Full text of Working Papers (Federal Reserve Bank of Atlanta) : Credit and the No-Surcharge Rule, Working Paper 2006-25

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

FEDERAL RESERVE BANK of ATLANTA

Credit and the No-Surcharge Rule
Cyril Monnet and William Roberds
Working Paper 2006-25
November 2006

WORKING PAPER SERIES

FEDERAL RESERVE BANK o f ATLANTA

WORKING PAPER SERIES

Credit and the No-Surcharge Rule
Cyril Monnet and William Roberds
Working Paper 2006-25
November 2006
Abstract: A controversial aspect of payment cards has been the “no-surcharge rule.” This rule, which is
part of the contract between the card provider and a merchant, states that the merchant cannot charge a
customer who pays by card more than a customer who pays by cash. In this paper we consider the design
of an optimal card-based payment system when cash is available as an alternative means of payment. We
find that a version of the no-surcharge rule emerges as a natural and advantageous feature of such a
system.
JEL classification: D830, E420
Key words: no surcharge, credit cards, payments, money, search

The views expressed here are the authors’ and not necessarily those of the European Central Bank, the Federal Reserve Bank of
Atlanta, or the Federal Reserve System. Any remaining errors are the authors’ responsibility.
Please address questions regarding content to Cyril Monnet, DG-Research, European Central Bank, cyril.monnet@ecb.int, or
William Roberds (contact author), Research Economist and Policy Adviser, Research Department, Federal Reserve Bank of
Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8970, william.roberds@atl.frb.org.
Federal Reserve Bank of Atlanta working papers, including revised versions, are available on the Atlanta Fed’s Web site at
www.frbatlanta.org. Click “Publications” and then “Working Papers.” Use the WebScriber Service (at www.frbatlanta.org) to
receive e-mail notifications about new papers.

1

Introduction

Even the most casual observer will have noticed that money is being displaced by
memory. Transactions that were once only conducted only with cash–purchases of
groceries, fast food meals, movies, taxi rides, etc.–are increasingly made using credit
cards, debit cards, and various other payment methods that electronically link buyers
to their payment histories.1
A commonly cited explanation for this phenomenon is the ongoing improvement in
information technology. As the cost of storing, transmitting, and authenticating data
falls, so the thinking goes, payment systems based on electronic accounts become
more attractive relative to cash. This explanation is in accordance with accepted
monetary theory (Kocherlakota 1998), which views cash as a second-best proxy for
credit when the latter is too costly or simply unavailable.
A practical di¢ culty with this argument, however, is that in many instances the
cost of making a cash transaction remains noticeably lower than any other type of
payment. The cost of simply handing over a banknote, after all, is still virtually zero,
and the burden imposed by in‡ation has fallen drastically over the past two decades.
Systematic studies, taking into account the costs of safekeeping, trips to the bank,
etc. place the merchant’s cost of a typical cash transaction in the U.S. at about $.10.
By contrast, the average merchant cost of a debit card transaction is in the range of
$.34, and the typical credit card transaction costs a merchant in excess of $.70.2 A
recent study by Garcia-Swartz, Hahn, and Layne-Farrar (2006) attempts to measure
the costs of various payment methods to all parties involved. It argues that card
payments are more competitive with cash, once buyers’“implicit cost”of using cash–
1

Aggregate statistics collected by the Bank for International Settlements (Committee on Payment

and Settlement Systems, 2006) show that the volume and value of card-based payments has sharply
accelerated over the past ten years in all developed countries. This trend is also apparent in U.S.
household survey data (Klee 2006) and recent Federal Reserve surveys (Gerdes at al. 2005). While
these numbers do not track cash payments, a 2005 survey conducted by Visa, cited in Garcia-Swartz,
Hahn, and Layne-Farrar (2006) indicates a dropo¤ in the use of cash in the U.S. over the past decade.
2
Figures are from an oft-cited 2001 Food Marketing Institute survey; see Humphrey et al. (2003).

1

especially the “shoe-leather” cost of visiting an ATM, estimated at more than $.28
per transaction–is taken into account. As this last number is necessarily somewhat
imprecise (for example cash can circulate in ways that are not easily observable by
econometricians), we would still argue that cash remains the cheapest way to pay in
many situations.
The dominant component of the cost of a card payment is the merchant fee (a.k.a.
“merchant discount”) paid by a seller of goods or services to the card company. In
the U.S. this fee averages about 2% of the purchase amount.3 Usually this fee is not
paid explicitly by the buyer, but is instead deducted from the merchant’s payment
by the card provider, and the buyer pays the same price as he would have using cash.
Payment card providers reinforce this practice with a contractual provision known as
a no-surcharge rule (NSR, a.k.a. “no-discrimination rule”) that prohibits merchants
from assessing a fee on customers who wish to pay with their credit or debit card.4
The no-surcharge rule has been extremely controversial, and has been banned
in some countries (e.g., Australia; see Lowe 2005) as a form of collusive price-…xing.
Critics of NSR have argued that it ine¢ ciently encourages the use of more costly forms
of payment (credit cards) to less costly (cash), leading to what the Governor of the
Reserve Bank of Australia has termed a “Gresham’s Law of Payments” (Macfarlane
2005).5
Against the cost disadvantages must be set the bene…ts of card payment: certainly
in the case of credit cards at least, paying by card allows buyers to tap into their credit
lines in a convenient and straightforward way. But this argument does not apply in
the case of debit cards or credit cards that are paid o¤ every month. “Paybacks”
3

Average merchant fees on credit card transactions in 2005 were 2.19% for MasterCard and Visa,

2.41% for American Express, and 1.76% for Discover (Nilson Report, Issue 862, 2006).
4
Under U.S. law consumers are still entitled to negotiate discounts if they o¤er cash. Such
discounts are rarely o¤ered for routine purchases, however. In some other countries even this practice
is prohibited.
5
See Chakravorti and To (1999) for a formal presentation of this idea. Lowe (2005) notes that
surcharging for card use is still uncommon in Australia, despite the regulatory removal of NSR.

