Using the Economics of the Pass-Through in Proving Antitrust Injury in Robinson-Patman Cases

• Published date: 01 December 2015
• Author: Alexei Alexandrov,Sergei Koulayev
• DOI: 10.1177/0003603X15602402
• Date: 01 December 2015

Article
The Antitrust Bulletin
2015, Vol. 60(4) 345-357
Using the Economics of the
ª The Author(s) 2015
Reprints and permission:
Pass-Through in Proving Antitrust sagepub.com/journalsPermissions.nav
DOI: 10.1177/0003603X15602402
Injury in Robinson-Patman Cases
abx.sagepub.com
Alexei Alexandrov* and Sergei Koulayev*
Abstract
We analyze and summarize microeconomic theory of pass-through rates. We start by analyzing a
monopolist firm in a standard frictionless market, then add more nuances to the model, including, but
not limited to, oligopolistic competition, menu costs, price points, endogenous quality and package size
choices, and consumer search costs. We proceed to show how each of these factors affects pass-
through rates.
Keywords
pass-through rate, antitrust, competition, frictions
I. Introduction
In a famous footnote, the Supreme Court in J. Truett Payne Co., Inc. v. Chrysler Motors Corp.1 stated
that one (but not only) way to establish that price discrimination injured the plaintiff is to demonstrate
that the favored buyer ‘‘passed on’’ the price advantage in a lower retail price:
If the favored purchaser has lowered his retail price, for example, the disfavored purchaser will lose sales to
the extent it does not match that lower price. Similarly, if the disfavored purchaser matches the lower price,
it will lose profits.2
In earlier cases, the Supreme Court refers to price advantages passed on.3 Yet the authors are aware of
no case law that explains when pass-on should occur.
1. 451 U.S. 557 (1981).
2. Id. at n. 4.
3. See, e.g., Perkins v. Standard Oil Co. of Cal., 395 U.S. 642, 649 (1969) (Evidence showed ‘‘Signal received a lower price
from Standard than did Perkins, that this price advantage was passed on. . . . ’’).
*U.S. Consumer Financial Protection Bureau, Washington, D.C., USA.
Corresponding Author:
Sergei Koulayev, U.S. Consumer Financial Protection Bureau, Office of Research, 1700 G St. NW, Washington, D.C. 20552,
USA.
Email: sergei.koulayev@gmail.com

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The Antitrust Bulletin 60(4)
In this article, we present an overview of what economic theory has to say about the existence and
the determinants of the magnitude of pass-through. We begin by presenting a standard microeconomic
theoretical model of the cost pass-through rate that measures the magnitude of a price change follow-
ing a firm experiencing a change in costs. Then we examine how various real-world features that are
not explicitly incorporated in the standard model affect the pass-through rate. We show that, except for
a few very particular circumstances, the pass-through rate is always positive: if there is a price differ-
ential, it will be passed on to consumers, resulting in diversion of sales. We then show how various
features of the industry and of the product affect the magnitude of the pass-through rate.
In addition to Robinson-Patman cases, the concept of the pass-through rate is also extensively used
in indirect purchaser litigation and merger analysis. Suppose several manufacturers form a cartel.
Often, these manufacturers do not sell directly to consumers, but rather they sell through retailers.
Thus, if the cartel harms competition, the cartel harms only the retailers directly. Final consumers are
harmed only indirectly: to the extent that the wholesale price increase due to the cartel’s existence is
passed on to the final consumers. If the pass-through rate on the retail level is close to zero, then con-
sumers are barely harmed. On the other hand, if the pass-through rate on the retail level is close to one
(100% or full pass-through), then consumers are harmed almost as much as they would have been had
they been buying from the cartel directly.
In Hanover Shoe, the U.S. Supreme Court decided that indirect purchasers cannot recover claims
against the cartel.4 Similarly, in Illinois Brick, the Supreme Court confirmed the decision.5 However,
later the Supreme Court legitimized provisions passed by many states allowing indirect purchaser
actions.6 Similarly, many international courts allow indirect purchaser actions as well.7
The pass-through rate is also used extensively in merger review.8 The upward pricing pressure
index is the opportunity cost of a price cut taking away sales from another product owned by the same
firm.9 This opportunity cost is the extent to which a merger would incentivize a firm to raise its prices
unilaterally postmerger. The pass-through rate in this case is the proportion of this opportunity cost that
gets passed on to consumers in terms of increased prices. Thus, getting the pass-through rate right is
integral in predicting whether the post-merger prices increase by 5% or more (or any other threshold).
II. Analysis of a Basic Model and Conclusions
A. A Model of a Monopolist Firm
Before diving deeper into the effect that different demand and supply side factors have on the pass-
through rate, it is informative to review the standard monopoly model of pass-through rates. Much
of the intuition in models that include competition and other variations is an extension of the relatively
straight-forward intuition of this basic model.
Let us start by analyzing a monopolist with a linear demand function of
DðpÞ ¼ a bp;
4. See Hanover Shoe, Inc. v United Shoe Machinery Corp., 392 U.S. 481 (1968).
5. See Illinois Brick Co. v. Illinois, 431 U.S. 720 (1977).
6. See California v. ARC America Corp., 490 U.S. 93 (1989); see also George Kosicki & Miles B. Cahill, Economics of Cost
Pass Through and Damages in Indirect Purchaser Antitrust Cases, 51 ANTITRUST BULL. 599 (2006) (discussing this and other
cases related to Hanover Shoe).
7. See, e.g., Frank P. Maier-Rigaud, Towards a European Directive on Damages Actions, 10 J. COMPETITION L. & ECON. (2014).
8. See, e.g., Gregory J. Werden, A Robust Test for Consumer Welfare Enhancing Mergers Among Sellers of Differentiated
Products, 44 J. INDUS. ECON. 409 (1996); Daniel P. O’Brien & Steven C. Salop, Competitive Effects of Partial
Ownership: Financial Interest and Corporate Control, 67 ANTITRUST L. J. 559 (2000).
9. See, e.g., Joseph Farrell & Carl Shapiro, Recapture, Pass-Through, and Market Definition, 76 ANTITRUST L. J. 585 (2010).

