p
A
+ p
B
c
p
A
+ p
B
¼
1
ε
A
ii
+ ε
B
ii
: (6.8)
This shows that the sum of the margins on the two sides of the market should be set equal
to the inverse of the sum of the own-price elasticities. From this, it is already obvious that
the traditional test for market definition, where the inputs consist of the margin and price
elasticity on just one side of the market (see Equation
6.3), will fail to capture the two-
sidedness. It is well known—as explained in the previous section—that margins can differ
substantially between the two sides. In fact, it can be profitable to have a negative margin
on one side in order to bring on board consumers from whom the other side can benefit.
It is then obvious that applying data from just one side of the market to conduct a critical
loss analysis can lead to major mistakes.
22
This is discussed in detail in Evans and Noel
(2008)
, who also extend the critical loss analysis to a two-sided market.
23
Unfortunately, it is difficult to detect the estimation bias if a one-sided market
approach is applied in a two-sided market. To see this, think about a newspaper market
with readers and advertisers.
24
A “naı
¨
ve” approach could be that we consider a price
increase for a hypothetical monopolist in the advertising market with a corresponding
drop in the volume of ads, ignoring the reader side. We would then ignore the readers’
response to a lower number of ads. If they are ad lovers, then a lower volume of ads would
lead to a lower circulation. If so, the naı
¨
ve approach would lead to a systematic under-
estimation of market size since it failed to take into account the reduction in revenues on
the reader side. On the other hand, the naı
¨
ve approach would overestimate the market
size of readers who dislike advertising.
Alternatively, we could use a more “sophisticated” version of the test where we con-
sider the overall change in revenue resulting from a specific price increase on the adver-
tising market only. Then we account for the change in revenues for readers. However, a
change in advertising prices would make it optimal to change the reader prices as well.
Since two instruments are better than one, it is obvious that allowing for changes in
reader prices would make the price increase on advertising more profitable. A critical loss
analysis with a change in advertising prices only would then underestimate the overall
effect on profits, and therefore imply that the estimated market size would be systemat-
ically larger than the market size obtained by considering the full pricing possibilities.
22
See also Evans (2003) and Oldale and Wang (2004), who both point out that there is not necessarily a
relationship between market power (or no market power) and the price-cost margin on one side of
the market.
23
Hesse (2007) also warns against a one-sided market definition in a two-sided market. On the other hand,
Ordover (2007) is not convinced that there is a need for new tools and new methods for antitrust policy
toward two-sided markets.
24
This distinction between a “naı
¨
ve” and a “sophisticated” approach follows from Calvano and Jullien
(2012)
.
248
Handbook of Media Economics