Question

Assume that a country is served by to telephone Campanies A telecom and B telecom Dus to their aggressive sales tactics each year 40% of a telecom customers switch to telecom on the others hand 30% of the B telecon telecom customers switch to A telecom if the initial market shares of the to Companies is 80% and 20% to A telecom and B telecom respectively.

A, Draw the transactions diagram
B, write the transactions matrix
C, What will be the market share of the two companies after the comnig year? ​

Answer 1

A. Transition Diagram:

A telecom gains 30% of B telecom's customers.

B telecom gains 40% of A telecom's customers.

B. Transition Matrix:

`\left[\begin{array}{ccc}0.6&0.3\\0.4&0.7\end{array}\right]`

C. Market Share After Coming Year:

A telecom: 0.8×0.6+0.2×0.4=0.56

B telecom: 0.8×0.3+0.2×0.7=0.44

In this telecom scenario, Company A and Company B experience customer transitions due to aggressive sales tactics. The transition diagram illustrates that 30% of Company B's customers switch to Company A, while 40% of Company A's customers switch to Company B.

The transition matrix, representing these changes, is given as

`\left[\begin{array}{ccc}0.6&0.3\\0.4&0.7\end{array}\right]`

To calculate the market share after the coming year, we multiply the current market share by the corresponding transition probabilities. For Company A, the calculation is 0.8×0.6+0.2×0.4=0.56, and for Company B, it is 0.8×0.3+0.2×0.7=0.44.

This implies that after the upcoming year, Company A is projected to hold 56% of the market share, while Company B is anticipated to have 44%, reflecting the impact of customer transitions on the telecom market landscape.