2

to card use, in the form of frequent ‡yer miles, cash-back, or other rewards, further
increase buyers incentives to use cards, but paybacks do not explain why still-cheaper
cash is not preferred.
Of course, the Coase Theorem would predict that the NSR is irrelevant, as long
as all parties to a transaction are able to contract around it. Papers in the industrial
organization literature, such as Rochet and Tirole (2002), contend that the Coase
Theorem can fail in a payments environment, due to an asymmetry in market power
between merchants and consumers.6 Absent a no-surcharge rule, it is argued, monopolistic merchants may ine¢ ciently shift the costs of a card payment system to
consumers, leading to the underprovision of credit and welfare losses.
Below, we abstract from industrial organization issues and instead focus on other
frictions that could cause the NSR to matter and the Coase Theorem to fail. These
are the standard frictions that give rise to the use of payment systems: time mismatches of agents’trading demands, private information about agents’preferences,
and limited enforcement of their pledges to repay. As in actual payment situations,
the term “limited enforcement”incorporates both the potential anonymity of buyers
and sellers, and, once identi…cation has occurred, a limited ability to apply penalties
when an agent defaults.
Next we introduce a transactions technology, which, at a cost, allows for relaxation
of these frictions. This technology, which we interpret as a credit-card payment
system, must compete with an alternative payments technology in the form of cash.
To make cash as attractive as possible, we assume it is uncounterfeitable, not subject
to theft, can transferred for free, and that it bears little or no in‡ation tax. We
then consider how a planner would structure an optimal credit card system when
cash is available, and …nd that a version of the no-surcharge rule can emerge as an
advantageous feature of such a system.
The intuition behind this result is simple. In our environment, agents early in
6

For surveys of the extensive I/O literature on card payments see Chakravorti (2003), Hunt

(2003), Rochet and Tirole (2004), Evans and Schmalensee (2005), and Rochet and Tirole (2006).

3

their life-cycle always need credit, whereas older agents never do. For young agents
to access credit, they must forsake the anonymity associated with cash payment and
join the credit-card payment system. But young agents’participation in this system
is pointless, unless a su¢ ciently large number of older agents also agree to take part.
A no-surcharge rule promotes ongoing participation in credit arrangements by, in
e¤ect, taxing the use of cash. Thus, in our model, the use of credit card system has
both a private and social bene…t, and a no-surcharge rule allows agents to internalize
the e¤ects of their participation.
This result should be cast in a proper light. Since our analysis pertains to the
design of an ideal card payment system, it renders no verdict on pricing structures
in existing card payment systems. Rather, it shows how the oft-discussed “network
bene…ts” of card payments can arise in a general-equilibrium world, and how an
absence of surcharges can be instrumental in the capture of these bene…ts.

2

The Environment

Modeling choices. Evaluation of NSR obviously requires an environment where
agents may pay either with cash or with a card To provide some minimal degree of
verisimilitude, credit cards in particular should incorporate both a “credit”or recordkeeping function and a “payment” function–identi…cation of otherwise anonymous
transactors (Kahn and Roberds 2005). That is, the credit cards in the model should,
just as with actual credit cards, serve the dual purpose of recording agents’ agents
transaction histories and correlating transactors with histories.
Versimilitude also requires that credit card debt be subject to some stringent
limitations on enforcement. Credit card debt is rarely collateralized and by its nature
somewhat risky. While most credit card debt is eventually paid o¤ (default rates
average about 4 percent in the U.S.), very little of the defaulted debt is ever collected.7
7

For example, in 2005, MasterCard and Visa were only able to collect about 9 percent of defaulted

credit card balances (Nilson Report Issue 851, 2006).

4

The need to incorporate limited enforcement sets our analysis o¤ from standard cashgood/credit-good approaches in the macro literature, e.g., Lacker and Schreft (1996),
where this friction does not arise.
The Lagos-Wright (2005) model is an attractive starting point for our study of
the NSR, since it provides a model of anonymous exchange where agents can hold
arbitrary money balances. Berentsen, Camera and Waller (forthcoming) have shown
how the Lagos-Wright environment can be modi…ed to incorporate uncollateralized
credit, and our analysis will follow their setup in many respects.
For the purposes of our analysis, an undesirable feature of Berentsen, Camera,
and Waller model is that credit is not needed to implement optimal allocations when
monetary policy follows the Friedman rule. This feature, common to many money
models with in…nite-lived agents, places sharp limits on the role of credit.8 Following Freeman’s (1996) celebrated model of payments, we therefore modify their
model to allow for overlapping generations, where agents’preferences, endowments,
and trading opportunities follow a very simple life cycle. For this type of model,
monetary exchange under the Friedman rule does not automatically deliver optimal
allocations (Bhattacharya, Haslag, and Russell 2005), potentially creating a demand
for credit/payment arrangements such as credit cards.
Finally, to keep track of surcharges it is important that someone will always use
cash. To this end our setup includes a group of in…nite-lived agents who, by assumption, are excluded from making use of credit arrangements.
Agents, Preferences, and technology. Time t = 0; 1; :::, is in…nite and discrete. The economy consists of a [0; 1] continuum of agents. A small group (measure
zero) of these agents live forever and discount the future at rate . All other agents
have …nite lives, and die each period with probability 1
measure 1
8

. A group of agents with

is also born during each period, so that the size of the population

In such models the operational distinction between money and credit is not always obvious; as

described in Kocherlakota (1998) and many other papers, money can function as a sort of portable
credit balance.

5

does not change from period to period. Associated with each agent is a unique …xed
quantity that we will call his “identity.”9
Agents produce and consume two types of nonstorable goods: a specialized good
and a numeraire good. Utility (disutility) of consumption (production) of the numeraire good is linear. Consumption of the numeraire good is denoted as the negative
of “hours worked”h.
There is a linear cost

qs of producing qs units of the specialized good. All agents

enjoy utility u(q) when they consume q units of the specialized good, where u0 (q) > 0;
u00 (q) < 0, u0 (0) = 1 and limq!1 u0 (q) = 0.
Trading stages. Each period has two sub-periods, each with its own market.
Markets in both sub-periods are Walrasian in the sense that no agent has market
power. The nature of trading is quite di¤erent in the two subperiods, however.
In the …rst subperiod, the numeraire good is exchanged and a trader’s identity can
be veri…ed by other agents at zero cost, should the agent decide to make his identity
available. We call this stage the settlement stage. At the end of the settlement stage
a randomly selected proportion 1

of the …nite-lived agents die and are replaced

by young agents. Upon reaching their second settlement period, …nite-lived agents
become inherently indistinguishable from other agents and are referred to as “adults.”
In the second sub-period, the trading stage, the specialized good is exchanged in
“incomplete anonymity.”This means that in this stage, agents are unrecognizable to
one another, absent the application of some costly identifying technology (discussed
in detail below). Application of this technology allows an agent’s identity to be
determined with perfect accuracy; however agents again always decide whether they
want to be identi…ed and may remain anonymous if they so prefer.
Within the trading stage, a proportion a 2 (0; 1) of the population has the opportunity to actively engage in trade. Of these, a randomly selected proportion 1

n

have the desire to consume specialized goods produced by others; otherwise they be9

Alternatively, an agent’s identity could be thought of as his “location,”although our model does

not rely on geographical dispersion.

6

come potential producers with probability n 2 (0; 1). The remaining proportion 1

a

of the population are inactive, meaning that during this stage they have neither the
desire to consume nor the opportunity to produce. A consumer’s trading-stage state
(buyer, seller, inactive) is private information. The timing of events within a period
is summarized in the following table.

