ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E19-12

Do Premium Payment Methods Increase Effective
Retail Prices?
byTakanori AdachiMark J. Tremblay

September 2019

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Do Premium Payment Methods Increase
Effective Retail Prices?∗
Takanori AdachiMark J. Tremblay

School of Economics

Farmer School of Business

Nagoya University

Miami University

adachi.t@soec.nagoya-u.ac.jp

tremblmj@miamioh.edu

September 18, 2019

Abstract
In this study we develop a tractable, yet general, framework to explain whether premium payment methods that impose no-surcharge rules are beneficial. This question
is fundamentally related to policy and we provide a robust answer by considering how
a variety of market structures are impacted by multiple payment methods. We findthat the no-surcharge rule, which suggests uniform pricing to consumers, results in
consumers paying different effective prices depending on their payment method. Instead, surcharging, which gives the impression of price discrimination, actually resultsin consumers paying the same effective price across payment methods. Most importantly, we also show that all consumers and all merchants earn greater surplus whensurcharging is allowed. Furthermore, our results are robust across market structures
suggesting that protected premium payment methods are generally harmful except forthe credit card industry.
Keywords: Payment methods, credit cards, online shopping, merchant fees, consumer
rewards, Ohio v.s. American Express, conduct parameter
JEL Classifications: L10, L20, L42∗

We are grateful to Sarit Markovich, Jason Walter and the participants in the 2019 International Industrial Organization Conference for helpful comments and discussions. Adachi acknowledges a Fund for
the Promotion of Joint International Research (16KK0054) and a Grant-in-Aid for Scientific Research (C)(18K01567) from the Japan Society for the Promotion of Science. Any remaining errors are ours.

1

Introduction

Over the last decade, merchants have engaged in an ongoing conflict surrounding the socalled “anti-steering” or “no-surcharge rule” clauses that various payment method companies
require. These clauses prevent merchants from asking or persuading their customers to use
certain payment methods. These clauses are naturally binding since merchants are motivatedto steer their customers away from premium reward payment methods that charge higher
merchant fees. This debate is especially important for online and digital retailers that are
unable to make implicit payment suggests “at the register” and often accept credit cards
and online payment methods exclusively. Many of these online retailers, including Amazon,argue that these premium merchant fees are being passed on to consumers in the form of
higher prices.1
While this conflict between merchants and payment method companies continues, therecent Supreme Court ruling in June 2018 on the case of Ohio v.s. American Express, No.
16-1454, was a major blow to retailers. In their ruling, the Supreme Court sided with
American Express and deemed these anti-steering clauses as acceptable. In particular, theSupreme Court argued that two-sided platforms should face more relaxed anti-trust scrutiny
because while these premium cards and anti-steering clauses might harm merchants, themajority of the Supreme Court justices argue that the premium cards have benefited many
consumers and expanded credit card usage.2
Since the Supreme Court ruling, the conflict between merchants and credit card companies has continued. Now, however, merchants are claiming that the justices focused entirelyon the effects on credit card competition and failed to account for the impact that protected
premium payment methods have on the underlying prices in retail markets. More specifi1

See “Are Other People’s Credit-Card Rewards Costing You Money? Amazon and other retailers believeso, and they’re going to war against high-end cards,” in the New York Magazine, October 16, 2018, for a
detailed discussion.
2
The Supreme Court’s ruling has spurred debates on the appropriateness and usefulness of platform
economics in antitrust enforcement. Katz (2019) summarizes the important notions that should be carefully
treated: including how to define a multi-sided platform in a meaningful way, how to define the “relevantmarket,” and how information on price and output should be used to judge a change in consumer welfare.

