Question

I PUT QUESTION 2 a. Suppose in country Bliss, 60% of its population lives in condominiums (denoted by () and 40% lives in houses (denoted by H). The observed yearly transition matrix. T. is: CH C10.35 0.65) 0.45 0.55 1. Interpret the elements in the second row of matrix T. (2 points) ii. After the lapse of one year, do the majority of country Bliss people still prefer to live in condominiums than to live in houses? (3 points) iii. Find the respective equilibrium percentages of people living in condominiums and houses. (5 points)

Answer 1

Answer: 2

a)

Гc н] |0.35 0.65 [0.45 0.55 |

i) SECOND ROW OF MATRIX DENOTES: The percentage of people preferring to change their livelihood from houses to condominiums is: 45%. The percentage of people preferring to continue their livelihood in the houses is: 55%. ii) The majority of country bliss people are living in condominiums, after the lapse of one year. The percentage of them preferring to continue living in condominiums is 35% while the percentage of people preferring to change their livelihood from condominiums to houses is 65% ..After the lapse of one year, the majority of country bliss people prefer to live in houses than condominiums. iii) The equilibrium percentage of people living in condominiums is: (0.6 x 0.35) + (0.4 x 0.45) = 0.39=39% The equilibrium percentage of people living in houses is: (0.6 x 0.65) + (0.4 x 0.55) = 0.61 = 61%

b) i) Matrix A= LA T] [A] 0.20 0.15 [T](0.40 0.30] 7 10.80 0.85])-([0.70 ii) (1 – A) ?= 0.60 0.70]) (-0.60 -0.85] 0.80 [ 14 1-12 -17] 16