Table 1: Events within a period

1. Settlement stage
1a. Agents produce, trade, and consume numeraire good
1b. 1

adult agents die and are replaced by young agents

2. Trading stage
2a. Agents learn if they are consumers, producers, or inactive
2b. Buyers and sellers trade specialized goods
2c. Buyers consume specialized goods

Immortal agents have exactly the same utility, endowments, and trading opportunities as …nite-lived agents, di¤ering in the detail that they do not die. The population
of immortal agents remains constant at some low (zero measure) level.
Allocations. In this economy, we will consider symmetric stationary feasible
allocations. A stationary allocation is a vector (q; qs ; q y ; qsy ; hs ; hb ; hi ), where the superscript y denotes young agents (superscripts are omitted for adults). (hs ; hb ; hi ) are
hours worked for an agent of type j when he was a seller (s), buyer (b), or inactive
(i) in the previous trading stage. The allocation is feasible if
(1

)[(1

n) q y

nqsy ] + [(1

a (nhs + (1

n) q

nqs ] = 0;

n) hb ) + (1

a) hi = 0:

7

The …rst equality is the market clearing condition for the specialized good in the trading stage. The second constraint is the market clearing condition for the numeraire
good during the settlement stage.

2.1

First best allocation

We begin by considering optimal allocations in the absence of information and enforcement constraints. The expected utility of a representative young agent just born,
in his very …rst period of life, is
W y = af(1

n)[u(q y )

hb ]

n(qsy

hs )g

(1

a)hi :

The expected utility of an adult at the start of a trading stage is likewise
W = af(1

n)[u(q)

hb ]

n(qs

hs )g

(1

a)hi :

We take the planner’s objective function to be the maximization of the populationweighted sum of the agents’ utility (ignoring the zero-measure group of immortal
agents)
W = (1

)Wy + W

Using the market clearing conditions, this reduces to
W = af(1

)(1

n) [u(q y )

qy ]

(1

n) [u(q)

q]g

Therefore a …rst best allocation is one that satis…es q y = q = q where
u0 (q ) = 1:
We will denote the …rst best allocation by q . In words, a …rst-best allocation requires
that the utility of consuming an additional increment of the specialized good equals
the cost of producing this increment, for almost all consumers, i.e., for both the young
and adults.

8

3

The cash economy

As agents are not readily indenti…able during the trading stage, they need some type
of recordkeeping in order to transact. In this section we consider the economy where
only cash –the simplest form of recordkeeping –is available. Cash is uncounterfeitable
and can be costlessly authenticated and transferred among agents. Agents may trade
numeraire for cash during the settlement stage; cash so acquired can then be used for
purchases during the trading stage.
Cash is provided by a central bank. Let M be the per capita supply of cash. A
transfer of cash takes place at the beginning of the settlement stage. More precisely
the central bank makes a lump sum transfer of
settlement stage. A share (1

M to all (adult) agents in the

) of this transfer reverts to the central bank when

some of the agents die. The central bank then redistributes it pro-rata to alive
adults. Hence, alive adults get a transfer of

0

) = ] M . The net stock

M = [ + (1

of money however grows as M+1 = (1 + )M . We will concentrate the analysis on
stationary monetary equilibria where M =

1M 1,

being the real price of money

in terms of numeraire. We will denote the growth rate of money M=M
also equals

1=

1

by . Hence

and we have
(1)

=1+ :

Let V (m) denote the discounted lifetime utility of an adult when he enters the
settlement stage holding m units of cash, while W (m) denotes the expected discounted
lifetime utility from entering the trading stage with money holding m. V (m) is de…ned
as
V (m) = max

h;m+1

s:t:

h + W (m+1 )
m+1 = h + m +

0

M:

The …rst-order and envelope conditions give
W 0 (m+1 ) = ;
9

V 0 (m) = :

(2)

It follows that m+1 is independent of the past trading history of agent which is
summarized in m, and all adults exit the settlement stage with the same holdings of
cash.
The discounted lifetime utility of adults when they enter the trading stage with
m units of cash is
W (m) = a f(1

n) [u(q) + V (m

pq)] + n [ qs + V (m + pqs )]g + (1

a)V (m);

where q and qs are set optimally as follows.
An adult producer at the trading stage solves
max qs + V (m + pqs );
qs

with …rst-order condition
pV 0 (m + pqs ) = 1:
Therefore using (2) we have
(3)

p = 1:
The problem of an adult consumer is
max

u(q) + V (m

q

s:t: pq

pq)

m:

and the …rst order condition gives
u0 (q)
where V 0 (m

pq) has been replaced by

p = p;
using (2). That is to say, either

> 0 in

which case the consumer’s budget constraint binds so that q = m=p and u0 (q) > p,
or the budget constraint does not bind,

= 0 and q solves u0 (q) = p .

The discounted lifetime utility of a young agent entering the trading stage is given
by
W y (m) = a f(1
+(1

n) [u(q y ) + V (m
a)V (m);
10

pq y )] + n [ qsy + V (m + pqsy )]g

where m = 0. The problem of a young producer and a young consumer are identical
to their adult counterparts. The solution of a young producer’s problem is identical
to that of an adult; however a young consumer must choose q y = 0 as he lacks the
necessary cash to make a purchase.
The market clearing condition for the trading stage re‡ects the fact that young
would-be buyers cannot consume, and is given by
1

n
n

q = qs = qsy :

It is now easy to determine the value of an additional unit of money when (adult)
agents exit the settlement stage. Using the solution to the buyer’s problem, this is
W 0 (m) = a(1
However, we know that p

n)[(u0 (q)

1
1) + ] + [an + (1
p

= 1 and W 0 (m) =

1=

a)] :

. Hence we obtain another

equilibrium condition, which characterizes the quantity consumed in the trading stage
as a function of the money growth rate
= a(1

n)[u0 (q)

(4)

1]:

We can now de…ne and characterize a stationary monetary equilibrium.
De…nition 1 A stationary monetary equilibrium is a list ( ; q) such that (1) and (4)
hold.
Proposition 1 A stationary monetary equilibrium exists for all
for all

and is unique

> . The equilibrium allocation q is strictly decreasing in .

The proof of the proposition follows immediately from condition (4). Note that if
the Friedman rule holds,

=

and adult consumers always hold enough money to

purchase the e¢ cient amount, i.e., in equilibrium u0 (qm ) = 1. This does not attain
the …rst best however, as young buyers must postpone consumption until they have
acquired the necessary stock of cash.10
10

We do not place too literal an interpretation on this very simple life-cycle pattern of consumption.

What is important is that the cash constraint binds at some point over agents’life cycle.

