Within a certain market area there are two brands of soap that most people use:\
ID: 3430635 • Letter: W
Question
Within a certain market area there are two brands of soap that most people use:super soap" and cheap soap", with the current market evenly split between two brands. A company is considering introducing a third brand called extra clean soap" and they did some initial market study. Their estimates of weekly shopping patterns are as below: If a customer buys super soap this week, there is 75% chance the super soap will be used next week, 10% chance extra clean will be used and 15% chance cheap soap will be used. If customer buys extra clean this there is a 50-50 chance the customer will switch to super soap next week. If a customer buys cheap soap this week, it is equally likely that next week the customer will buy any of the 3 brands.
(a) Give the Markov matrix for the above data, where Xn is the type of soap used in week n
.(b) What is the long-run market share for the new soap?
(c) What will be the market share of the new soap two weeks after it is introduced?
(d) The market consists of approximately 1 million customers each week. Each purchase of super, cheap and extra clean soap yield a prot of 15, 10 and 25 cents respectively. Assume the market was at steady state with the even split between the 2 products. The initial advertising to introduce the new product was $100,000. How many weeks will it be until the $100,000 is recovered from the added revenue of the new product?
Explanation / Answer
Expected purchase of new soap in 2 weeks = 0.10+0.333 = 0.433
a) Long run market share for new soap = 0.2165 per week
Extra cost incurred = 100000
Profit increase due to new soap in 2 weeks =
1.583(15)+0.833(10)+0.433(25)
= 23.745+8.33+10.825
= 42.9
For 1000 to be adjusted no of weeks = 1000x2/42.9 = 46.62
or 47 weeks.
Supersoap clean soap new soap I week Yes II week 0.75 0.15 0.10 I week Yes II week 0.50 0.50 I week yes II week 0.333 0.333 0.333Related Questions
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