Question

A research study in a big metropolitan area shows that 2% of individuals living within the city limits move to suburbs during one-year period while 1% of individuals living in the suburbs move to the city during a one-year period.

1. In a particular metropolitan area, 40% of the population lives in the suburbs. What population changes do your long run probabilities project for this metropolitan area?

2. A group of 100 individuals are now living in the city, how many of them will stay after 3 years.

Answer 1

ANSWER::

5.

From our calculations in part (4) we get,

Thus in long run probability,

• 33.33% of population of this metropolitan area lives in city.
• 66.67% of population of this metropolitan area lives in suburbs.

Thus changes in long run probability are

• Suburbs population increases by (66.67-40)% = 26.67%
• City population decreases by {(100-40)-33.33}% ={60-33.33}% = 26.67%

6.

Initial population distribution is given by

After 3 years population distribution is given by

Hence, after 3 years 94 of those people will stay in the city.

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