11

4

The cash-credit economy

When all trading-period transactions are in cash, young agents cannot consume in
their …rst period of life. The requirement to transact in cash also constrains old agents
when monetary policy does not follow the Friedman rule. Hence the availability of
credit can potentially improve welfare by relaxing agents’ cash constraints. In this
section, we consider how a credit arrangment a¤ects welfare. This part of the paper
draws on the private information approach used by Koeppl, Monnet, and Temzelides
(2006, KMT).
The anonymity prevalent during the trading periods means that agents cannot increase their consumption by simply issuing bonds: absent some means of identifying
the bond issuer, such a bond would be worthless. Consequently the credit arrangement must also incorporate some technology for identifying debtors. To …x ideas, we
imagine that this identi…cation occurs using credit cards.
More speci…cally, we may imagine that the planner relies on a club arrangement
known as a credit card institution (CCI).11 The CCI incurs monitoring and set-up
costs

0 in ascertaining the identity of new credit card holders (“members”).12

This cost is denominated in the numeraire good and must be borne by agents using the
CCI. Once it has incurred this cost, the CCI can costlessly verify agents as members
and record a member’s transactions. However it cannot observe whether an agent’s
state is “active” or “inactive” at the trading stage, or whether an agent trades with
cash in the trading stage. The identities of in…nite-lived agents are unveri…able, which
11

A club arrangement is quite natural since identi…cation of an agent is a sort of nonrival good.

Reliance on the club implicitly assumes that the planner is solving a constrained Pareto problem
of maximizing the welfare of those within the club. This constraint will be inessential in the cases
studied below, where (almost) all agents decide to join the club.
12
As in Kahn and Roberds (2005, KR), each new member, upon veri…cation of his identity, receives
a unique, uncounterfeitable credit card that may be subsequently veri…ed at zero cost. Following KR,
we will exclude the possibility of fraud on the supplier (“merchant”) side. This means that in every
trading period, once a CCI member identi…es himself as a supplier, his delivery (or nondelivery) of
specialized goods within that period becomes observable.

12

prevents them from joining the CCI.
The CCI will seek to implement the …rst best allocation q in the trading stage.
Hence, CCI does not seek to maximize pro…t but only to achieve q and to recover
costs. Following KMT, we will design the terms of the credit card institution so that
agents truthfully reveal their state (consumer, producer, inactive) and so that they
are willing to participate in the credit card arrangement given the outside option of
using cash. The CCI has no control over monetary policy and takes the money growth
rate

as given.

As in KMT, we assume that the CCI assigns credit balances to participants. It
speci…es rules for how the balances are updated given the histories of reports regarding
transactions in the trading round. During the settlement stage, participants can
trade balances for the numeraire good. Here the settlement stage is modelled as
a competitive market in which agents who are “low” can increase their balances
by producing numeraire, while those with high balances end up as consumers of
numeraire. During the settlement stage, balances are exchanged for numeraire at price
b.

We let d denote the amount of balances with which agents exit the settlement

stage.
Momentarily ignoring agents’ balances, there are three possibilities regarding
meetings: an agent can be a consumer, a producer, or inactive. The vector of policy
rules (Lt ; Kt ; Bt ; q ) then determines the respective balance adjustments for each type
of agent and the quantity consumed by each consumer, q . More precisely, Lt (Kt ) is
the adjustment for an agent who consumes (produces), while Bt is the adjustment
for an inactive agent. These functions in general may depend on the agents’histories
of transactions, as summarized by their current balances, as well as on the distribution of balances when agents exit the settlement stage. Balances are represented by
real numbers not restricted in sign, while production of goods in the trading stage is
restricted to be positive. After each trading stage, agents enter the settlement round
knowing their new balances.
We should note that the CCI cannot impose any direct penalty on a member with

13

low balances who does not readjust his balance during a settlement period. That is,
a CCI member can walk away from the arrangement at any time. The only penalty
that the CCI can apply is denial of future access.
We de…ne a credit card system (CCS) to be an array of functions fLt ; Kt ; Bt ; q g.
A CCS is feasible if it satis…es some incentive and participation constraints (speci…ed
below). A CCS is simple if balance adjustments do not depend on the agents’current balances and are therefore history independent. A feasible CCS is optimal if it
implements the e¢ cient trading-period allocation q . Note that a CCS requires the
existence of a CCI in order to identify agents.
Assumption 1 The …rst best allocation satis…es u (q ) > q .
Under assumption 1, KMT show that there exists a simple optimal CCS, where
balances upon exiting the settlement stage dt are equal to zero for all t. In other
words, if a member of the CCI exits the settlement stage with d 6= 0, then the CCI
shuts down the account of this member so that his credit card becomes invalid. It
follows that the equilibrium distribution of balances is degenerate at d = 0, when
CCI members exit the settlement stage.
As in the cash economy, the trading stage is still a Walrasian market. The auctioneer has a list transmitted by the CCI of those eligible to use credit. The auctioneer
then calls a price p and quantities (qm ; qs;m ) consumed and produced when cash is
used, as well as the terms of the CCS. Then CCI members decide if they will participate, and if so, whether they will use cash or credit. That is, they may participate
anonymously as cash agents, or they may allow themselves to be identi…ed, and participate in the credit market. CCI members thus have the opportunity to use cash
rather than credit at any time. In…nite-lived agents remain outside the CCI, and will
always use cash. Hence, while an active cash market will always exist, a successful
CCS should contain incentives such that CCI members transact using credit.
In such a system, prices and quantities have to clear the market. We assume that
the auctioneer does not cross-subsidize consumption across those agents that use cash
14

and those that use credit.13 More precisely, the auctioneer faces two market clearing
conditions. Given that active agents are sellers with probability n and buyers with
probability 1

n, these market clearing conditions are
(1

n) q

= nqs ;

(1

n) qm = nqs;m :

We also exclude the possibility of cross-subsidization through the central bank: only
agents holding currency in the settlement period are eligible to receive lump-sum
transfers from the central bank. This might occur, for example, if currency becomes
worn after a single period, so that cash holders must submit old banknotes in order
to obtain new ones.
In the previous section, we have studied the problem of agents who only have
access to cash. We now describe the problem of agents with access to the CCI.

4.1

Settlement stage

Let Z(b; m) denote the value function of a CCI member who exits the trading round
with balance b and cash holdings m. Let H(d; m+1 ) denote the value of an agent who
exits the settlement round with balance d = 0 and cash holdings m+1 . Given the
price in the settlement round is

b,

CCI members at the beginning of the settlement

round solve the following:
Z(b; m) = max f h + H(b+1 ; m+1 )g
h;m+1

s.t.

m+1 +

b b+1

= h+

bb

(5)

+ m:

The …rst order condition with respect to money gives
Hm (0; m+1 )
13

with strict inequality if m+1 = 0.

(6)

Some policy discussions of NSR have focused on the issue of potential cross-subsidization between

purchasers using cash and those using cards. The present model does not address this issue since, in
equilibrium, the CCS will be utilized by (almost) all agents or none. We abstract from this issue in
order to focus on the patterns of “subsidization” across heterogeneous cardholders, that are needed
to sustain the CCS when cash is available as an alternative.

