1. Horizontal mergers with one capacity constrained firm increase prices
David J. Balan (FTC)
Patrick DeGraba (FTC)
Jason O’Connor (FTC)
April 21, 2018
The views expressed in this paper are those of the authors and do not necessarily reflect those of the Federal Trade Commission.

2. UPP and Merger Effects Why do mergers of substitutes raise prices?
Often explained in terms of Upward Pricing Pressure
e.g., 2010 DOJ/FTC Horizontal Merger Guidelines
UPP > 0 if and only if D12(P2 –C2) > EC1
This is fundamentally about recapture of lost sales
Start with the pre-merger price
Benefit to Firm 1 ↑ its price by a small amount equal to the loss
After the merger, benefit is the same, loss is smaller
This is because a fraction D12 of the lost sales go to Firm 2
Those sales, and the profit (P2 –C2) are “recaptured”
If this effect exceeds the efficiencies EC1, then P1 ↑

3. UPP and Merger Effects This is a valuable way to think about mergers
It is intuitive and it is useful as a pedagogical device
It may also be useful for quantitative merger simulation
Weyl & Jaffe (2013), Miller et al. (2016,2017)
But recapture is not the only source of merger effects
And applying the recapture intuition in the context of capacity constraints is positively misleading

4. UPP with a Capacity Constraint
Pre-merger, Firm 1 faces binding capacity constraint K
Let Firm 1 and Firm 2 merge
For a given P2, Firm 1 will not want to change its price
Price ↓ is unprofitable (lower price for same sales of K units)
Price ↑ is ruled out by the assumption that the constraint binds
Firm 2 should want to raise its price as long as D12 > 0
This is the logic of UPP
But Firm 1 cannot accommodate any diverted sales
So it might appear that Firm 2 will not ↑ its price
That is, the logic of UPP appears to suggest no merger effect with even one constrained firm

5. UPP with a Capacity Constraint
This has been claimed explicitly in defense of mergers
Q. So that was a lot about Hershey. What about Pinnacle?
A. Pinnacle is in a different situation because while there is some demand side substitutability as there is between Hershey and Pinnacle, but between Pinnacle and Hershey, as well, there's some overlap, it's just in the context of one being community and the other being academic, it is not all that substantial, but there's some, to be sure, without taking the capacity constraint into account.
But once capacity is taken into account, there can't be substantial diversion of patients from anywhere, but, in particular, from Pinnacle to Hershey, say as a result of some imagined price increase or some competitive event that is being assessed, because Hershey just doesn't have the capacity to take on a major influx of patients from Pinnacle as a possible result of whatever, a natural disaster, we hope not, or a price rise. No, it just -- it won't happen.
So that the practical diversion between Pinnacle and Hershey is insignificant due to Hershey's capacity constraint, as well as due to the differentiation of their services. But that means that the diversion ratio, in practical terms, because of the capacity constraint, is de minimis. And the conclusion is at the bottom of the slide. That means that upward pricing pressure in that direction, the upward pricing pressure from the merger on Pinnacle is negligible.
(Expert testimony of Professor Robert Willig in Federal Trade Commission and Commonwealth of Pennsylvania vs. Penn State Hershey Medical Center and Pinnacle Health System, April 15, 2016.)
Other examples exist as well

6. Non-UPP Merger Effects
UPP is about internalizing recaptured sales
With the constraint, there are no net recaptured sales
But after the merger, Firm 2 DOES internalize the fact that an increase in P2 increases the price at which Firm 1 sells out its constraint K
This is sufficient for an increase in both prices
This is a simple point, but commonly misunderstood

7. Model Using Bertrand The natural way to model this would be Bertrand
But there is a well-known problem with Bertrand
Pure strategy equilibrium may not exist when MC ↑
Certain not to exist when MC is vertical at the constraint
Could try to model a mixed-strategy equilibrium
See Chen & Li (2018)
But that is not what we do

8. Model Using Cournot
In standard Cournot, mergers are not always profitable
But when they are profitable, they ↑ prices
Salant et al. (1983), Perry & Porter (1985)
The intuition is that the each of the merged firms internalizes the effect of a reduction in its output on its merger partner, via the resulting price increase
Having one merging firm be capacity constrained does not change this basic intuition
The idea that merger effects come from recapture of lost sales following a price increase does not apply to Cournot, so the confusion discussed above does not arise

9. Model Using Stackelberg
The claim that mergers have no effect in the presence of a capacity constraint is usually made in the context of price-setting games
As discussed above, there are problems with Bertrand
So instead we use Stackelberg
Firm 2 (and other rivals) choose prices in Stage 1
Firm 1 (constrained firm) chooses its price in Stage 2
(Results for the opposite case, where Firm 1 chooses its price in Stage 1 and Firm 2 and rivals choose in Stage 2, are in process but we believe the answer to be the same)

10. Model Using Stackelberg
Pre-merger, Firm 1 chooses price to sell exactly K
Given this, effect for Firm 2 of small change in P2 is 0
But higher P2 ↑ the price at which Firm 1 sells K
So the effect of a small change in P2 is positive for P1
Pre-merger Firm 2 does not care about this
But after the merger this effect is internalized
So following the merger both prices will ↑
Even though there was no recapture of lost sales
At the post-merger equilibrium, Firm 1 may produce at the constraint K or may produce less (i.e., may cease to be constrained)
But either way both prices ↑

11. Conclusion The logic of UPP is useful
But it is not a complete account of where merger effects come from
Usually this is not a serious problem, but it becomes one when UPP is used to analyze a merger with one capacity constrained firm
The logic of UPP appears to indicate that such mergers have no effect
This is simply incorrect: merged firms internalize price effects even when there are no net recaptured sales