As noted in our earlier blog posts, FCC Chairman Julius Genachowski seems to be of two minds when it comes to spectrum policy. On one hand, he has taken great pains throughout his tenure to warn about the crucial issue of spectrum exhaust for commercial spectrum. As also noted in our earlier blog posts, the FCC under Chairman Genachowski has at the same time expressed grave concerns about the concentrated nature of the U.S. wireless market in its *CMRS Reports* and, as such, has condemned large transactions such as AT&T/T-Mobile and imposed a *de facto* spectrum cap when it approved the creation of the company known as LightSquared. In a similar vein, the Chairman and his allies are now loudly complaining about legislative language in a House bill that would constrain his agency’s ability to impose market participation restrictions in any voluntary incentive auction.

So, let’s get this straight—the two pillars of FCC current spectrum policy are as follows: According to “Pillar Number One”, the FCC says we have a spectrum constraint problem that could mean higher prices. Yet, according to “Pillar Number Two”, the agency says we have an industry concentration problem that could mean higher prices and, therefore, we should preclude the largest carriers from acquiring more spectrum. Importantly, these “could means” are contemporaneous. What is lacking from the FCC (and the policy debate generally) is any effort to integrate these two key issues—spectrum exhaust and industry structure. As I previewed in a post last week, we did the analysis the agency should have conducted. Yesterday, we released our formal results in a paper entitled *Wireless Competition Under Spectrum Exhaust*, and our findings are significant.

For those of you who may not have the time and/or inclination to read the full twenty-one page paper complete with formulas and footnotes, the purpose of this particular blog post is to provide an overview of the paper that may prepare you for the more thorough analysis.

Economic models are all about the assumptions, and we make two key assumptions in our new paper.

First, we assume that price falls as the number of competitors increases (e.g., the Hirschman Herfindahl Index or “HHI” falls). More formally, we assume Cournot Competition in Quantities. This view of competition is the same as that adopted by the FCC and the Department of Justice (“DOJ”), so we thought it was sensible to embrace it. (But, it is an assumption, and may not reflect actual economic outcomes.)

Second, we assume that the amount of capacity from spectrum is not linearly related to the amount of spectrum a firm has. That is, if we double the amount of spectrum, then the capacity provided to a firm from that additional spectrum more than doubles. This assumption should not be controversial since it is based on the basic technical laws governing communications networks. How strong this effect may be is an interesting question, but this issue need not be resolved for the theoretical analysis we present. In fact, if we assume the effect is very small, the theoretical results remain intact. Practically, this assumption implies the following. Say you have 100 MHz of spectrum and you divide it among 4 firms so that each gets 25 MHz. Say this generates 100 units of capacity. If instead you divided 100 MHz among two firms, so that each gets 50 MHz, then the amount of total capacity would be something like 150. Or, if you increased total spectrum to 200 MHz, so that each firms gets 50 MHz, then total capacity would be 300 (not just 200).

Now we are prepared to see what happens when we integrate spectrum exhaust into a standard model of competition. However, let’s start with the simple case where there is no spectrum constraint so that we have some type of benchmark for comparison purposes. Without a spectrum constraint, we have a simple Cournot model of competition – price falls as the number of firms increases (or the HHI falls). In the figure below, the equilibrium price (P*) falls as *n* (the number of firms) increases (along segment XYZ).

To make it more interesting, let’s impose a binding spectrum constraint such that all capacity is used up. In other words, as much service as can be sold is sold. If this constraint is binding, then firms are no longer at liberty to choose their quantities (which is what they choose under Cournot Competition), since they can sell only up to the capacity constraint. Once quantity is stuck at the constraint, price is stuck as well (since each quantity has a unique price associated with it per the demand curve). However, under the technical assumption about spectrum and capacity, we can get quantity unstuck by reallocating the fixed amount of spectrum to fewer firms (like in our numerical example above where we increased capacity from 100 to 150). Doing so increases capacity and thus output, and therefore lowers price. This is significant, because when there is a spectrum constraint (or exhaust, crunch, or whatever you wish to call it), price and concentration begin to move in the same direction. That is, a higher HHI (fewer firms) leads to lower prices. Fewer competitors is good for consumers!

In the figure, the line segment labeled XYW illustrates the equilibrium price when the capacity constraint is binding. At the chosen parameter values (an arbitrary choice), the capacity constraint is binding at *n* = 2 (point Y). Thus, price falls as the number of firms increases from monopoly to duopoly, but then price rises (along segment YW) when the number of firms exceeds duopoly and the constraint is binding. So, while the standard Cournot-type framework holds that prices are lower with six firms than with two firms, under a spectrum constraint this need not be true. Indeed, for the chosen parameters, the six-firm outcome is essentially the same as the monopoly outcome.

(Note that if we assume that capacity and spectrum holdings are proportional, then the line segment YW is flat. Thus, the number of competitors has no effect on price when the constraint is binding.)

I think most of you would agree that these results are very important for public policy. They are derived from fairly standard and uncontroversial assumptions. In fact, the Cournot assumption is highly favorable to the FCC’s concentration-driven mindset, which is the same mindset underlying the arguments against legislation which would limit the FCC’s authority to impose gratuitous, exclusionary restrictions on market auctions for spectrum. Government efforts to manage market share have not gone all that well over time but that’s another post. Back to the issue at hand.

Despite using the Cournot model of competition, the addition of a spectrum constraint turns the standard view that high industry concentration in wireless is a bellwether of poor economic performance on its head. Our analysis finds that under a binding spectrum constraint, the wireless industry is more likely to produce lower prices with fewer firms armed with more spectrum, than a market with a large number of firms holding smaller amounts of spectrum. The model also suggests (formally) that higher concentration may increase sector investment and employment.

Keep in mind that this analysis is economic theory. We cannot and do not reach conclusions about how many competitors is the right number under existing market conditions. What we do demonstrate is this: if it is true that there is spectrum exhaust, then the argument that more competitors leads to lower prices is not true. In fact, it is more likely the case that lower industry concentration leads to higher prices. Since the FCC (and in particular Chairman Genachowski) consistently admits to spectrum exhaust, then the agency’s effort to reduce industry concentration by socially-engineering auctions (and by other means) is thus wrongheaded. Perhaps having Congress putting limits on the FCC’s efforts to manipulate industry structure via auction rules is for the Chairman’s own good (imagine the outcry when consumer bills skyrocketed as market after market becomes spectrum constrained across the country).

In light of our new paper, it seems clear that the FCC needs to rethink the way it thinks about the mobile communications industry. If the agency wants to maintain its “expert” status, then it needs to square up its theory of competition with its theory of spectrum exhaust. Alternately, if the agency plans to blindly follow a generalist philosophy about competition based on the Merger Guidelines, then perhaps we should just shift communications policy to those non-expert agencies (the DOJ and FTC) better equipped to think in such rigid and constricted terms.

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