Amazon has 100 million prime members. The annual prime membership fee is $100. Amazon is thinking about raising the prime membership fee to $150. By such a price increase 30 million prime members will cancel their membership. However, those who remain a member are more likely to buy from Amazon. The marketing department uses a Markov chain to model customer purchase behavior. In each day a customer may buy from Amazon or other retail stores. When the membership price is $100, If a member customer buys from Amazon today, with probability 0.6 will buy from Amazon tomorrow; if a member customer buys from other retail stores today, with probability 0.5 will buy from Amazon tomorrow. When the membership price is $150, If a member customer buys from Amazon today, with probability 0.7 will buy from Amazon tomorrow; if a member customer buys from other retail stores today, with probability 0.6 will buy from Amazon tomorrow. For simplicity assume that a customer purchases once a day and the net value of each purchase to Amazon is $200. Should Amazon increase the prime membership fee? Why?

Amazon has 100 million prime members. The annual prime membership fee is $100. Amazon is thinking about raising the prime membership fee to $150. By such a price increase 30 million prime members will cancel their membership. However, those who remain a member are more likely to buy from Amazon. The marketing department uses a Markov chain to model customer purchase behavior. In each day a customer may buy from Amazon or other retail stores. When the membership price is $100, If a member customer buys from Amazon today, with probability 0.6 will buy from Amazon tomorrow; if a member customer buys from other retail stores today, with probability 0.5 will buy from Amazon tomorrow. When the membership price is $150, If a member customer buys from Amazon today, with probability 0.7 will buy from Amazon tomorrow; if a member customer buys from other retail stores today, with probability 0.6 will buy from Amazon tomorrow. For simplicity assume that a customer purchases once a day and the net value of each purchase to Amazon is $200. Should Amazon increase the prime membership fee? Why?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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