Employees of a company have two choices of health insurance

Employees of a company have two choices of health insurance: Blue Shield and White Sword. Each person signs up for just one choice at the beginning of each year, with the option to change choices only at the end of each year. Statistics show that 10% of those enrolled in Blue Shield one year change to White Sword the following year, and 15% of those enrolled in White Sword one year change to Blue Shield the following year. The others do not change their insurance. Assume the total number of employees of the company never changes.

Solution

Thus transition matrix is

To find eigen values of A

(0.1-k)(-0.1-k) +0.0225 =0

Or k²+0.0125 =0

Eigenvalues:

Eigenvectors:

When n becomes very large white increases to full strength and blue decreases to 0.

		After I yr
Blue shield	0.5	0.505
white sword	0.5	0.495