Question

Benfel Ltd
and 10% to Samtec Ltd. Furthermore, Samtec Ltd retains 50% while it loses 30% to Cromwell
Ltd and 20% to Benfel Ltd. It has been determined that there will be 3,500, 4,300 and 2,200
customers shopping with Benfel Ltd, Cromwell Ltd and Samtec Ltd respectively at the start of the
month of September 2019.
a) Formulate the transition matrix for this system. (1mark)
b) Evaluate the distribution of the sample surveyed as at the beginning month of August 2019.
(5 marks)
c) Compare the long run state of the market amongst the three companies.

Answer 1

a. Full information for transition matrix is not available in the question
b. Distribution of the sample at the beginning of Aug 2019
Customers Shopping at the beginning of Sep 2019
	Beginning of Sep 2019	Distribution of Samtec loss of Customers to Benfel and Cromwell	Ratio for distribution	Increase in Sep	Beginning of Aug 2019
Benfel	3500	20%	40%	880	2620
Cromwell	4300	30%	60%	1320	2980
Samtec	2200	50%	-100%	-2200	4400
C. Long Run State of the Market
Assuming a simliar transition of market share between Samtec to Cromwell and Benfel
	Beginning of Aug 2019	Beginning of Sep 2019	Ratio for distribution	Beginning of Sep 2020
Benfel	2620	3500	40%
Cromwell	2980	4300	60%
Samtec	4400	2200	-100%
		Samtec	Cromwell	Benfel
	Sep-19	2,200	4,300	3,500
	Oct-19	1,100	4,960	3,940
	Nov-19	550	5,290	4,160
	Dec-19	275	5,455	4,270
	Jan-20	138	5,538	4,325
	Feb-20	69	5,579	4,353
	Mar-20	34	5,599	4,366
	Apr-20	17	5,610	4,373
	May-20	9	5,615	4,377
	Jun-20	4	5,617	4,378
	Jul-20	2	5,619	4,379
	Aug-20	1	5,619	4,380