1

cally, the merchants argue that with more premium card holders, the higher fees incurredby merchants are passed onto consumers resulting in higher retail prices than would otherwise be the case if surcharging were allowed.3 And with higher prices, sales decrease, adead-weight loss is generated, and consumers and merchants are harmed.
One caveat that is missing from the merchants’ argument is how the effective retail price is
impacted by the availability of a premium payment method. By effective price, we mean the
rewards inclusive price that consumers pay. By considering the effective price with respect
to the merchants’ argument, it is possible that the pass-through from higher merchant fees
is less than the improved consumer reward from a premium method so that premium users
benefit from anti-steering. However, if the merchant fee pass-through is greater than the
consumer benefit from a premium reward, then both premium and non-premium users areworse off in the retail market.4
To understand how the Supreme Court’s ruling impacts effective prices, we depart fromthe two-sided market approach that considers consumer and merchant payment method
acquisition.5 Instead, we take the acquisition of payment methods as given (to start) andconsider the impact that multiple payment methods have on a retail market. Given theimperative connection between market structure and economic pass-through,6 we implement
the conduct parameter approach in which the mode of competition is taken as an exogenous
parameter in the retail market. This allows us to determine the extent to which merchantmarket power influences the welfare effects from the no-surcharge rule.
We find that when the no-surcharge rule is implemented, the effective price that premium
users pay is often higher than the effective price that would be charged if no consumer werepremium. However, under certain demand structures, it is possible that premium consumers
3

See “Are Other People’s Credit-Card Rewards Costing You Money? Amazon and other retailers believeso, and they’re going to war against high-end cards,” in the New York Magazine, October 16, 2018, for a
detailed discussion.
4
Note, that non-premium users are always worse off because they incur the pass-through from thepremium merchant fee but do not earn the premium benefit.
5
In our discussion, we consider the implications of our model to the acquisition subgame.
6
See Weyl and Fabinger (2013) for details.

2

pay a lower effective price when merchants have high levels of market power. At first glance,
this suggests that the premium payment method might act as a redistribution mechanismthat reduces the dead-weight loss generated by merchant market power.
Unfortunately, the potential benefits from the premium method disappear when comparing the effective prices between the surcharge and no-surcharge cases. More specifically,
we find that all consumers pay the same effective price when surcharging is allowed and thepremium method accounts for no sales. Furthermore, the effective prices with surcharging
are less than the no-surcharge effective prices for all consumers. Altogether, our result imply
that a premium payment method requires the no-surcharge rule to survive and is welfare destructive to consumers and merchants. It is important to note that these results are robust
across all forms of merchant competition, suggesting that the no-surcharge rule is indeed
protecting premium payment companies at the expense of higher prices.
Much of the literature on payment methods takes a two-sided market approach to analyze
credit card acquisition, competition, and optimal fee structures. Rochet and Tirole (2002),
Rochet and Tirole (2003), Wright (2003), and Wright (2004) pioneered this work by considering the connection between payment cards, card issuers, and merchants and consumers.
These papers have been highly influential in terms of how different interchange fees impact
credit card acquisition, how a no-surcharge rule is required to ensure acquisition, and how
issuers and credit card companies set optimal fees.7 These papers, and the literature that
follows, typically take a simplistic approach in how the final goods market is modeled andinstead focus on optimal acquisition and interchange fees. This implies that these models
are unable to determine the impact that different market structures have on consumers andmerchants when multiple payment methods are present.
Following these seminal papers, others have considered important features of credit card
markets that relate to no-surcharge rules or premium credit cards. In a similar effort to
7

There has been very little empirical evidence that considers the issue of steering in credit card markets.
One paper by Briglevics and Shy (2014) find that the use of surcharge rules that provide discounts to cash
and debit payment methods steer consumers towards those methods; however, the cost savings for merchants
is small.

