# Question 3: [5 points] Consider a Hotelling line of length 1 with firms currently located at 0.29 and 0. Prices for all firms are fixed at p.

Question 3: [5 points] Consider a Hotelling line of length 1 with firms currently located at 0.29 and 0.75. Prices for all firms are fixed at p. You are advising a third firm about where to locate on the line. What is the best location you can suggest? Assume locations can only be chosen to two decimal points.

(a) 0.52 (b) 0.29 (c) 0.76

(d) None of the above

Answer: A location of 0.28 yields market share of 0.285 which is the maximum. Locating at 0.29 yields half of the market from [0, 0.52] = 0.26. Locating between 0.29 and 0.75 yields at most 0.23. Locating at 0.75 yields 0.24. Locating at 0.76 yields 0.235. So the answer is none of the above.

Answers are already there, but i still don’t get it. i do not understand how you get the marketshare how it is described on the answer

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