Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(b) Find the transition matrix T and then express it in the form QDQ-¹, where D is a diagonal matrix. (c) Suppose that the total number of firms in the industry remains fixed at 4000. By considering what happens to D" as n→ ∞, determine how many firms fall into each category in the long term.

(b) Find the transition matrix T and then express it in the form QDQ-¹, where D is a diagonal matrix. (c) Suppose that the total number of firms in the industry remains fixed at 4000. By considering what happens to D" as n→ ∞, determine how many firms fall into each category in the long term.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
4 Suppose that firms in a particular industry fall into one of three size categories: large, medium and small. If a firm is large one year, the probabilities that it will remain large, fall into the medium size category, or become small in the next year are, respectively, 0.7, 0.2 and 0.1. For a firm of medium size, the corresponding probabilities are, respectively, 0.1, 0.8 and 0.1. For a small firm, the probabilities are, respectively, 0, 0.1 and 0.9. (a) Let Ln, Mn and Sn represent the number of firms in each category after n years have elapsed. Express the above information in the matrix equation form Zn+1 = TZn, where Zn = Lin Mn Sn (You may wish to draw a network diagram to represent the above situation.)
Transcribed Image Text:4 Suppose that firms in a particular industry fall into one of three size categories: large, medium and small. If a firm is large one year, the probabilities that it will remain large, fall into the medium size category, or become small in the next year are, respectively, 0.7, 0.2 and 0.1. For a firm of medium size, the corresponding probabilities are, respectively, 0.1, 0.8 and 0.1. For a small firm, the probabilities are, respectively, 0, 0.1 and 0.9. (a) Let Ln, Mn and Sn represent the number of firms in each category after n years have elapsed. Express the above information in the matrix equation form Zn+1 = TZn, where Zn = Lin Mn Sn (You may wish to draw a network diagram to represent the above situation.)
(b) Find the transition matrix T and then express it in the form QDQ-¹, where D is a diagonal matrix. (c) Suppose that the total number of firms in the industry remains fixed at 4000. By considering what happens to D" as n→ ∞o, determine how many firms fall into each category in the long term.
Transcribed Image Text:(b) Find the transition matrix T and then express it in the form QDQ-¹, where D is a diagonal matrix. (c) Suppose that the total number of firms in the industry remains fixed at 4000. By considering what happens to D" as n→ ∞o, determine how many firms fall into each category in the long term.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS