Data collected from selected major metropolitan areas in the eastern United States show that 2% of individuals living within the city limits move to the suburbs during a one-year period, while 1% of individuals living in the suburbs move to the city during a one- year period. Answer the following questions assuming that this process is modeled by a Markov process with two states: city and suburbs.
a. Prepare the matrix of transition probabilities.
b. Compute the steady-state probabilities.
c. In a particular metropolitan area, 40% of the population lives in the city, and 60% of the population lives in the suburbs. What population changes do your steady-state probabilities project for this metropolitan area?