Question 25. Suppose buyers of ice-cream are uniformly distributed on the interval [0, 1]. Ice-cream sellers 1 and 2 simultaneously locate on the interval, each locating so to maximize her market share given the location of the rival. Each seller's market shar the proportion of buyers who are located closer to her location than (a) Both will locate at 1/2. (b) One will locate at 1/4 and the other at 3/4. (c) One will locate at 0 and the other at 1. (d) One will locate at 1/3 and the other at 2/3. corresponds to the rival's location. Question 26. In the context of previous question, suppose it is understood by all players that seller 3 will locate on [0, 1] after observing the simultaneous location choices of sellers 1 and 2. Seller 3 aims to maximize market share given the locations of 1 and 2. The locations of sellers 1 and 2 are as follows: (a) Both will locate at 1/2. (b) One will locate at 1/4 and the other at 3/4. (c) One will locate at 0 and the other at 1. (d) One will locate at 1/3 and the other at 2/3. edustre.in ; 9E
Question 25. Suppose buyers of ice-cream are uniformly distributed on the interval [0, 1]. Ice-cream sellers 1 and 2 simultaneously locate on the interval, each locating so to maximize her market share given the location of the rival. Each seller's market shar the proportion of buyers who are located closer to her location than (a) Both will locate at 1/2. (b) One will locate at 1/4 and the other at 3/4. (c) One will locate at 0 and the other at 1. (d) One will locate at 1/3 and the other at 2/3. corresponds to the rival's location. Question 26. In the context of previous question, suppose it is understood by all players that seller 3 will locate on [0, 1] after observing the simultaneous location choices of sellers 1 and 2. Seller 3 aims to maximize market share given the locations of 1 and 2. The locations of sellers 1 and 2 are as follows: (a) Both will locate at 1/2. (b) One will locate at 1/4 and the other at 3/4. (c) One will locate at 0 and the other at 1. (d) One will locate at 1/3 and the other at 2/3. edustre.in ; 9E
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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The question is based on product differentiation. Please solve both problems 25 and 26 in the image given below. Also, please accurately describe how to calculate 'market share' in the question. Please provide a complete mathematical as well as intuitive explanation for the problem. Thank you.
![Question 25. Suppose buyers of ice-cream are uniformly distributed on the interval [0, 1].
Ice-cream sellers 1 and 2 simultaneously locate on the interval, each locating so to maximize
her market share given the location of the rival. Each seller's market shar
the proportion of buyers who are located closer to her location than
(a) Both will locate at 1/2.
(b) One will locate at 1/4 and the other at 3/4.
(c) One will locate at 0 and the other at 1.
(d) One will locate at 1/3 and the other at 2/3.
corresponds to
the rival's location.
Question 26. In the context of previous question, suppose it is understood by all players
that seller 3 will locate on [0, 1] after observing the simultaneous location choices of sellers 1
and 2. Seller 3 aims to maximize market share given the locations of 1 and 2. The locations
of sellers 1 and 2 are as follows:
(a) Both will locate at 1/2.
(b) One will locate at 1/4 and the other at 3/4.
(c) One will locate at 0 and the other at 1.
(d) One will locate at 1/3 and the other at 2/3.
edustre.in ; 9E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39f4412a-18c0-4f64-8bcf-4dffb42656da%2F9c100f9f-98e2-45b3-ab0f-c5b9722bb44b%2Fsomslpk_processed.png&w=3840&q=75)
Transcribed Image Text:Question 25. Suppose buyers of ice-cream are uniformly distributed on the interval [0, 1].
Ice-cream sellers 1 and 2 simultaneously locate on the interval, each locating so to maximize
her market share given the location of the rival. Each seller's market shar
the proportion of buyers who are located closer to her location than
(a) Both will locate at 1/2.
(b) One will locate at 1/4 and the other at 3/4.
(c) One will locate at 0 and the other at 1.
(d) One will locate at 1/3 and the other at 2/3.
corresponds to
the rival's location.
Question 26. In the context of previous question, suppose it is understood by all players
that seller 3 will locate on [0, 1] after observing the simultaneous location choices of sellers 1
and 2. Seller 3 aims to maximize market share given the locations of 1 and 2. The locations
of sellers 1 and 2 are as follows:
(a) Both will locate at 1/2.
(b) One will locate at 1/4 and the other at 3/4.
(c) One will locate at 0 and the other at 1.
(d) One will locate at 1/3 and the other at 2/3.
edustre.in ; 9E
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