3

explain the Supreme Court’s ruling, Carlton and Winter (2018) compliment our work byfocusing on the impact of the no-surcharge rule on the two-sided credit card market (insteadof investigating the impact of these rules on the underlying retail markets). They highlight
how the methods for evaluating vertical most-favored-nation (vMFN) clauses in traditional
markets remain effective for evaluating the credit card no-surcharge rules in two-sided markets. By taking different approaches to consider a similar problem, our results collectively
suggest that the Supreme Court’s ruling was misguided for two reasons: (i) they show thatthe no-surcharge rule ensures credit card fees that are higher than the monopoly credit cardcompany case and (ii) we show that the no-surcharge rule results in higher effective prices
for all consumers across all retail markets.8
One paper that is similar to ours is Shy and Wang (2011) who consider a model where
credit cards are already saturated in the market and consumers purchase some items withcash and other items with a credit card. They focus on the impact of different types of credit
card fees: fixed or proportional. However, merchants specialize in either goods purchasedby credit cards or goods purchased with cash; thus, no goods are purchased with multiple
payment methods in their model. This implies that one is unable to determine how multiple
payment methods within a particular market impact pricing and efficiency in their model.9
Two other papers that relate to ours are Edelman and Wright (2015) and Liu et al.
(2019). Edelman and Wright (2015) present a general framework for intermediaries using
no-surcharge rules and they find that consumer surplus is harmed by no-surcharging but theeffect on welfare is ambiguous. In their setting, the retail sector is modeled as an oligopoly
market where the entire consumer demand is satisfied (implying no extensive margin). This
8

Schwartz and Vincent (2019) consider the impact that asymmetric credit card fees have on credit
card competition. They find that pure strategy equilibria in credit card fees cannot exist because credit
cards compete by trying to outdo each other’s spread between the merchant fee and consumer reward.
Unfortunately, Schwartz and Vincent (2019) model the retail market by considering a monopoly merchantand they only consider fixed fees and rewards (opposed to the proportional ones observed and modeled inthis paper); these assumptions naturally generate specific results about merchant fee pass-through and so aricher model of retail is required. Similarly, Schwartz and Vincent (2006) also consider the no-surcharge rulebut model merchants as monopolists and largely focus on optimal fee structures.
9
Bourguignon et al. (2019) also provide a rich set of predictions for merchant payment policy as well as
the fee structure designed by assuming that card acceptance and surcharging are “shrouded” for consumers.

4

is an important assumption since the extensive margin is crucial for determining dead-weightloss and any double marginalization effect that may arise from premium fees. Instead, Liuet al. (2019) include an extensive margin on demand by considering a market with logconcave demand that is served by a monopoly merchant. They find that the no-surcharge
rule can increase consumer surplus much like third-degree price discrimination can improve
consumer surplus under the right demand specifications.
There are a few notable differences that drive the differences in results between these two
papers and our own. First and foremost, both Edelman and Wright (2015) and Liu et al.
(2019) use fixed, not ad valorem, consumer rewards and merchant fees which naturally havepass-through rules that differ from the ad valorem structure used in our model and that are
actually observed in payment method markets. Second, like Liu et al. (2019), we include anextensive margin on demand; however, we also allow for a variety of competition structuresin the retail market. As a result we find that the no-surcharge rule unambiguously harms all
consumers and all merchants across all competition structures suggesting that surcharging
would improve welfare in retail markets.

2

The Model

There are a plethora of markets where multiple payment methods are used to make purchases(e.g., cash, debit cards, standard credit cards, premium credit cards, cryptocurrencies, etc.).
For simplicity, suppose that there are two payment methods: a premium payment method
and a regular payment method which could simply be cash. We normalize the regular
payment method fees and rewards to zero but assume that the premium method includes a
consumer reward and a merchant fee.
Suppose that the market for some product has a unit mass of consumers that each haveunit demand. Consumer values, υ, are drawn from the distribution F (·), and if all consumers
use the regular payment method for a product sold at posted price p, then the standard

5

demand curve follows: q = 1 − F (p). However, with multiple payment methods, consumers
pay different effective prices because consumers that use the premium method earn rewards.
Premium rewards are proportional to the posted price so that an item purchased at posted
price p generates f1 · p cash back, where f1 > 0 denotes the reward to consumers. Thisimplies that the effective price paid by a premium consumer is (1 − f1 )p while consumers
using the regular method face an effective price of p.
Let λ ∈ [0, 1] capture the mass of premium consumers so that there is a mass of (1 − λ)regular consumers. Given the distribution of payment methods, an item sold at posted pricepi , i = p, r, has premium and regular demands given by:

