*We are greatly indebted to the Editor and an anonymous referee for valuable comments that significantly improved this paper. We also thank Ramon Caminal and seminar participants at the University of Castellon, the University of Alicante, UAB, EEA, EARIE, WCR, JEI and ASSET for helpful suggestions. Financial support from SEJ 2007-62656 and the IVIE is also gratefully acknowledged. Any remaining errors are ours.
This paper analyzes the effects of ATM surcharges on deployment and welfare, in a model where banks compete for ATM and banking services. Foreign fees, surcharges and the interchange fee are endogenously determined. We find situations in which surcharges are welfare enhancing. Under strategic fee setting, the increase in deployment caused by surcharging might compensate the surplus loss caused by the increase in prices.
When a customer of bank a (the home bank) makes a withdrawal from an ATM owned by bank B (the foreign bank), the transaction may involve up to three prices. Bank A pays an interchange fee to bank B. This ‘wholesale’ price underlies a foreign fee that the home bank charges to its customer. On top of that, bank B may directly apply a surcharge to the cardholder. In this case, the final ATM usage fee for the customer equals the foreign fee plus the surcharge. In the U.S., surcharges were banned by the main ATM networks (Cirrus and Plus) until 1996. But they have been widely used ever since. By contrast, in Europe and Australia surcharges are still uncommon, although banks charge interchange and foreign fees.1
This paper analyzes the effect of the surcharges on consumer surplus and social welfare taking into account their impact on ATM deployment and prices. We propose a model in which two horizontally differentiated banks compete both for banking and ATM services, and compare a setting where surcharges are banned with one where they are allowed.
Our study is motivated by an ongoing debate on the role of withdrawal fees.2 Especially in the U.S., consumer groups repeatedly questioned the rationale for surcharging. Ceteris paribus, surcharging increases the cost of foreign transactions and reduces ATM network compatibility, so it harms consumers. But, ATM service providers defended surcharges because they generate direct revenues which provide incentives to increase the size of ATM networks, and ATM deployment boosts welfare.
We find deployment patterns in which surcharging increases the price of foreign withdrawals. However, endogenous ATM deployment is an important factor which can overturn the negative effect of higher prices on consumer surplus. Our main result is that surcharges might enhance social welfare and consumer surplus by stimulating deployment enough to offset the eventual increase in foreign ATM transaction prices.3 This indicates that policy makers need to assess not only the price increase brought about by surcharging, but also its effect on ATM deployment. The positive effect of surcharges on deployment and welfare comes partly from the fact that they are a direct source of revenue. But, we also identify a strategic effect: because surcharging leads to higher foreign transaction prices, the incremental value of an additional ATM to a bank's own customers is higher and, thus, banks deploy more ATM's.
To study deployment in a model where banks set all the prices involved in a foreign transaction, we assume that banks deploy ATM's at exogenous locations referred to as ‘shopping malls.’ In contrast, most theoretical models with exogenous deployment build on standard spatial competition for ATM services. However, when both deployment and pricing are endogenous, these models become intractable. In our setting, consumers visit any one of the available shopping malls with equal probability. Then, the decision to visit a particular shopping mall does not depend either on ATM availability or withdrawal price. Once at a mall, consumers can purchase ATM services only at that location, i.e., changing location is prohibitively costly. But, ATM usage at that given location does depend on ATM fees.4 Our assumptions reduce the elasticity of the demand for withdrawals at a given location, by exaggerating the travel costs in the ATM space.5
We model the size of the ATM network as a long run decision, which precedes price setting, and capture the impact of strategic deployment. When banks set prices, they can fully internalize any relative ATM network advantage.