15

The envelope conditions are Zb =

b

and Zm = . Since the CCI requires credit users

to carry zero balances when they exit the settlement stage, under the threat of credit
exclusion, we have b+1 = 0. When CCI members do not carry cash m+1 = 0 and it
follows that
h=

b b:

Note that the linearity in preferences implies that the value function Z (b; m) is linear
in credit balances and cash holdings.
Also, for any b, it should be the case that CCI members are better o¤ (at the
settlement stage) staying in the system than choosing to use cash forever after. This
no-default constraint imposes that for any b,
Z (b; m)

(m

m+1 ) + W (m+1 ) :

In the Appendix, we show that this requirement reduces to
bL

qm +

a (1
1

n)

[u (qm )

u (q )

(qm

q )]

(7)

The cost-recovery constraint in the settlement stage requires that CCI members
cover monitoring costs for young agents joining the CCI14
a

4.2

b

[nK + (1

n) L] + (1

a)

bB

+ (1

)

= 0:

(8)

Trading stage

We now turn to the problem faced by CCI members during the trading round. Agents
make reports to the auctioneer about their state (consumer, producer, inactive).
Those that report “producer” receive instructions from the auctioneer to produce
14

Expression (8) is somewhat restrictive in that it apportions the veri…cation costs equally across

all CCI members. More complicated schemes are feasible, but these are not observed in practice and
are unlikely to change the results below. In particular, note that the planner cannot simply assign
the veri…cation costs to the bene…ciaries of the CCI–the young. For su¢ ciently low in‡ation rates,
this would imply that every young consumer would default during his …rst settlement stage and the
CCI would collapse.

16

qs . Consumers receive q . The auctioneer subsequently communicates the identity
and reports of those CCI members that made use of the CCS to the CCI, which then
makes balance adjustments depending on these reports.
For agents to report their state truthfully, some conditions have to be satis…ed.
In particular, incentive constraints require that the following inequalities hold:
u (q ) + Z(L; m)

Z(B; m);

qs + Z(K; m)

Z(B; m);

Z (B; m)

Z (L; m) :

The …rst (second) constraint states that a consumer (producer) must be at least as
well o¤ declaring his true state than reporting he is inactive. The third constraint
states that an inactive agent does not …nd pro…table to claim that he is a consumer.
Since the value function Z is linear, these conditions simplify to
u (q ) +
qs +

bL

bB

(9)

bK

bB

(10)

B

(11)

L

In addition, participation constraints require that producers, consumers, and inactive
CCI members respectively, are better o¤ using credit than cash; i.e.,
qs + Z(K; m)

qs;m + max fZ(B; m + pqs;m ); V (m + pqs;m )g ;

u(q ) + Z(L; m)

u (qm ) + max fZ (B; m

Z(B; m)

maxfZ(B; m); V (m)g:

pqm ) ; V (m

pqm )g ;

where m can be zero. The …rst constraint states that a seller is better o¤ producing
the e¢ cient amount and incurring balance adjustment K than reporting inactivity,
incurring adjustment B (if he stays in the credit arrangement) and selling his good for
cash instead. The second constraint states that a consumer is better o¤ consuming
the e¢ cient quantity using credit than reporting inactivity (or opting out of the credit
arrangement) and using cash. The third condition, the participation constraint for
17

the inactive agents, is just a special case of the no-default condition (7) and drops
out. Note that condition (7) implies that if they use cash, active credit agents will
prefer to stay in the credit arrangement. Exploiting the linearity of the value function
Z, the nonredundant participation constraints can be rewritten as
qs +

b

u(q ) +

(K

B)

(L

B)

b

qs;m + pqs;m
u (qm )

pqm :

Simplifying these expressions using p = 1, these reduce to
qs +
u(q ) +

b

(K

B)

0

(L

B)

u (qm )

b

(12)
(13)

qm :

Now, if (12) and (13) hold then (10) and (9) hold as well.
As before we con…ne our attention to stationary equilibria and require that
M . We also require that

bX

=

b;+1 X+1 ,

ments. In the following we will normalize

+1 M+1

where X denotes any balance adjustb

= 1 and consider constant balance

adjustments. We are now in a position to de…ne a cash-credit equilibrium and state
the main results of the paper (proofs are in the Appendix).
De…nition 2 A stationary cash-credit equilibrium is a credit system (L; K; B; q ) and
a list ( ; qm ) satisfying the (1),(4), (7), (8), (11), (12) and (13).
In words, a cash-credit equilibrium must satisfy the conditions for a stationary
monetary equilibrium, as well as the no-default, cost-recovery, incentive, and participation constraints necessary to sustain the CCI. In such an equilibrium, only the
zero-measure group of in…nite-lived agents transacts with cash. All other transactions
occur through the CCI.
Proposition 2 A stationary cash-credit equilibrium exists if
, where

0

( ) > 0.

18

<

and

( )

=

Therefore, there is an equilibrium where credit coexists with cash as long as the
monitoring cost is low enough. Indeed, if the cost of monitoring agents were too
large (say in…nite), then the …nancing of the credit arrangement would violate the
participation constraint in the credit arrangement, independently of the value of cash.
However, when the participation constraint is satis…ed for low monitoring costs, the
value of cash then matters by a¤ecting the no-default constraint (7). The intuition is
as follows. As the monitoring cost increases, participants in the credit arrangement
have to contribute more to the credit arrangement in each period. Their incentive
to use cash then increases. The credit arrangement will then only exist for relatively
high values of , i.e., high implicit costs of holding cash. As

increases, then from

(4) the value of cash decreases and the level of consumption obtainable with cash
decreases, making the credit arrangement more attractive.
Proposition 3 Credit increases welfare if

<

a (1

n) [u (q )

The proof for this proposition considers the case where

q ]

q .

= , so that cash is

costless to hold for all agents. In this case only young agents are penalized in a
cash economy, as they cannot consume in their …rst trading period. However, if the
monitoring cost is low enough, young agents are better o¤ ex-ante if they access the
credit arrangement and then amortize the cost of the monitoring over subsequent
periods, than by foregoing the chance to consume in their …rst period of life. The
threshold

is given by the the expected gain from participating in the trading stage

in the …rst period of life, minus the cost of acquiring cash in the next settlement stage
to consume q , that is, q = q .
The threshold value

obviously depends on the probability of consuming in the

trading stage: if this probability is too low, then
increase welfare.