Qp = λ · [1 − F ((1 − f1 )pp )],Qr = (1 − λ) · [1 − F (pr )].
We allow for two types of pricing regimes. The no-surcharge rule is the first. In this casethe merchants must charge the same price across all payment methods so that pp = pr ≡ p.
This no-surcharge rule is currently implemented by premium credit card companies andprovided the controversy that led to the Supreme Court ruling. To determine the impact of
the no-surcharge rule, we also consider the case where merchants surcharge across payment
methods.
For merchants, sales made to premium consumers generate (1 − f2 ) · pp in revenues,
where f2 is the merchant fee taken by the premium payment method. We assume that
1 > f2 ≥ f1 > 0 so that profit for credit card companies is non-negative.10 Depending on
the nature of competition within the market, the number of merchants may vary. However,10

Typically a premium credit card offers between 0.5-1.5% cash back to consumers and charges merchants
a 1.5-3.5% fee which corresponds to f1 ∈ [0.005, 0.015 and f2 ∈ [0.015, 0.035].

6

the total profit across all merchants is given by:11

Π(pp , pr ) = [(1 − f2 )pp − c]Qp + (pr − c)Qr
= λ[(1 − f2 )pp − c] · [1 − F ((1 − f1 )pp )] + (1 − λ)(pr − c) · [1 − F (pr )],where c denotes a merchant’s marginal cost and for simplicity we assume that marginal costs
are equal across merchants.
Ideally, we prefer results that are consistent across market structures so that unambiguous
policy recommendations can be made. However, the presence of premium payment methods
or the implementation of a no-surcharge rule might impact a monopoly market differently
than an oligopoly one. Thus, to comprehensively investigate the impact that payment methods have on effective prices we must consider the role of market structure. To do so, we
implement the conduct parameter approach as proposed by Weyl and Fabinger (2013). The
conduct parameter, θ ∈ [0, 1], captures the level of competition between symmetric merchants where greater θ corresponds to less competition. At the extremes, θ → 0 capturescompetition approaching perfect, and θ → 1 corresponds to competition approaching thecase of a monopoly merchant. In this way, we are able to capture the degree of competition in a continuous manner with a single parameter without specifying the specific type ofcompetition.12
To illustrate the conduct parameter approach in our setting, first consider the simple
case with a single (cash) payment method. In this case, an industry’s optimal retail price ischaracterized by(p − c)· || = θpordQ
= (p − c)
.
dp
|
{z
}
Marg. Benefit
θ·Q
|{z}

(1)

Marg. Loss

This relationship shows that if the conduct parameter decreases (corresponding to an increase11

At this point, we assume that all merchants accept the two payment methods (as is the case in mostmarkets where merchants accept cash, debt, and credit).
12
Note that θ = n1 corresponds to Cournot competition with n symmetric merchants.

7

in competition), then the marginal benefit from increasing ones price goes down. As a result,the equilibrium price decreases with greater competition.
Applying the conduct parameter approach to our setting implies that the surcharge prices(pp 6= pr ) and the no-surcharge price (p = pp = pr ) are given by (the derivations are shownin the appendix):θ · Qr = (pr − c) ·

∂Qr
,
∂pr

θ · (1 − f2 ) · Qp = [(1 − f2 )pp − c] ·λ · θ(1 − f2 )Qp + (1 − λ) · θQr = λ · [(1 − f2 )p − c] ·

(2)
∂Qp
,
∂pp

(3)

∂Qp
∂Qr
+ (1 − λ) · (p − c) ·
. (4)
∂p
∂p

The timing of the game is as follows. First, merchants observe premium fees and rewards(f2 > f1 > 0), the nature of competition (θ), the distribution of payment methods (λ), thedistribution of consumer values (F (·)), and the surcharge rule (surcharge or no-surcharge).
Then the equilibrium price(s) are determined. Lastly, consumers observe their value andmake purchasing decisions.

