Question

Currently, it is known that 85 percent of the population own an automobile and 15 percent do not. Based upon past experience, in a year 1¼ of the nonowners will become owners, and 1/1000 of one percent of the owners will become nonowners.

1. What are the expcted percentages of owners and nonowners for next year?

2. What is the expected steady state?

 

Answer 1

Solution:

Currently, the population having an automobile $=85\%$

And the population not having an automobile $=15\%$

In a year, non-owners who become owners $=1\frac 14\%=1.25\%$

And owners who become non-owners$=\frac 1{1000}\%=0.001\%$

(1):   For next year:

Expected $\%$ of owners $= 85\% + 15\% \times 1.25\% = 85.1875\%$

Expected $\%$ of non-owners $= 15\% + 85\% \times 0.001\%=15.00085\%$

(2): Expected steady state:

Of owners$=85\%(1+15\%\times1.25\%)^n$

Of non-owners$=15\%(1+85\%\times 0.001\%)^n$

where $n$ is the number of years.