In a large city, there are 4 mobile network operators M, M, M3, M4 which have...

 

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In a large city, there are 4 mobile network operators M, M, M3, M4 which have stable market shares 24.7%, 30.8%, 21.4%, 23.1% respectively. A new operator M5 wants to enter the market and has done a market survey. The survey report can be summarized by the following matrix: 0.89 0.03 0.04 0.03 0.02 0.04 0.89 0.04 0.04 0.02 0.03 0.03 0.86 0.03 0.03 0.03 0.03 0.03 0.89 0.03 0.01 0.02 0.03 0.01 0.90 where for each year, under the assumption that M5 has entered the market, the (i, j)-entry of B is the ratio of customers of M; that will change to M. B = Let xn be the vector that its ith entry represents, in the nth year after M5 has entered, the market share (in percentage) of M. Observe that Xn = Bxn-1 = Bxn-2 = Bhxo where xo = (24.7, 30.8, 21.4, 23.1, 0)T represents the initial market shares. In MATLAB, enter the matrix B and the column vector x0 = xo. (You can download the matrix B and vector x0 from the data file Lab B4.mat.) In the command window, type: >> eig(B) What is the eigenvalue that has the largest magnitude? What is the eigenvalue that has the smallest magnitude? Will the market shares stabilize in the long run? (yes/no) In the command window, type: >> B^4 * x0 Write down the market share (in percentage) of each operator in the 4th. year. (Round your answers to one decimal place. Answers with different format are considered incorrect.) M: % M: M3: M4 M5: % % % % What is the market share (in percentage) of M5 in the long run? See Activity 3 of Lab 2. (Round your answer to one decimal place. Answers with different format are considered incorrect.) % If the operator M5 will enter the market if they can be sure to get a market share of at least 10% in the 5th. year. Will M5 enter the market? (yes/no) no In a large city, there are 4 mobile network operators M, M, M3, M4 which have stable market shares 24.7%, 30.8%, 21.4%, 23.1% respectively. A new operator M5 wants to enter the market and has done a market survey. The survey report can be summarized by the following matrix: 0.89 0.03 0.04 0.03 0.02 0.04 0.89 0.04 0.04 0.02 0.03 0.03 0.86 0.03 0.03 0.03 0.03 0.03 0.89 0.03 0.01 0.02 0.03 0.01 0.90 where for each year, under the assumption that M5 has entered the market, the (i, j)-entry of B is the ratio of customers of M; that will change to M. B = Let xn be the vector that its ith entry represents, in the nth year after M5 has entered, the market share (in percentage) of M. Observe that Xn = Bxn-1 = Bxn-2 = Bhxo where xo = (24.7, 30.8, 21.4, 23.1, 0)T represents the initial market shares. In MATLAB, enter the matrix B and the column vector x0 = xo. (You can download the matrix B and vector x0 from the data file Lab B4.mat.) In the command window, type: >> eig(B) What is the eigenvalue that has the largest magnitude? What is the eigenvalue that has the smallest magnitude? Will the market shares stabilize in the long run? (yes/no) In the command window, type: >> B^4 * x0 Write down the market share (in percentage) of each operator in the 4th. year. (Round your answers to one decimal place. Answers with different format are considered incorrect.) M: % M: M3: M4 M5: % % % % What is the market share (in percentage) of M5 in the long run? See Activity 3 of Lab 2. (Round your answer to one decimal place. Answers with different format are considered incorrect.) % If the operator M5 will enter the market if they can be sure to get a market share of at least 10% in the 5th. year. Will M5 enter the market? (yes/no) no