3

Equilibrium

We solve the game backwards and we start with the subgame where the no-surcharge ruleis implemented. To simplify our analysis, suppose that consumer values are distributed
uniformly, v ∼ U (0, 1), and that c ∈ (0, 1). This implies that demand is linear: Qp =λ[1 − (1 − f1 )p] and Qr = (1 − λ)(1 − p).

3.1

The No-Surcharge Subgame

For the no-surcharge rule case (which is observed in reality), we have the following nosurcharge subgame equilibrium price:
Lemma 1. If merchants cannot surcharge across payment types, then the equilibrium retail8price isp∗ (λ, θ) =(1 − λf1 )c + θ · (1 − λf2 ).
(1 + θ)[1 − λ(f1 + f2 − f1 f2 )]

(5)
∗

(λ,θ)
>0
Not surprisingly, greater premium usage or less competition increase prices: ∂p ∂λ∗(λ,θ)
for all θ and ∂p ∂θ
> 0 for all λ. However, an arguably more important considerationis the comparison between the effective prices that consumers pay with and without theexistence of the premium payment method. In particular, if (1 − f1 )p∗ (λ, θ) > p∗ (0, θ), thenall consumers (both premium and regular) pay a higher effective price when the premium
payment method exists. And if this is in fact the case, then the premium payment method
generates a double marginalization effect that is harmful to all consumers. We find that thisis the case when the mass of premium consumers is sufficiently large:
Proposition 1. All consumers pay a higher effective price when the premium method exists,
f1 (c+θ)≡ λ.
(1 − f1 )p∗ (λ, θ) > p∗ (0, θ), if and only if λ > c[f2 −f
1 (f2 −f1 )]In other words, Proposition 1 implies that premium consumers pay a lower effective pricewhen the premium method exists, (1 − f1 )p∗ (λ, θ) < p∗ (0, θ), only if λ < λ. Furthermore,
notice that an increase in market power amongst merchants (i.e., an increase in θ) implies
that λ increases. This implies that the premium payment method might combat market
power markups by maintaining a lower effective price for the premium consumers. This
result is especially important in the context of double marginalization. For example, if
f1 , f2 , and c are such that λ > 1 for high values of θ, then the premium payment method
acts as a redistribution between merchants with market power and their consumers so thatpremium consumers pay a lower effective price than if the premium method did not exist.
This implies that if all consumer were premium, then the premium payment method serves
as a redistribution mechanism that takes surplus from merchants with market power andoffers it to consumers so that total sales expand.
There are several additional results from Proposition 1 that are worth mentioning. First
note that if the credit card company charges a higher markup so that f2 increases, then λ9decreases so that there is a greater number of λ where all consumers are made worse off fromthe existence of premium payment methods. Second, if we consider the case of perfection
competition, then Proposition 1 implies that all consumers are worse off when λ > ff12 (since
f1 · f2 ≈ 0 in practice). If we consider the case where premium merchant fees are 3% while
rewards are 1%, then premium consumers are better off when at most a third of consumers= 31 . Unfortunately, data on the percent of credit card transactions
are premium, λ < 0.01
0.03
is limited; especially at disaggregated levels (like a single market that is clearly served byperfectly competition merchants). Luckily the Federal Reserve provides some information
on payment method usage. Using survey data, Greene and Stavins (2018) find that 27%
of payments are made with credit cards (relative to cash and debit options). At the sametime, Greene and Stavins (2018) also point out that credit card purchases are more common
for more expensive purchases and for purchases made online. These numbers suggest thatcredit card users are better off in markets that are perfectly competitive since 0.27 < 0.33.

