Within a certain market area there are two brands of soap th

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?

Solution

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.