Newsweek and Time Are Two Competing Weeklies, Each of Which $\mathrm{N}$

Newsweek and Time are two competing weeklies, each of which tries to keep their readership while trying to get the other's readers to switch. Among all the households holding yearly subscription to Newsweek or Time but not both, let $\mathrm{N}$ and $\mathrm{T}$ denote the states that a household is a current Newsweek or Time subscriber, respectively. The probabilities of switching from one state to the other after one transition (when they renew) are given by the tree diagram. (For simplicity, it may be assumed that all annual subscriptions expire on December 31st of the year and are renewed by all of them for one or the other but not both magazines for one year.) If the current number of households subscribing for Newsweek and Time respectively was 4000 and 2000, then both magazines would have the same number of subscribers in the very long run.