ers tend to exhibit loyalty to product brands but may be persuaded through Custo
ID: 3353656 • Letter: E
Question
ers tend to exhibit loyalty to product brands but may be persuaded through Custom clever marketing and advertising to switch brands, Consider the case of three brands: A, B, and C. Customer "unyielding" loyalty to a given brand is estimated at 75%, giving the competitors only a 25% margin to realize a their advertising campaigns once a year. For brand A customers, the probabilities of switching to brands B and C are 1 and .15, respectively. Customers of brand B are likely to switch to A and C with probabilities .2 and.05, respectively. Brand C customers can switch to brands A and B with equal probabilities. (a) Express the situation as a Markov chain. (b) In the long run, how much market share will each brand command? (e) How long on the average will it take for a brand A customer to switch to brand B? switch. Competitors launch To brand C?Explanation / Answer
Three states (brands) = A, B and C
Loyalty probability = 0.75; disloyalty = 0.25
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As a Markov chain, transition state is the following:-
a b c
a 0.750 0.100 0.15
b 0.200 0.750 0.05
c 0.125 0.125 0.75
---- PART b: R-code to solution ----
install.packages("markovchain")
library("markovchain")
# Number of states = 3
States = c("a","b","c")
byRow = TRUE
lMatrix = matrix(data = c(0.75,0.1,0.15,0.2,0.75,0.05,0.125,0.125,0.75), byrow = byRow, nrow = length(States), dimnames = list(States, States))
mcl = new("markovchain", states = States, byrow = byRow,
transitionMatrix = lMatrix, name = "loy.")
## Part b [ANSWER]
steadyStates(mcl)
a b c
0.3947368 0.3070175 0.2982456
---- PART b: R-code to solution ----
---- PART c ----
Time taken on average to reach Brand B for a Brand A customer = Expected value of N
N = 1 when customer goes from A to B in 1 round
N = 2 when customer goes from A to B in 2 rounds
N = 3 when customer goes from A to B in 3 rounds
.
.
.
N = n when customer goes from A to B in n rounds
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Expected time can be calculated by sum of multiplication of (number of steps --> 1 to infinity) and (prob. of this happening --> calculated using Markov chain)
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