Triangles versus trapezoids, spectrum auction edition

Good news! The FCC is going to auction off more radio spectrum! This is a huge win for sensible policy no matter what your ideology; let us all rejoice.

Nevertheless, there is still some ideological and self-interested debate over the auction itself. Harold Feld reports that AT&T and T-Mobile, among others, are fighting over the FCC’s ability to impose eligibility restrictions on the auction. Effectively, the question is whether AT&T and Verizon should be allowed to participate in the auction since they are such dominant incumbents in the wireless industry.

Under some circumstances, it makes sense to keep dominant incumbents out of auctions. Klemperer shows how the presence of dominant incumbents, combined with poor auction design, can reduce entry and facilitate collusion in spectrum auctions. The important point, however, is that good auction design can virtually eliminate these problems. We’ve learned a lot about spectrum auctions in the last 10 years, much from Klemperer himself, so I really don’t think this is a very good reason to impose eligibility restrictions on spectrum auctions any more.

Feld advances a different possible rationale for eligibility restrictions. He argues that there is a tradeoff between auction efficiency and competition policy. Since AT&T and Verizon have deeper pockets and economies of scale, they can win any auction they want to win, which further entrenches their duopoly. So either we accept some inefficiency in terms of spectrum allocation from eligibility restrictions in the auction or we accept some inefficiency in terms of mobile service allocation from reduced competition in the wireless industry.

I don’t quite agree with Feld that this is much of a tradeoff. I’m not terribly worried about competition in the wireless industry, which strikes me as much more Bertrand than Cournot. I also think that modern finance can pretty much handle funding for smaller players or new entrants, and that at some point, there must be diminishing marginal utility to spectrum even for AT&T and Verizon; if the wireless industry is not competitive enough, it should be dealt with by auctioning off even more spectrum.

But putting these issues to one side, my intuition is that it’s still much more important that the spectrum be allocated efficiently than that competition in the wireless industry be maintained. Consider the graph below, which shows the market for wireless services.

If the market is imperfectly competitive and the price and quantity are given by the dashed lines, then the shaded triangle represents the deadweight loss from diminished competitiveness.

Now consider a different graph for the wireless services market:

This graph shows the situation when the most efficient producer is kept out of the market. The marginal cost rises from MC₁ to MC₂, and the deadweight loss is represented by the shaded trapezoid.

Now I will say something that is obviously absurd to a geometrician, but is nevertheless true in economics: most of the time, trapezoids are much bigger than triangles. Is it a totally rigorous statement? No. But when you are talking about changes on the same order of magnitude, you are almost always better off if you accept the deadweight loss triangle to avoid the deadweight loss trapezoid.

My intuition, therefore, is that we should not restrict participation in spectrum auctions. To turn that intuition into rigorous analysis, obviously we would need to estimate some parameters and bring back in those issues we put to the side earlier. Nevertheless, I think some of these intuitive concepts can take us a long way to better economic policy.