The Upside of Monopoly

So here's a neat model I've been taught twice in law school. I don't know where it comes from, so alas I can't give credit.

Imagine you have a market with three television stations. There are different kinds of programming, with the following number of viewers for each:

Reality singing contest - 10,000
Police procedural - 7,000
News - 4,000
Political debate show - 1,000

Now imagine that if two networks are showing the same show, they split the viewers evenly. The question is, should we prefer independent ownership or a monopoly?

In this particular model, we want monopoly. If the stations are independently owned, they will show 2 reality singing contests and a police procedural, with total viewership of 17,000. This is because the third station to choose programming will do better to take 5,000 from another station than to get 4,000 with news programming.

With a monopoply, each station shows unique content - the top three categories are all aired, for a total viewership of 21,000. The monopolist has no desire to rob 5,000 from himself, so he airs news on the third channel.

So this is mildly interesting for telecommunications policy. For me, it's more interesting as a counter-intuitive model that captures a market failure. I'll post more thoughts on that soon.