3.2

The Surcharge Subgame

Allowing merchants to charge different prices across consumers that use different payment
methods is currently not allowed. Merchants have attempted to challenge the no-surcharge
rule that has been implemented by premium credit card companies. However, at this time,
the courts have ruled against the merchants so that surcharging does not currently occur inpractice. To better understand how surcharging might impact effective prices across market
structures, we consider the surcharge subgame.
Note that when surcharging is allowed, a premium consumer is enticed to use the regular
payment method when their effective premium price is greater than the effective regular
price; that is, when (1 − f1 )pp ≥ pr . Naturally, this allows merchants to discourage premium
usage and increase profits which is detrimental to the premium payment companies. Solving
the surcharge subgame, we have the following result:Lemma 2. If merchants surcharge, then all consumers pay the same effective price for all
10θ ∈ [0, 1] and for all f2 ≥ f1 , and equilibrium prices are given by:p∗r = (1 − f1 )p∗p =(1 − λf1 )c + (1 − λf2 )θ
≡ p∗SR .
(1 − λf1 ) + (1 − λf2 )(6)

The fact that all consumers pay the same effective price in equilibrium implies thatsurcharging eliminates premium sales and the premium payment companies earn no revenue.
Furthermore, this result is robust across all market structures, highlighting how the premiumcompanies require the no-surcharge rule in order to survive.

3.3

Comparing Effective Prices

Comparing prices between the two subgames shows that surcharging is preferred from aneffective price perspective:
Proposition 2. If f1 > f22 , then effective prices with surcharging are less than effective
prices with the no-surcharge rule: p∗SR < p∗ for all θ ∈ [0, 1].
Anecdotally, premium and non-premium payment methods have f1 considerably larger
than f22 . This suggests that all consumers pay a lower effective price when surcharging isallowed, regardless of the market structure that exists between merchants. In other words,
the no-surcharge clauses set by premium companies result in higher effective prices for all
consumers in every market throughout the business-to-consumer economy. While we donot model welfare explicitly, the welfare implications are crystal clear: (i) merchant profit
increases with surcharging since merchants face fewer pricing constraints, and (ii) consumer
surplus increases since all consumers pay lower effective prices. These results highlight
how the implementation of the no-surcharge rule by premium card companies creates adouble marginalization effect that harms all consumers and merchants. Thus, the potential
benefits from the premium method that were discussed following Proposition 1 disappear
when surcharging is allowed.

11

Altogether, our results conclude that the having a premium payment method that is
protected by a no-surcharge rule harms consumers and merchants across all markets. In termsof the current policy debate, this suggests that the merchants’ point is a valid one: protected
higher premium fees are passed on to consumers creating a double marginalization effect that
increases effective prices and reduces sales. Furthermore, by showing that premium usage
disappears in the surcharge subgame equilibrium, we highlight how the no-surcharge rule isnecessary for premium credit card companies to earn any revenues.

4

Discussion

In this section, we briefly discuss the implications of our findings to the context of existing
policy debates. In particular, we apply our results to the ongoing debate of premium cardacquisition, premium v.s. standard credit cards, merchant steering and “accept all cards”
clauses, and retailer credit card offerings.

4.1

Payment Method Acquisition: A Prisoner’s Dilemma Game?

While we do not model acquisition explicitly, our findings do have implications towards
payment method acquisition. For the case where surcharging is allowed, Lemma 2 implies
that effective prices will be equalized across payment methods; as a result, consumers have no
incentive to acquire the premium payment method and this is consistent with the previous
literature (Rochet and Tirole (2002), Wright (2003), and Wright (2004)). When the nosurcharge rule is implemented, a consumer that does not use the premium payment loses
out on the premium rewards that effectively lower their price. At the same time, a merchantmight lose sales by not accepting a premium method. This implies that both consumers
and merchants have an incentive to acquire the premium payment method. However, by all
agents acquiring the premium payment method, Proposition 1 implies that all consumers
might still pay a higher effective price than if no consumer used the premium method. In

12this case, the payment method acquisition game between consumers and merchants is akinto the prisoner’s dilemma game where every agent has an incentive to acquire the premium
method but all agents would be better off if they collectively avoid the premium option. Thissuggests that the use of policy or side payments (in the form of surcharges) is necessary toobtain the welfare improving outcome.