19

is negative and credit does not

4.3

The No-Surcharge Rule

A version of NSR arises quite naturally from the cash-credit equilibrium described
above. We say that a cash-credit equilibrium follows a no-surcharge rule when a
consumer’s per-unit cost of purchasing a specialized good through the CCS does not
exceed his cost of making the same purchase using cash.15 Expressing consumers’
cost of a credit purchase of q specialized goods (and so incurring balance L) in terms
of the numeraire good, then NSR holds if
L
q

p

Recalling that in equilibrium p = 1 and rearranging, this reduces to
q

(14)

L

In the Appendix we that that if the Friedman rule is in e¤ect so that

=

and

qm = q , then the no-default condition (7) reduces to
(

q )

which implies the no-surcharge rule (14). Since

(15)

L
q < (

q ), then by continuity,

no-surcharge must also hold for rates of money growth slightly larger than . We
state this as
Corollary 4 In the cash-credit equilibrium, the no-surcharge rule (14) must hold for
su¢ ciently close to :
Hence, for monetary policies su¢ ciently close to the Friedman rule, NSR is an
integral feature of a welfare-enhancing credit arrangement. At higher money growth
rates, however, no-surcharge may not hold. In other words, no-surcharge is needed
exactly when the implicit cost of using money is low, and some enticement is necessary
to induce agents to transact through the CCS.
15

By stating this rule as an inequality we allow for the possibility of paybacks for card use.

20

The cash-credit equilibrium may also require that producers of specialized goods,
in e¤ect, pay a form of merchant fee when they receive credit payments, i.e., that they
receive less compensation per unit sold than producers who sell for cash. Analogous
to no-surcharge condition (14), we can say that a merchant fee is charged when
a producer obtains less by selling on credit (and so obtaining balance K) than he
would have by selling for cash, i.e., when
nK
<1
1 n
To see that a merchant fee can be charged in equilibrium, note that cost-recovery
condition (8), combined with incentive constraint (11), places an upper bound on
the compensation K of producers who sell for credit, as measured in terms of the
numeraire
1

K

1

an
L
an

an

(16)

When the Friedman rule is in e¤ect, we can then use (15) to get the following upper
bound on the credit producer’s compensation
1

K

an
q
an

1
an

(17)

Producers who sell for cash obtain
p

1

n
n

q =

1

n
n

q

(18)

Thus, merchants pay a merchant fee to receive credit payments if RHS(17) < RHS(18),
which can clearly occur for a close to 1.
These calculations demonstrate that a cash-credit equilibrium in the model can
mimic the seemingly paradoxical real-world preference for card payments over cash.
For the cases considered, adult consumers who have a low-cost alternative to the
credit arrangement (i.e., cash) still have an incentive to pay by credit, since the price
of paying by credit is no more than paying by cash. Producers agree to sell goods
on credit, even though they receive less (in numeraire terms) than they would if they
sold for cash.
21

The key to this somewhat magical arrangement is the possibility that an agent may
be in an inactive state during the trading stage, combined with the agent’s private
knowledge of his state. The possibility of inactivity is meaningful because it implies
that nonparticipation in the trading-stage market does not necessarily coincide with
defection from the credit arrangement. Agents can be induced to truthfully reveal
themselves as consumers, however, by in e¤ect “charging a fee” to inactive agents,
thereby keeping consumers’ price of credit purchases low. This in turn discourages
consumers from defaulting and going over to cash. Inactive agents and producers in
our model continue to participate because they realize that at some point they will
bene…t as consumers.
The critical role of the inactive state can be illustrated if we now suppose the
Friedman rule holds and simultaneously drive a ! 1, so that agents are always active
during the trading stage. In the case we must set the inactive agents’balance B = 0 in
conditions (9)-(13). Under the Friedman rule, the producers’participation constraint
(12) reduces to
L

1
1

q

n

(19)

which is inconsistent with the no-default condition (15). Not coincidentally, (19) also
violates the no-surcharge condition (14); adult agents would have no incentive to keep
making credit purchases, and the credit arrangement collapses.
To summarize, in our model NSR plays the socially valuable role of making people
demand credit who don’t need it. The use of credit by adults who are not creditconstrained is bene…cial to the young agents who are. No-surcharge is a way of bribing
the adults into supporting the young. No-surcharge would not matter without limited
enforcement: if adults could be compelled to transact through the CCI, the no-default
constraint (7) would drop out and the planner would have more ‡exibility about how
to allocate the costs of the credit arrangement.

22

5

Literature review

The approach outlined above follows the papers in the money literature that model
credit arrangements as clubs, where membership in a club implies mutual knowledge
of club members’ identities and histories (or a su¢ cient subset thereof).16 As in
many of these papers, our model also allows club members the option of transacting
anonymously with cash, which serves to tighten members’participation constraints.
In such models, if money is divisible then credit arrangements become di¢ cult or
impossible to sustain when the monetary policy follows the Friedman rule. Our model
avoids this fate by introducing young (credit-constrained) agents, and by restricting
the ability of the central bank to make transfers to these agents. Thus credit is still
useful even when cash is cheap.17
Paralleling other papers in this literature, “network e¤ects”arise quite naturally in
our model, since membership in (and repeated use of) the credit arrangement amounts
to a kind of club good. What is new is that we show how a no-surcharge rule can be
instrumental in supporting the credit arrangement, by causing agents to internalize
the gains of club participation. This result will hardly surprise people familiar with
the literature on the industrial organization of the payment card industry, where
network e¤ects have been a dominant theme of discussion (e.g., Rochet and Tirole
2006). As noted in the introduction, however, our emphasis here is not on industrial
organization, but on understanding the role of NSR in the context of monetary theory.
Telyukova and Wright (2006) employ a model similar to ours to explain another
puzzling aspect of credit cards, which is why people do not use their non-interestbearing cash to pay o¤ interest-bearing credit-card balances. They show that this
16

Including Aiyagari and Williamson (2000), Corbae and Ritter (2004), Kahn and Roberds (2005),

and Martin, Orlando, and Skeie (2006). In Berentsen, Camera, and Waller (forthcoming) this
information is managed by specialized intermediaries (banks).
17
Bhattacharya, Haslag, and Russell (2005) demonstrate that optimal allocations can be sustained
in OG models under the Friedman rule, if su¢ ciently complex, non-monetary intergenerational
transfer schemes are also available. Such schemes are not studied here as our focus is on the design
of private arrangements and not on …scal policy.

23

situation can persist if buyers are credit-constrained (so that credit cards have value),
but cash is more widely accepted than cards (so cash has value). Again our focus is
somewhat di¤erent, as we try to provide an explanation of how credit cards might
displace cash under an optimal payments arrangement, even for purchases by buyers
who are not credit constrained.

6

Conclusion

Above we have presented an environment where some type of payment system is
needed for exchange. Fiat money allows some trades to occur but does not attain a
…rst best allocation, even when the central bank follows the best possible policy, the
Friedman rule. A credit-based payment system can improve on allocations attainable
by trading only with cash. For monetary policies that are close to the Friedman
rule, a no-surcharge rule may be necessary to ensure the viability of the credit-based
system.
In the environment studied, no-surcharge is only valuable when there is both
limited enforcement of debts and private information about cardholder’s ability to
supply a good, i.e., “repay.” But since these frictions are pervasive in real-world
payment situations, this restriction may be seen as more a feature than a limitation.
More generally we have attempted to illustrate how the tools of monetary theory
can be applied to the analysis of payment systems. Although our model is quite
stylized, it also highlights the key services provided by these systems–identi…cation
(authentication) and recordkeeping–in a fully dynamic, general-equilibrium environment. This approach may prove a useful one in exploring the nature of the bene…ts
such systems provide, as well as the many policy issues associated with their operation.

