Three FM radio stations ( A , B , and C ) are competing for customers in the sam

Question

Three FM radio stations (A, B, and C) are competing for customers in the same market area.

Through an aggressive advertising campaign, each month station A is capturing 8% of station B's customers and 5% of station C's customers. (Hint: The phrase "station A is capturing 8% of station B's customers" means that 8% of the listeners are moving from B to A, not the other way around.) At the same time, station A is losing only 2% of its customers to B and 2% of its customers to C. Additionally, each month 1% of B's customers switch to C, and 1% of C's customers switch to B.

Initially, A and B each have 30% of the listeners and C has 40%.

Use this information to answer the following questions. (Give your answers correct to three decimal places. Note that you are asked to give decimal values and not percentages. For example, you would need to enter 0.628 as opposed to 62.800%.)

(a) What fraction of the listeners will A have after 3 months?


(b) What fraction of the listeners will B have after 3 months?


(c) What fraction of the listeners will C have after 3 months?

Explanation / Answer

(a) What fraction of the listeners will A have after 3 months?
fractions : 0.08 - 0.02 = 0.06

(b) What fraction of the listeners will B have after 3 months?
fraction : 0.05 - 0.02 = 0.03

(c) What fraction of the listeners will C have after 3 months?

fraction : 0.01 + 0.01 = 0.02

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