Newspaper/Subscription/Movement of customers/Matrix/Exercise

The newspapers ${}A,B$ and ${}C$ sell subscriptions, and they compete in a local market with ${}100000$ customers. Within a year, one can observe the following movements.

1. The subscribers of ${}A$ stick with a percentage of ${}80\%$ to ${}A$, ${}10\%$ switch to ${}B$, ${}5\%$ switch to ${}C$ and ${}5\%$ become nonreaders.
2. The subscribers of ${}B$ stick with a percentage of ${}60\%$ to ${}B$, ${}10\%$ switch to ${}A$, ${}20\%$ switch to ${}C$ and ${}10\%$ become nonreaders.
3. The subscribers of ${}C$ stick with a percentage of ${}70\%$ to ${}C$, nobody switches to ${}A$, ${}10\%$ switch to ${}B$ and ${}20\%$ become nonreaders.
4. Among the nonreaders, ${}10\%$ subscribe to ${}A,B$ or ${}C$, the rest remains nonreaders.

a) Establish the matrix, which describes the movement of customers within a year.

b) In a certain year, each of the three newspapers has ${}20000$ subscribers and there are ${}40000$ nonreaders. How does the distribution look like after a year?

c) The three newspapers expand to another city, where there are no newspapers at all so far, but also ${}100000$ potential customers. How many subscribers does each newspaper have (and how many nonreaders)

after three years, if the same movements hold in the new city?

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