There has been much interest in whether industries in the United States are moving from the Northeast and North Central regions to the South and West, motivated by the warmer climate, by lower wages, and by less unionization. Here is the transition matrix for large firms in Electric and Electronic Equipment.

For example, a firm in the Northeast region will be in the West region next year with probability 0.111. (The Z entry is a "birth-death" state. For instance, with probability 0.102 a large Electric and Electronic Equipment firm from the Northeast will move out of this system next year: go out of business, move abroad, or move to another category of firm. There is a 0.021 probability that a firm in the National Census of Manufacturers will move into Electronics, or be created, or move in from abroad, into the Northeast. Finally, with probability 0.954 a firm out of the categories will stay out, according to this research.)
(a) Does the Markov model assumption of lack of history seem justified?
(b) Assume that the initial distribution is even, except that the value at Z is 0:9.
Compute the vectors for n = 1 through n = 4.
(c) Suppose that the initial distribution is this.

Calculate the distributions for n = 1 through n = 4.
(d) Find the distribution for n = 50 and n = 51. Has the system settled down to an equilibrium?

NE NC NEI 0.787 0 NC 0 0. 0.102 0.966 0.034 0 0.063 0.37 0 w 0 0.074 0.612 0.314 0.021 0.009 0.005 0.010 0.954 NE NC S 0.0000 0.6522 0.3478 0.0000 0.0000