Radio Days

    A professor of mine, remarking on the decline of American culture, bemoaned that the Bay Area's two classical radio stations are commercial rather than public, so that he has to listen to advertisements betwixt the music.  I pointed out that this regrettable situation occured because there were TOO MANY classical music listeners in the Bay Area, not too few.  He did not seem to grasp the point.

    The point was, that if there were fewer classical music lovers around, the commerical stations would not be able to turn a profit, hence would not exist, so the Bay Area would be served by a public classical station instead.

    There are a number of interesting questions raised by this analysis.

    Empirical facts (assumptions):

  1. No region is served by both a commerical and a public station in the same area (i.e., both classical, or both jazz, etc.)
  2. Public stations serve areas with few listeners, commercial stations areas with many.
    Why?  There is a plausible reason for (1):  A public station can't serve the same region as a commercial station because people are unwilling to make donations to a public station when there is a commercial station in the region.

    But why (2):  Why do public stations serve areas with fewer listeners?

    It makes sense that, the fewer  listeners, the less likely a commercial station is to be profitable--fewer listeners mean less advertising revenue.  But it also seems plausible that the fewer listeners, the harder it is to support a PUBLIC station, since fewer listeners means fewer potential donors.  So there's no obvious reason why public stations should survive where commercial stations can't.

    Here's a plausible model to explain the facts:

  1. It costs the same amount to run radio station, no matter whether it's commercial or public, and no matter how many potential listeners (L) there are..

    2. Ccom(L) = Cpub(L) = C
     
  2. Revenues of both public and commercial stations are increasing functions of the number of potential listeners in the region

    3. Rcom and Rpub and both increasing functions of number of potential listeners, L.
     
  3. Wherever a commercial station will make a positive profit, it will exist.

    4. Commercial stations exist for all regions where Rcom(L) > C
     
  4. Wherever a commercial station exists, public stations cannot exist.

    5. Rpub < C whenever a commercial station is in the region.
    There is some minimum potential listenership for a commercial station to exist.  This is the breakeven listenership, call it bcom, where the station makes zero profits, so we assume it doesn't bother to exist.  We know that

    Rcom(bcom) < Rpub(bcom)

    i.e., in an area with bcom potential listeners, a public radio station can generate more revenues through donations than a commercial station can generate through advertising.  We know this, because public stations do exist where commercial stations don't.  If we reduce listeners enough, to bpub, even the public station can't make it and there's no classical station at all.

    Here's the first interesting thing:  there is a level of listeners, bcom, at which a public station can earn more in donations than a commercial station can earn in advertising revenues.  This is interesting because the public station relies on generosity, while the commercial station relies on self-interest.

    Here's the second interesting thing:  it is possible that public stations can ALWAYS earn more in donations than commercial stations can earn in advertising revenue.  Why then do commercial stations ever exist?  Because public stations' revenues plummet whenever a commercial competitor shows up; even if the public station would earn more money on its own, it can't stand the competition.

    How plausible is it that public stations (alone) always earn more than commercial stations (alone)?  Well we know that public stations can sometimes earn more, as argued above.  The question then becomes, as listenership increases, do commercial revenues increase faster than public revenues?  Is R'(bcom) > R'(bcom)?
    I don't see any obvious reason commercial revenues should rise faster than public.

    Public stations get much funding from the government.  But suppose all government funding was removed.  Surely public stations would still sometimes exist.  If so, it is still true that public stations at least sometimes can earn more in donations than private stations can in ad revenue.

    I don't know how station licensing works--perhaps it's cheaper for public stations.  But public stations should be less efficient (no residual claimant).

    Incidentally there is no obvious reason why a public (non-profit) station couldn't earn revenues from advertising in stead of donations; in fact, public stations increasingly do earn ad revenues.  Also, there's no obvious reason why a private (for-profit) station couldn't earn revenues from donations, even in stead of advertising.
 
 

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