1. Suppose three companies A, B and C dominate the market for a certain product and are
competing against each other for a large share of the market. Currently company A has 2/9 of the
market, company B has 4/0 of the market and company C has 1/3 of the market. The market
survey indicates that every 6 months Company A retains of its customer and loss 1/6 to
company B and 1/12 to company C. Company B retains 12 of its customers and loss 1/3 to
company A and 1/6 to company C. Company C retains 3/8 of its customers and loss A to
company A and 3/8 to company B. Find the market share of each company in the long run is
about

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MrRoyal MrRoyal · Answer 1 · 2022-04-16T12:34:41+02:00

The market share of the companies is an illustration of fractions.

The market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively

The current market shares are:

After 6 months, we have:

Company A:

Company B:

Company C:

The amount of customers lost by each company is

Lost = Market share * [Share retained - Share lost to the other two companies].

So, we have:

A = 2/9 * [3/4 - 1/6 - 1/12] = 1/9

B = 4/9 * [1/2 - 1/3 - 1/6] = 0

C = 1/3 * [3/8 - 1/4 - 3/8] = -1/12

The amount of customers gained by each company is

Gain = Market share of company gained from * Share gained

So, we have:

A = 1/3 * 4/9 + 1/4 * 1/3 = 25/108

B = 1/6 * 2/9 + 3/8 * 1/3 = 35/216

C = 1/12 * 2/9 + 1/6 * 4/9 = 5/54

The total gain in 6 months is:

Total Gain = Gain + Loss.

This gives

A = 25/108 + 1/9 = 37/108

B = 35/216 + 0 = 35/216

C = 5/54 - 1/12 = 1/108

Hence, the market share of each company in the long run (i.e. after 6 months) is 37/108, 35/216 and 1/108, respectively