24

7

Appendix: proofs

7.1

Derivation of the no-default condition

By de…nition, agents with balance b 2 fK; L; Bg do not default whenever
Z (b; m)

(m

m+1 ) + W (m+1 ) :

The inactive agents’incentive constraint (11) imposes B

L. Also, from the incentive

constraint for sellers (10), we have K > B. Hence, consumers receive the minimum
balance adjustment from participation in the CCS. It is therefore enough to consider
the no-default condition for consumers, or
Z (L; m)

(m

(20)

m+1 ) + W (m+1 ) :

From the linearity of Z in m we have
m + Z (L; 0)

(m

m+1 ) + W (m+1 ) ;

so that the no-default constraint (20) becomes
Z (L; 0)

m+1 + W (m+1 )

Again using linearity of Z, this is
bL

+ H (0; 0)

m+1 + W (m+1 )

From the budget constraint of cash buyers in the trading stage we have m+1 = p+1 qm .
Also, from (3) we have

+1 p+1

= 1. Therefore m+1 =

+1

+1 p+1 qm

=

qm . So

condition (20) becomes
bL

+ H (0; 0)

qm + W (m+1 )

Using linearity of H this is
bL

+

1

fa (1

n) [u (q )

q ]+a

b

[nK + (1

n) L] + (1

a)

b Bg

qm + W (m+1 ) ,
bL

+

1

fa (1

n) [u (q )
25

q ]

(1

) g

qm + W (m+1 )

where the last inequality follows from (8). Therefore we may restate (20) as
bL

+

a (1
1

n)

[u (q )

q ]

qm + W (m+1 )
qm +

a (1
1

n)

[u (qm )

qm ]

To derive the second inequality, we used the fact that the expected hours worked on
the settlement stage for a cash agent are by market clearing a [(1
(1

a) hi = 0. Rearranging terms, the no-default condition is then given by
bL

7.2

n) hb + nhs ] +

a (1
1

qm +

n)

[u (qm )

u (q )

(qm

q )]

Proof of Proposition 2

Proof. Normalizing

b

= 1 we have two equilibrium equations characterizing the

cash side of the economy:
n) [u0 (qm )

= (1

1]

= 1+ :
Hence, we need

(1

. The constraints on the credit side of the economy are
B

L

q +K

B

0

u(q ) + L

B

u (qm )

n)
n

L
a [nK + (1

n) L] + (1

a) B =

qm
a (1
qm +
1
(1
)

n)

[u (qm )

u (q )

(qm

q )]

From these constraints it follows that setting B = L slackens all the other constraints,
thus increasing the set of parameters for which a cash-credit equilibrium exists. Hence
we set B = L in what follows. The inequalities for the credit side of the economy

26

then become
(1

n)
n

u(q )
L

a (1
1

qm +
a [nK + (1

q +K

u (qm )
n)

(22)

qm

[u (qm )

n) L] + (1

(21)

L

u (q )

a) L =

(qm

(1

(23)

q )]

(24)

)

Condition (22) is always satis…ed and is therefore redundant. From the cost-recovery
condition we get an expression for K as a function of L.
(1

K=

an) L + (1
an

)

(25)

(Note that the merchant fee measured in terms of the numeraire is p K=
1

h

i

(1 n)
q
n

=

n) q ].) Substituting (25) in (21) we can reduce the constraints for the

nK= [(1

credit arrangement to
(1

n)
n

(1

q

an) L + (1
an

)

L

L

qm +

a (1
1

n)

[u (qm )

u (q )

(qm

Arranging terms we get
a (1

n) q

(1

)

L

L

qm +

a (1
1

n)

[u (qm )

u (q )

(qm

q )]

Therefore an equilibrium exists if
a (1

n) q

(1

)

L

qm +

a (1
1

n)

[u (qm )

u (q )

(qm

q )]

or if
a (1

n) q

qm +

a (1
1

n)

[u (qm )

u (q )

(qm

q )]

which is equivalent to
a (1

n) q +

a (1
1

n)

[u (q )

q ]
27

qm

a (1
1

n)

[u (qm )

qm ] :

(26)

q )]

When

> , the left hand side of (26) is constant in , while the derivative of the

right hand side is
dqm
d

qm +

a (1
1

n)

[u0 (qm )

1]

dqm
d

where using the equilibrium condition on the money market
n) [u0 (qm )

= a (1

1]

we have
1 =

dqm
; and
d

a (1

n) u00 (qm )

a (1

1
<0
n) u00 (qm )

dqm
=
d

Therefore, the derivative of the right hand side is
qm +

dqm
d

= qm +

1
dqm
d

1
1
1
1
1

= qm +
= qm +
= qm +

dqm
d

dqm
d
1
n) u00 (qm )

a (1

1
1

a (1

1
n) u00 (qm )

Now
= a (1

n) [u0 (qm )

1] +

so the derivative of the right hand side is
qm + 1

which is guaranteed if

a (1

n) [u0 (qm ) 1] +
1
=
1
a (1 n) u00 (qm )
[u0 (qm ) 1]
1 2
qm
+
> 0
00
(1
) u (qm ) a (1 n) u00 (qm )

is higher than 1=2. Therefore under this condition the RHS

of (26) is increasing in . Now, at
a (1

= , we have qm = q so that (26) becomes
n) q +
28

q

This condition is satis…ed if
condition holds for some

is close enough to one and

, then (26) holds for all

condition does not hold, then

is small enough. If this

> . However if the above

must be increased. Then either there is a ( ) high

enough so that (26) holds with equality (and therefore holds with strict inequality for
all

> ( )), or (26) never holds (this is the case if for instance

RHS of (26) reaches an asymptote as

! 1, which depends on the third derivative

of the utility function). Therefore, there is a
( ). Furthermore

and only if

0

is large and the

0

such that for all

0

<

, (26) holds if

( ) > 0.