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Alexandrov and Koulayev
347
where p is the price that the firm charges (for example, retail price of gas) and a > 0 and b > 0 are
parameters (intercept and slope) of the demand function. The linear shape of the demand curve is cho-
sen mainly for analytical convenience; empirically, the linear form provides an approximation to the
actual shape of demand only if prices vary within a small range.
Say that the firm has a constant marginal cost c (for example, the wholesale price of gas that the firm
has to pay to the refinery or the wholesaler) and a fixed cost F. Then, the firm’s profit is
pðpÞ ¼ DðpÞp DðpÞc ¼ ða bpÞðp cÞ F:
The firm chooses its price to maximize its profit, resulting in10):
a
1
p ¼
þ c:
2b
2
The pass-through rate is the extent to which price reacts to changes in cost. In the case of linear
demand, the equation above tells us that the pass-through rate is 50%. For a dollar increase in cost,
the price increases by 50 cents; and for a dollar decrease in cost, the price decreases by 50 cents.
What happens if the demand function is not linear, say a more general function D(p)? In this case,
the firm chooses the price to maximize its profit
pðpÞ ¼ DðpÞp DðpÞc F;
in the same manner as with linear demand (again, via solving qpðpÞ ¼ 0 for p), except that the expres-
qp
sion becomes a little harder to interpret:

D pðcÞ
p ¼ c þ
;
D0 pðcÞ
where the symbol of prime denotes derivative of the demand function. If the marginal cost changes, so
does the price. If the price changes, so does the quantity demanded. Therefore, both the numerator and
the denominator of the fraction in the equation above depend on marginal cost.
If cost changes are relatively small, we can obtain the pass-through rate by implicitly differentiating
the equation above with respect to marginal cost. Skipping a few steps of algebra, we obtain:
qp
1
¼
;
ð1Þ
qc
2 D00 D
ðD0Þ2
where double prime denotes the second derivative of the demand function. Both the demand function
and its derivatives are calculated at the original price, that is, the price that prevailed before any cost
increase.
B. Conclusions from the Model
Now that we have done the hard work, let us see what conclusions can be established.
The first notable conclusion is that the pass-through rate is the rate of pass-through of marginal cost
only. Fixed cost does not determine the optimal price; therefore, any decreases or increases of fixed
cost are not reflected in the price level. In other words, the pass-through rate of fixed cost is
always zero. From now on, whenever we refer to the pass-through rate, we are implying the
pass-through rate of marginal cost. Similarly to fixed cost being irrelevant for price calculations,
the only component of the average cost that matters is the marginal cost; thus, it is difficult to
discuss pass-through of average cost.
10. Via solving qp(p)/qp ¼ 0 for p.

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The Antitrust Bulletin 60(4)
The second thing to note is that linear demand is a knife-edge case. Examining the terms in the
equation above, it is easy to see that if the demand function is concave (D00 through rate is lower than 50%, but if the demand function is convex (D00 > 0), then the pass-
through rate is higher than 50%. The linear function is at the boundary (since D00 ¼ 0), and thus the
pass-through rate is exactly 50%. Thus, the second derivative (concavity) of...