57 Channels (and Nothin' On)

How come that with so many channels competing for the viewer's attention on the TV, there can be, as in the lyrics to the Bruce Springsteen song, as many as "57 CHANNELS (AND NOTHIN' ON)"? Even though some of us have tastes that differs from each others, free media such as TV and radio often display a strong tendency to serve only the mainstream. Indeed, even though the preferences of the audience may be diverse enough to make you think about landscapes at least as wide as a river delta, one often talks about if it were a river, dominated by a "mainstream".

To making an extra viewer able to watch a channel costs virtually nothing compared to the cost of producing the content. So my first though was that this in itself causes the market to fail to fulfill viewers preferences. The case however, is according to my simple investigation (outlined below), rather the reverse. With a large enough number of broadcasting stations, all viewers will be able to find stations that perfectly match their taste. Furthermore, the market will easily produce a mix of stations that maximizes viewer's welfare under standard assumptions.

So what's the problem then? Well, out here in the Blogosphere, it seems to me that my analysis holds, we have many blogs and good allocation. Also, Abiola Lapite (in a discussion on his blog preceding this post) thinks radio in the future will give us a myriad of stations producing a varied content. But when it comes to TV, and much of radio today, I guess fixed costs still keep the number of stations down. It is also easy to get the impression that there are even fewer production companies than TV-channels, and that the channles mostly are dealing with repackaging of the productions into an ever more streamlined mix.

And scarcity of stations may make the market's perfect allocation to collapse: Viewers with odd tastes far out in the media landscape that don't share their tastes with enough co-viewers, cannot support a whole station. So if they still keep the radio on or stick to the screen, they effectively lose much of their market power when settling for the next best. And when viewers off the mainstream are sidelined, the market moves the stations towards the mainstream. Which makes even more viewers seeing their favorite stations shutting down. Which all in all produces a spiral, which might in worst case, eventually result in 57 channels and nothing on.

Public service broadcasting should hence have opportunities under these circumstances. Not by competing with the commercial stations, but by offering alternatives. The goal for them should not be to have as many viewers on simultaneously, but rather to have as many viewers finding at least something they like and wouldn't find elsewhere. And tax funding shouldn't really be any more problematic than the fact that the average consumer more or less has to contribute via vendors and advertisers of common consumer goods, to some 57 channels that really doesn't show anything better than the barely acceptable.

Note: The same mainstream collapse happens in the "Vendors on the Beach" problem, and in the "Median Voter Theorem". However, these models does not illustrate the market success with many enough stations. Mathematically, they seem complex and has lead to some discussion among researchers over solutions ( as mentioned in this nice overview, again via Abiola).

Model: Viewers sits in a media landscape, an n-dimensional "tastespace", where their position define their preferences, and viewers close to each other have similar tastes. The effort for a broadcaster to change his product is small when moving between fulfilling preferences of two viewers sitting close to each other. This ordering of tastes might seem a very strong assumption. Consider however how well even a single line might do: "50's classics", "60's hits", "70's favorites"; here we have an arbitrary number of dimensions. Viewer density at each location is v(x). Stations sit in the same landscape, a station at a specific point perfectly satisfies viewers at that point. Viewers at x share their attention equally between station at x, but view nothing else. Station density is s(x), v and s are both positive non-zero real numbers and x an n-dimensional vector. Stations move continuously along the direction where v(x)/s(x) increase the most trying to increase profits from advertising. Hence, in equilibrium: s(x)=const*v(x); that simply stops stations from moving. Total utility derived hereof by all viewers in any point is v(x)*U(s(x)), remember that only broadcasters on the same location compete, not viewers. For utility to be maximized, the derivative of utility with respect to the station density have to equal in all points: v(x)dU(s(x))/ds = constant with x (d for partial derivative here). With our solution, then s*dU/ds = constant, which is satisfied for U=const*ln(s). Under the standard assumption of log utility the market's allocation is optimal!

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