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. Define the approach that should be used to solve the problem and identify all your inputs of the model

2. Assume that a person is now living in the city, what is the probability that the person will move the the suburb after two year? Use a tree diagram to answer the question.

3. Assume that a person is now living in the suburbs, what is the probability that the person will stay there next year?

4. What is the proportion of people who are living in the city in the long run?

5. 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?

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

Answer 1

1. We can use a Markov chain to decribe this problem.