4.2

Premium v.s. Standard Credit Cards

In many ways, our results suggest that credit card usage is harmful. However, it is important
to note that there are many potential benefits from credit cards that we abstracts from in ourmodel. As a result, one must be very considerate when interpreting our results to certain
credit card issues. If we use our model to consider the comparison of cash and standard
credit cards, then our results imply that standard credit cards increase the effective pricesthat consumers pay. But we also know that standard credit cards also provide many benefits
to consumers that are not accounted for in our model (e.g., theft protection and easier online
shopping). Thus, the benefits from standard credit cards clearly outweigh the inefficiency
that they generate in the form of higher effective prices.
Instead, if we use our model to consider the comparison between standard and premium
credit cards, then our model is no longer abstracting from these benefits since the standard
credit cards already provide theft protection and easier online shopping. In this case where
the main benefits from credit cards are already obtained through standard cards, our results
suggest that premium credit cards that are protected by no-surcharging are harmful toconsumers and merchants.

4.3

Steering and Accept All Cards Clauses

The majority of credit card companies like Visa, Mastercard, and American Express havean “accept all cards” requirement that forces retailers to accept all of their standard andpremium cards. To circumvent the accept all cards requirement, retailers hoped to steer their13

consumers either by asking for particular payment methods (cash or standard cards) or bypenalizing certain payment methods (premium cards) with a surcharge. If such steering
practices are effective (as we show in the for the surcharge case), then premium usage isprevented and efficiency restored.
Unfortunately, the recent Supreme Court ruling sided with the credit card companies
and prevents steering. The main consideration throughout this debate was over competition
between credit cards. However, such a focus failed to consider the repercussions of premium
credit cards on effective retail prices. Moving forward, one way for merchants to bypass
steering is to target these accept all cards requirements. In fact, this is what several major
retailers are currently pursing under the argument that such clauses are anticompetitive atthe bank level (with respect to interchange fees). While this lawsuit is currently ongoing,a federal court ruling in favor of the retailers would allow retailers to directly steer theirconsumers by declining premium credit cards while accepting standard ones, and we findthat such a policy would lower effective prices for all consumers and improve efficiency
within retail markets.

4.4

Retailers Offering Credit Cards

In several ways, our findings resemble the issue of double marginalization in the verticalsupply chain. Naturally, the vertical integration solution to double marginalization might
apply to the premium payment method problem that exists in retail. In particular, merchants
can vertically integrate by offering their own credit card. This is common for major retailers
like Macy’s, Amazon, and Target. Another potential solution is for merchants to negotiate
rates with credit card companies as a kind of vertical integration. Following the Supreme
Court’s ruling on surcharging, many major retailers began negotiating alternative rates onpremium cards.13 The retailers claim that the intention of these negotiations is to keep retailprices low, and our model suggests that this objective is legitimate and will improve market
13

See “ Are Other People’s Credit-Card Rewards Costing You Money? Amazon and other retailers believeso, and they’re going to war against high-end cards,” in the New York Magazine, October 2018, for details.

14efficiency. Thus, policy makers should not necessarily consider such negotiations between
retailers and credit card companies as collusive or anti-competitive.

5

Concluding Remarks

In this paper, we aim to determine how the effective prices, defined as prices inclusive of
payment method rewards, are impacted by the use of multiple payment methods and how
this impact depends on the surcharge rule that is in place. When the no-surcharge ruleis implemented, we find that the premium merchant fee pass-through is often greater thanthe premium reward to consumers so that all consumers, premium and non-premium, pay
a higher effective price when premium payment methods are available in the market. If
merchants can surcharge across payment methods, then all consumers pay the same effective
price so that premium payment methods account for no sales. Furthermore, by comparing
prices across the two rules we find that effective prices are always lower with surcharging.
Our results are consistent across all market structures, suggesting that the presence ofpremium payment methods that are protected by no-surcharge rules harms consumers andmerchants in all retail markets. This suggests that the Supreme Court ruling to prevent
steering (i.e., surcharging) benefited premium credit card companies at the expense of consumers and merchants. However, our findings also imply that policy makers can rectify thismistake by banning credit card company “accept all cards” clauses. Such a ruling would
enable merchants to lower effective prices by limiting premium card purchases without losing
sales to consumers using standard credit cards.

