteration of IESDS. c. Find the NE prices.
Duopolistic firms without cost compete on price with product differentiation. Demand for firm i is q₁ = 2 - 2p; + p;, where i is that individual firm and j is the other firm. a. Find the best response functions in the static game. (Be very careful since you'll keep using the best response functions.) b. Prices are nonnegative. Given this, do the first iteration of IESDS. c. Find the NE prices.
Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.4P
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![Q2. Static Games/Dynamic Games/IO
Duopolistic firms without cost compete on price with product differentiation. Demand for
firm i is q; = 2 - 2p; +p;, where i is that individual firm and j is the other firm.
a. Find the best response functions in the static game. (Be very careful since you'll keep
using the best response functions.)
b. Prices are nonnegative. Given this, do the first iteration of IESDS.
c. Find the NE prices.
d. Suppose firm 1 sets prices first, then firm 2 observes and sets prices. Find the prices
that result from the SPNE.
e. What price would a cartel charge?
f. Suppose the static game is repeated 100 times. Find the SPNE.
g. Suppose the static game is repeated indefinitely. Describe the (symmetric) strategy
each player could take that supports playing the cartel prices indefinitely for a high
enough 6. Note you should not be doing any math in this part! Wait just a moment,
we'll get there!
h. What is the lowest & can be to support the strategy above? [Note, doesn't come out
neatly]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48ceae03-ce82-43df-b816-3449c4a6aa24%2F51f95b00-d697-4a4b-8a5f-c1b8984c119f%2Fo0iq7x7_processed.png&w=3840&q=75)
Transcribed Image Text:Q2. Static Games/Dynamic Games/IO
Duopolistic firms without cost compete on price with product differentiation. Demand for
firm i is q; = 2 - 2p; +p;, where i is that individual firm and j is the other firm.
a. Find the best response functions in the static game. (Be very careful since you'll keep
using the best response functions.)
b. Prices are nonnegative. Given this, do the first iteration of IESDS.
c. Find the NE prices.
d. Suppose firm 1 sets prices first, then firm 2 observes and sets prices. Find the prices
that result from the SPNE.
e. What price would a cartel charge?
f. Suppose the static game is repeated 100 times. Find the SPNE.
g. Suppose the static game is repeated indefinitely. Describe the (symmetric) strategy
each player could take that supports playing the cartel prices indefinitely for a high
enough 6. Note you should not be doing any math in this part! Wait just a moment,
we'll get there!
h. What is the lowest & can be to support the strategy above? [Note, doesn't come out
neatly]
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Please solve Part G and Part H. Thank you so much!
Solution
by Bartleby ExpertFollow-up Question
Please continue to solve from Part D to Part F
![Q2. Static Games/Dynamic Games/IO
Duopolistic firms without cost compete on price with product differentiation. Demand for
firm i is q; = 2 - 2p; +p;, where i is that individual firm and j is the other firm.
a. Find the best response functions in the static game. (Be very careful since you'll keep
using the best response functions.)
b. Prices are nonnegative. Given this, do the first iteration of IESDS.
c. Find the NE prices.
d. Suppose firm 1 sets prices first, then firm 2 observes and sets prices. Find the prices
that result from the SPNE.
e. What price would a cartel charge?
f. Suppose the static game is repeated 100 times. Find the SPNE.
g. Suppose the static game is repeated indefinitely. Describe the (symmetric) strategy
each player could take that supports playing the cartel prices indefinitely for a high
enough 6. Note you should not be doing any math in this part! Wait just a moment,
we'll get there!
h. What is the lowest & can be to support the strategy above? [Note, doesn't come out
neatly]](https://content.bartleby.com/qna-images/question/48ceae03-ce82-43df-b816-3449c4a6aa24/1c547fea-84b2-43d6-9a1f-8a0c2d7bc896/2gbugcp_processed.png)
Transcribed Image Text:Q2. Static Games/Dynamic Games/IO
Duopolistic firms without cost compete on price with product differentiation. Demand for
firm i is q; = 2 - 2p; +p;, where i is that individual firm and j is the other firm.
a. Find the best response functions in the static game. (Be very careful since you'll keep
using the best response functions.)
b. Prices are nonnegative. Given this, do the first iteration of IESDS.
c. Find the NE prices.
d. Suppose firm 1 sets prices first, then firm 2 observes and sets prices. Find the prices
that result from the SPNE.
e. What price would a cartel charge?
f. Suppose the static game is repeated 100 times. Find the SPNE.
g. Suppose the static game is repeated indefinitely. Describe the (symmetric) strategy
each player could take that supports playing the cartel prices indefinitely for a high
enough 6. Note you should not be doing any math in this part! Wait just a moment,
we'll get there!
h. What is the lowest & can be to support the strategy above? [Note, doesn't come out
neatly]
Solution
by Bartleby ExpertFollow-up Question
Please continue to solve from Part D to Part H. Thank you very much.
Solution
by Bartleby ExpertFollow-up Question
Please continue to solve from Part d to Part h. Thank you!
![Q2. Static Games/Dynamic Games/IO
Duopolistic firms without cost compete on price with product differentiation. Demand for
firm i is q; = 2 - 2p; +p;, where i is that individual firm and j is the other firm.
a. Find the best response functions in the static game. (Be very careful since you'll keep
using the best response functions.)
b. Prices are nonnegative. Given this, do the first iteration of IESDS.
c. Find the NE prices.
d. Suppose firm 1 sets prices first, then firm 2 observes and sets prices. Find the prices
that result from the SPNE.
e. What price would a cartel charge?
f. Suppose the static game is repeated 100 times. Find the SPNE.
g. Suppose the static game is repeated indefinitely. Describe the (symmetric) strategy
each player could take that supports playing the cartel prices indefinitely for a high
enough 6. Note you should not be doing any math in this part! Wait just a moment,
we'll get there!
h. What is the lowest & can be to support the strategy above? [Note, doesn't come out
neatly]](https://content.bartleby.com/qna-images/question/48ceae03-ce82-43df-b816-3449c4a6aa24/0d2be38d-0839-45c8-9d4c-abd9e7632075/llvdwt_processed.png)
Transcribed Image Text:Q2. Static Games/Dynamic Games/IO
Duopolistic firms without cost compete on price with product differentiation. Demand for
firm i is q; = 2 - 2p; +p;, where i is that individual firm and j is the other firm.
a. Find the best response functions in the static game. (Be very careful since you'll keep
using the best response functions.)
b. Prices are nonnegative. Given this, do the first iteration of IESDS.
c. Find the NE prices.
d. Suppose firm 1 sets prices first, then firm 2 observes and sets prices. Find the prices
that result from the SPNE.
e. What price would a cartel charge?
f. Suppose the static game is repeated 100 times. Find the SPNE.
g. Suppose the static game is repeated indefinitely. Describe the (symmetric) strategy
each player could take that supports playing the cartel prices indefinitely for a high
enough 6. Note you should not be doing any math in this part! Wait just a moment,
we'll get there!
h. What is the lowest & can be to support the strategy above? [Note, doesn't come out
neatly]
Solution
by Bartleby ExpertKnowledge Booster
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