Our analysis reveals a non-monotonic relationship between deployment costs and the impact of surcharging on welfare. That is, surcharging enhances welfare and consumer surplus if deployment costs are low, it reduces welfare and consumer surplus if deployment costs are intermediate, and it once again increases welfare and consumer surplus if deployment costs are high. To provide more intuition, let us first consider low ATM costs. Under surcharging, banks deploy ATM's at all available locations, while under a surcharge ban, there is only one ATM per location. Surcharging boosts deployment enough for consumers to use ATM's free of cost. ATM duplication is not too socially costly as ATM cost is low. It follows that surcharging is welfare increasing. Let us turn to intermediate ATM costs. Regardless of the surcharging regime, there is only one ATM per location. However, because surcharging is used strategically to gain deposit market share, it supports higher prices, and a surcharge ban is welfare increasing. Finally, consider high ATM costs. Without surcharges there is no deployment, while surcharging supports the existence of an ATM market. Hence, surcharges are once again beneficial as they provide incentives for socially desirable deployment.
This non-monotonic relation is novel in the ATM literature and suggests that regional variations in the deployment cost could be one of the factors underlying the observed differences in the deployment patterns across markets in the U.S.. Notice that the ATM cost includes both the machine and the operating costs.6
A comparison of exogenous deployment profiles reveals that banks with a larger share of monopolized ATM locations set higher surcharges and account fees.7 We find that equilibrium surcharges are above the level that maximizes ATM revenues. Hence, surcharges are not only a source of ATM revenues, they are also a strategic device employed to decrease the elasticity of the demand for banking services by widening the incompatibility of rival ATM networks. By increasing the surcharge, a bank can make its ATM network more valuable to its own depositors and, in effect, it can increase its market power in the banking market.8 Consequently, surcharging leads to higher foreign transaction prices and account fees. With endogenous deployment, surcharging increases banks' ability to exploit an ATM network advantage and, ultimately, it gives them incentives to deploy more ATM's in order to create such an advantage. A large cash dispenser network is more attractive to depositors when the cost of foreign transactions is higher. Equilibrium deployment configurations show that banks install (weakly) more ATM's when surcharges are allowed.
In our study, the surcharging regime crucially changes the effect of the interchange fee on ATM prices and, consequently, on banks' deployment incentives. With surcharges, a bank is unilaterally determining its earnings per foreign transaction carried out on its ATM network. Then, the interchange fee is neutral and does not affect either deployment or profits.9
In many countries the interchange fee is chosen jointly by the network members and has raised competition concerns.10 For most of the present paper, we consider that the interchange fee is set cooperatively by banks to maximize joint profits. However, real banking practices are rather opaque and have been the subject of much controversy. An extension of the model allows for different ways of setting the interchange fee. Changes in the interchange fee-setting affect only the ranges of deployment costs for which surcharges are welfare increasing.
Our model highlights the interplay between the deposit and the ATM markets. To gain deposit market share, banks provide ATM transactions to their own customers at marginal cost and set high surcharges, if allowed. These results echo the theoretical literature on ATM surcharging. Massoud and Bernhardt  identify the same pricing incentives although they consider on-us fees (charged to their own consumers when using a home ATM) and surcharges, and ignore foreign-fees and the interchange fee. They interpret surcharges as different prices for on-us and foreign transactions, rather than positive prices for foreign transactions.11Croft and Spencer  also show that competing banks strategically increase surcharges and reduce foreign fees to make their accounts more attractive.12 A difference in our analysis is that we recognize the effect of this pricing strategy on deployment.
Massoud and Bernhardt  study the interaction between deployment decisions and ATM pricing. In a spatial model where consumers receive bank specific location shocks and banks set account fees, on-us fees and surcharges, they find that competition among banks gives rise to overprovision of ATM services (compared to the socially optimal network size). However, they do not analyze a surcharge ban.13
The next section presents the benchmark model. Sections 3 and 4 analyze the cases without and with surcharges, respectively. The effects of surcharges on deployment and welfare are identified in section 5. Section 6 unfolds two extensions of the model. First, it allows for alternative interchange fee-setting. Second, it examines a different order of moves where banks are unable to commit to ATM prices. We conclude in section 7. All proofs missing from the text are relegated to the appendix.