15

Appendix of Proofs
Deriving Equations (2), (3), and (4):Taking the classic conduct formula from Equa-tion (1) we have that p−c= − · θ = −θQ(p)and this implies that 0 = θQ(p) + Q0 (p) · (p − c).
pp·Q0 (p)Notice that this is the first-order condition from the Cournot model after symmetry is imposed with θ = n1 .
Applying this approach to the regular consumer market, we have that 0 = θQr + (pr − c) ·∂Qrrwhich implies that θ · Qr = (pr − c) · ∂Q
∂pr∂pr

. Now consider the premium consumer market

where profit from the premium consumers is given by: Πp = [(1 − f2 )pp − c]Qp . With the(1−f2 ) distortion in the markup term, applying the conduct formula implies that 0 = θ ·(1−ppso that θ · (1 − f2 )Qp = [(1 − f2 )pp − c] · ∂Q
. Lastly, by weighingf2 )Qp + [(1 − f2 )pp − c] · ∂Q∂pp∂pp

the two equations across the λ premium consumers and the (1 − λ) regular consumers weprhave that λ · θ(1 − f2 )Qp + (1 − λ) · θQr = λ · [(1 − f2 )p − c] · ∂Q+ (1 − λ) · (p − c) · ∂Q
. 
∂p
∂p

Proof of Lemma 1:

The equilibrium price for the no-surcharge subgame is given by

Equation (4). Solving for p with Qp = λ[1 − (1 − f1 )p] and Qr = (1 − λ)(1 − p) implies that(1−λf1 )c+θ·(1−λf2 )p∗ (λ, θ) = (1+θ)[1−λ(f.
1 +f2 −f1 f2 )]Proof of Proposition 1:Equation (5) implies that (1 − f1 ) · p∗ (λ, θ) > p∗ (0, θ) if andonly if (1 − f1 )[(1 − λf1 )c + (1 − λf2 )θ] > (c + θ)[1 − λ(f1 + f2 − f1 f2 )] which holds if and
f1 (c+θ)≡ λ.
only if λ > c[f2 −f
1 (f2 −f1 )]Proof of Lemma 2:

Solving for pr and pp independently using Equations (2) and (3)c+θimplies that θ(1 − pr )(1 − λ) = (pr − c)(1 − λ)| − 1| so that pr = 1+θ
and that θ(1 −θcf2 )λ[1 − (1 − f1 )pp ] = [(1 − f2 )pp − c]λ(1 − f1 ) so that pp = (1+θ)(1−f+ (1+θ)(1−f. However,
1)2)with these prices we have that (1 − f1 )pp ≥ pr if and only if f2 ≥ f1 . Thus, a corner
solution occurs where the two consumers pay the same effective price which we denote bypSR ≡ pr = (1 − f1 )pp . Using Equation (4) and substituting pSR for pr and (1 − f1 )pp implies
that λθ(1 − f2 )(1 − p∗SR ) + (1 − λ)θ(1 − p∗SR ) = λ(p∗SR − c)(1 − f1 ) + (1 − λ)(p∗SR c) so that
1 )c+θ·(1−λf2 )p∗SR = (1−λf.
(1−λf1 )+(1−λf2 )16

Proof of Proposition 2:

Equations (5) and (6) imply that p∗SR < p∗ if and only if(1 + θ)λf1 f2 < 1 − θ + θλ(f1 + f2 ). Notice that the left-hand side is increasing in θ while theright-hand side is decreasing in θ. Thus, if the inequality holds for θ = 1, then the inequality
holds for all θ < 1. Thus, p∗SR < p∗ if and only if 2f1 f2 < f1 + f2 . Note that if f22 < f1 , then
2f1 f2 < 2f22 < 2f1 ≤ f1 + f2 so that f22 < f1 implies that p∗SR < p∗ .

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

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