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Unformatted text preview: Let c n = % of Coke drinkers at the end of month n p n = % of Pepsi drinkers at the end of month n The initial conditions or initial market distribution is: c = .6 and p = .4 NOTE: the subscript 0 indicates "at the end of month 0", i.e at the start of month 1 Sec 3.6 Saturday, February 06, 2010 11:17 PM Section3dot6 Page 1 Let c n = % of Coke drinkers at the end of month n p n = % of Pepsi drinkers at the end of month n The initial conditions or initial market distribution is: c = .6 and p = .4 NOTE: the subscript 0 indicates "at the end of month 0", i.e at the start of month 1 After month 1: c 1 = .7 c + .1 p and p 1 = .3 c + .9 p 3.6.1 Saturday, February 06, 2010 11:17 PM Section3dot6 Page 2 Let c n = % of Coke drinkers at the end of month n p n = % of Pepsi drinkers at the end of month n The initial conditions or initial market distribution is: c = .6 and p = .4 NOTE: the subscript 0 indicates "at the end of month 0", i.e at the start of month 1 After month 1: c 1 = .7 c + .1 p and p 1 = .3 c + .9 p As a matrix equation: c 1 .7 .1 c .7 .1 .6 .46 = = = p 1 .3 .9 p .3 .9 .4 .54 This says that after 1 month, 46% of the market will be Coke drinkers and 54% will be Pepsi drinkers. 3.6.2 Saturday, February 06, 2010 11:17 PM Section3dot6 Page 3 Let c n = % of Coke drinkers at the end of month n p n = % of Pepsi drinkers at the end of month n The initial conditions or initial market distribution is: c = .6 and p = .4 NOTE: the subscript 0 indicates "at the end of month 0", i.e at the start of month 1 After month 1: c 1 = .7 c + .1 p and p 1 = .3 c + .9 p As a matrix equation: c 1 .7 .1 c .7 .1 .6 .46 = = = p 1 .3 .9 p .3 .9 .4 .54 This says that after 1 month, 46% of the market will be Coke drinkers and 54% will be Pepsi drinkers After month 2: c 2 = .7 c 1 + .1 p 1 and p 2 = .3 c 1 + .9 p 1 3.6.3 Saturday, February 06, 2010 11:17 PM Section3dot6 Page 4 Let c n = % of Coke drinkers at the end of month n p n = % of Pepsi drinkers at the end of month n The initial conditions or initial market distribution is: c = .6 and p = .4 NOTE: the subscript 0 indicates "at the end of month 0", i.e at the start of month 1 After month 1: c 1 = .7 c + .1 p and p 1 = .3 c + .9 p As a matrix equation: c 1 .7 .1 c .7 .1 .6 .46 = = = p 1 .3 .9 p .3 .9 .4 .54 This says that after 1 month, 46% of the market will be Coke drinkers and 54% will be Pepsi drinkers After month 2: c 2 = .7 c 1 + .1 p 1 and p 2 = .3 c 1 + .9 p 1 As a matrix equation: c 2 .7 .1 c 1 .7 .1 .46 .376 = = = p 2 .3 .9 p 1 .3 .9 .54 .624 After 2 months, 37.6% of the market will be Coke drinkers and 62.4% will be Pepsi drinkers 3.6.4 Saturday, February 06, 2010 11:17 PM Section3dot6 Page 5 Note that the market distribution of any specific time period depends solely on the market distribution in the preceding time period 3.6.5 Monday, February 15, 2010 8:10 AM Section3dot6 Page 6 Note that the market distribution of any specific time period depends solely on the market distribution in the preceding time period...
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 Fall '07
 Tom
 Math, Linear Algebra, Algebra, Markov chain, Garber

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