Question

2. (7 pts) Assume that each year 10% of renters become homeowners, and 1% of homeowners sell their home and become renters. We assume that 90% of the population are renters. We denote by In and hn the percentage of renters and homeowners, respectively, at the beginning of n-th year. (a) (1 pt) Determine ro and ho. (b) (1 pt) Sketch the corresponding transition diagram. (c) (1 pt) Deduce the iterative and general relations satisfied by (rn) and (n). (d) (1 pt) Determine the corresponding equilibrium points. (e) (1 pt) How long it takes to have 20% of renters? (f) (1 pt) Determine the percentages after 10 years? (g) (1 pt) Is it possible to have 92% of homeowners? Justify.
just answer a through c

Answer 1

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a 90 7. a0-90)7 - 10% 99 homean renter 0.01 hm) P0) O.01 + (6-10) Tn- Yenter Temain nenter 0.90 Tm- be came homeower Ten ter Pemain homaswer NomeowneY homeowner became Yen ter POCO SHOT ON POCO F1