Finally, a cash-credit equilibrium will not exist if the expected payo¤ from participating in the credit scheme is negative, that is if
a (1

n) [u (q )

q ]

(1

)

0;

or if
b=

a (1
(1

n)
[u (q )
)

q ]

:
= max fb; 0 g :

Therefore a cash-credit equilibrium exists if and only if

7.3

Proof of Proposition 3

Proof. Credit increases welfare relative to cash whenever the expected welfare in the
credit economy is higher than the expected welfare in the cash economy, i.e., when
1

fa (1

1

n) [u (q )

q ]

an ( qsy + pqsy )+ m+1 +

) g

(1

1

a (1

n) [u (q )

Recalling that p = 1 and m+1 = qm , this is equivalent to
1
1

fa (1

n) [u (q )

q ]

) g

(1

qm +

1

a (1

n) [u (q )

q ]

Which, under the best-case scenario for cash (Friedman rule) is the same as
1
1
(1

fa (1
) a (1

n) [u (q )
n) [u (q )

q ]
q ]

(1
(1

) g
)

q +
(1

29

1
) q

a (1

n) [u (q )

q ],

q ]

Therefore credit dominates cash for
>

7.4

a (1

n) [u (q )

q ]

q

Derivations of NSR and merchant fees

Recall the NSR holds if
q

L

Using the lower bound on L from (26), this will hold when
qm +
setting

a (1
1

n)

[u (qm )

u (q )

(qm

q )]

q

= , this reduces to
q ,

q
(1

)q

which is always true.
Let us now check the upper bound value for K. Again using the lower bound on
L we have
anK =

anK
When

(1

)

(1

an) L

(1

)

(1

an)

(1

an )

(1

a (1 n)
[u (qm ) u (q ) (qm q )] ,
1
a (1 n)
[u (qm ) u (q ) (qm q )]
qm +
1
qm +

an)

= , the last inequality becomes
K

(1

an)
q
an

(1

an )
an

When they sell for cash, producers get p (1 nn) q which equals in terms of the numeraire
good p (1 nn) q =

(1 n)
q
n

(1

. But since

an)
q
an
(1 an) q

(1

an )
an
(1 an )
30

(1

n)

q ,
n
a (1 n) q

holds for a close enough to 1 and

> 0, producers paid by credit are receive less

than those who are paid by cash (note however that a cash producer must still make
a payment to the CCS as an “inactive”agent to remain within the CCS). Under the
no-default condition, however, producers are still willing to participate in the CCS,
and receive payment through the CCS, as they will bene…t from the CCS when they
are consumers.

31

References
[1] Aiyagari, S. Rao and Stephen D. Williamson, 2000. “Money and Dynamic Credit
Arrangements with Private Information,” Journal of Economic Theory, 91 (2),
248-79.
[2] Bhattacharya, Joydeep, Joseph Haslag, and Steven Russell, 2005. “The Role of
Money in Two Alternative Models: When is the Friedman Rule Optimal and
Why?”Journal of Monetary Economics 52, 1401-1433.
[3] Berentsen, Aleksander, Gabriele Camera, and Christopher Waller, (forthcoming). “Money, Credit and Banking,” forthcoming in the Journal of Economic
Theory.
[4] Chakravorti, Sujit, 2003. Theory of Credit Card Networks: a Survey of the
Literature, Review of Network Economics 2, 50-68.
[5] Chakravorti, Sujit and Ted To, 1999. “A Theory of Credit Cards.” Federal Reserve Bank of Chicago Working Paper 1999-16.
[6] Committee on Payment and Settlement Systems, 2006. Statistics on payment
and settlement systems in selected countries-Figures for 2004 (Basel, Bank for
International Settlements).
[7] Corbae, Dean and Joseph Ritter, 2004. “Decentralized Credit and Monetary
Exchange without Public Record Keeping,”Economic Theory, 24, 933-951.
[8] Evans, David S., and Richard Schmalensee, 2005. “The Economics of Interchange
Fees and Their Regulation: an Overview.” Paper delivered at Interchange Fees
in Credit and Debit Card Industries: What role for Public Authorities?, Federal
Reserve Bank of Kansas City, May.
[9] Freeman, Scott, 1996. “The Payments System, Liquidity, and Rediscounting,”
American Economic Review 86, 1126-1138.
32

[10] Garcia-Swartz, Daniel D., Robert W. Hahn, and Anne Layne-Farrar, 2006. “The
Move Toward a Cashless Society: A Closer Look at Payment Instrument Economics,”Review of Network Economics 5(2), 175-198.
[11] Gerdes, Geo¤rey, Jack K. Walton II, May X. Liu, and Darrel W. Parke, 2005.
“Trends in the Use of Payment Instruments in the United States,” Federal Reserve Bulletin 91, 180-201.
[12] Humphrey, David, Magnus Willesson, Ted Lindblom, and Göran Bergendahl,
2003. “What Does It Cost to Make a Payment?”Review of Network Economics
2(2), 159-174.
[13] Hunt, Robert M., 2003. “An Introduction to the Economics of Payment Card
Networks,”Review of Network Economics 2, 80-96.
[14] Kahn, Charles M. and William Roberds, 2005. “Credit and Identity Theft,”
Federal Reserve Bank of Atlanta Working Paper 2005-19.
[15] Klee, Elizabeth, 2006. “Families’Use of Payment Instruments during a Decade of
Change in the U.S. Payment System,”Board of Governors of the Federal Reserve
System Finance and Economics Discussion Paper 2006-01.
[16] Kocherlakota, Narayana R., 1998. “Money is Memory,” Journal of Economic
Theory 81, 232-251.
[17] Koeppl, Thorsten, Cyril Monnet, and Ted Temzelides, 2005. “A Dynamic Model
of Settlement.”
[18] Lacker, Je¤rey M. and Stacey L. Schreft, 1996. “Money and Credit as Means of
Payment,”Journal of Monetary Economics 38, 3-23.
[19] Lagos, Ricardo, and Randall Wright, 2005. “A Uni…ed Framework for Monetary
Theory and Policy Analysis,”Journal of Political Economy 113(3), 463-484.

33

[20] Lowe, Philip 2005. “Payments System Reform:

the Australian Expe-

rience,” Remarks prepared for the Federal Reserve Bank of Kansas
City Conference on “Interchange Fees in Credit and Debit Card Industries:

What

role

for

Public

Authorities?” Accessed

online

at

www.kansascityfed.org/publicat/psr/proceedings/2005/lowe.pdf.
[21] Macfarlane,
at

the

Ian

AIBF

J.,

2005.

Industry

“Gresham’s

Forum.

Accessed

Law

of

online

Payments,” Speech
at

www.rba.gov.au/

speeches/2005/sp_gov_230305.html.
[22] Martin, Antoine, Michael Orlando, and David Skeie, 2006. “Payment Networks
in a Search Model of Money.”
[23] Rochet, Jean-Charles and Jean Tirole, 2002. “Some Economics of Payment Card
Associations,”Rand Journal of Economics 33(4), 549-570.
[24] Rochet, Jean-Charles and Jean Tirole, 2004. “Two-sided Markets: an Overview.”
IDEI working paper, University of Toulouse.
[25] Rochet, Jean-Charles and Jean Tirole, 2006. “Externalities and Regulation in
Card Payment Systems,”Review of Network Economics 5(1): 1-14.
[26] Telyukova, Irina A., and Randall Wright, 2006. “A Model of Money and Credit,
with Application to the Credit Card Puzzle.”

34