Question 71) A certain firm has noticed that employees’ salaries

71) A certain firm has noticed that employees’ salaries from year to year can be modeled by Markov analysis. The matrix of transition probabilities follows.

(a) Set up the matrix of transition probabilities in the form:

(b) Determine the fundamental matrix for this problem.

(c) What is the probability that an employee who has received a raise will eventually quit?

(d) What is the probability that an employee who has received a raise will eventually be fired?

72) The vector of state probabilities for period n is (0.4, 0.6). The accompanying matrix of transition probabilities is: 

Calculate the vector of state probabilities for period n+1.

Answer: (0.50, 0.50)

Diff: 2

Topic: PREDICTING FUTURE MARKET SHARES

AACSB: Analytic Skills

73) Given the following matrix of transition probabilities, find the equilibrium states.

74) Given the following vector of state probabilities and the accompanying matrix of transition probabilities, find the next period vector of state probabilities.

(0.4 0.4 0.2) 

75) There is a 30% chance that any current client of company A will switch to company B this year. There is a 40% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 500 clients and company B has 300 clients,

(a) how many clients will each company have next year?

(b) how many clients will each company have in two years?

76) Over any given month, Hammond Market loses 10% of its customers to Otro Plaza and 20% to Tres Place. Otro Plaza loses 5% to Hammond and 10% to Tres Place. Tres Place loses 5% of its customers to each of the two competitors. At the present time, Hammond Market has 40% of the market, while the others have 30% each.

(a) Next month, what will the market shares be for the three firms?

(b) In two months, what will the market shares be for the three firms?

77) The fax machine in an office is very unreliable. If it was working yesterday, there is an 90% chance it will work today. If it was not working yesterday, there is a 5% chance it will work today.

(a) What is the probability that it is not working today, if it was not working yesterday?

(b) If it was working yesterday, what is the probability that it is working today?

78) There is a 30% chance that any current client of company A will switch to company B this year. There is a 20% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 1000 clients and company B has 1000 clients, in the long run (assuming the probabilities do not change), what will the market shares be?

79) There is a 60% chance that a customer without a smart phone will buy one this year. There is a 95% chance that a customer with a smart phone will continue with a smart phone going into the next year. If 30% of target market currently own smart phones, what proportion of the target market is expected to own a smart phone next year?

80) There is a 60% chance that a customer without a smart phone will buy one this year. There is a 95% chance that a customer with a smart phone will continue with a smart phone going into the next year. If 30% of target market currently own smart phones, what is the long-run percentage of the target market that will own smart phones?

81) Three fast food hamburger restaurants are competing for the college lunch crowd. Burger Bills has 40% of the market while Hungry Heifer and Salty Sams each have 30% of the market. Burger Bills loses 10 % of its customers to Hungry Heifer and 10% to Salty Sams each month. Hungry Heifer loses 5% of its customers to Burger Bills and 10% to Salty Sams each month. Salty Sams loses 10% of its customers to Burger Bills while 20% go to Hungry Heifer. What will the market shares be for the three businesses next month?

Our website has a team of professional writers who can help you write any of your homework. They will write your papers from scratch. We also have a team of editors just to make sure all papers are of HIGH QUALITY & PLAGIARISM FREE. To make an Order you only need to click Ask A Question and we will direct you to our Order Page at WriteDemy. Then fill Our Order Form with all your assignment instructions. Select your deadline and pay for your paper. You will get it few hours before your set deadline.