We consider two banks (A and B) located at the extremes of a segment of unit length where consumers' locations are uniformly distributed. They obtain gross utility V from banking services. Consumers' transportation cost is given by C(d)=d, where d represents distance. In order to open an account at bank j, customers must pay an account fee Fj, j=A, B. The total number of consumers is normalized to one.
Apart from deposit accounts, banks offer to customers ATM cash withdrawal services. The marginal costs of providing ATM and banking services are normalized to zero. The use of an ATM of the home bank (with which the consumer has an account) is priced at marginal cost.14 In order to use an ATM of a foreign bank i (with which the customer does not have an account) the customer has to pay a foreign fee Fj to the home bank and, eventually, a surcharge si to the owner of the ATM. Furthermore, the home bank pays an interchange fee a to the foreign bank. Our assumptions on the pricing of ATM transactions are meant to describe actual practices.
We assume that banks can only deploy ATM's at exogenously given locations denominated ‘shopping malls.’ Consumers visit any of the M available shopping malls with an exogenous equal probability, 1/M. This implies that ‘distance’ plays no role in the demand for ATM services. At a mall, consumers require ATM services only at that specific location. Switching locations is assumed to be prohibitively costly. Although consumers' choice of a shopping location is not driven by the existence of ATM's and their withdrawal fees, at a given mall consumers' decisions to withdraw depend on ATM prices. Consumers' valuation of an ATM withdrawal at a shopping mall is denoted by v, where v is a random draw from a uniform distribution on [0,1]. This framework allows us to study deployment in a model where the three prices involved in a foreign transaction are considered.
In the main body of the paper, we analyze the following five-stage game. In the first stage, banks cooperatively choose the interchange fee to maximize industry profits. In the second stage, banks decide in which shopping malls to deploy an ATM. The cost of deploying an ATM is denoted by k, where k0. In the third stage, banks set the account fees, the surcharge (if allowed) and the foreign fee. In the fourth stage, consumers choose a bank in which to open an account. In stage five, each consumer goes to the shopping mall, observes her realization of v, and decides whether to use an ATM (if available) or not.
Notice that with this order of moves, consumers take into consideration ATM fees when they decide where to open an account. In this case, banks are able to commit to ATM prices and to use them strategically to increase their market share. We solve for the subgame perfect Nash equilibrium of the model by backward induction. We first analyze the case where surcharges are banned and then extend the model to allow for surcharges.
III. THE CASE WITHOUT SURCHARGES
In the last stage, if a customer ends up in a shopping mall with an ATM of the home bank, she uses that ATM since it is free of charge. However, if the customer is at a shopping mall with a stand-alone ATM of the foreign bank, she uses the cash dispenser if her valuation of a withdrawal exceeds the ATM fee, that is, if vFj.
In stage 4, consumers decide where to open an account.15 They have to compare their expected utility of opening an account at bank A and B. For a consumer located at x, they are given respectively by:
where C denotes the number of malls with overlapping ATM's and where Ni represents the number of malls with a stand-alone ATM belonging to bank i. Observe that the first three terms in (1) and (2) capture the consumer's net utility from general banking services, whereas the last two terms represent her expected net utility from the ATM market.
Consider a customer of bank A. With probability (C+NA)/M, she visits a mall with a home ATM. Her expected valuation of a cash withdrawal is 1/2 and home ATM usage is free of cost. With probability NB/M, she visits a mall with a stand-alone foreign ATM. Given that the cost of a withdrawal is fA, her expected net utility is (1−fA)2/2.
This expression makes clear that, despite the symmetry in the banking service market, the ATM market introduces an element of vertical differentiation: banks offer different ATM services. The magnitude of the vertical differentiation is captured by the first term in (3). The ‘quality’ of the overall services of bank A increases in (NA−NB). The reason is that consumers prefer to withdraw cash from a home ATM (at zero cost) than from a stand-alone foreign ATM (at cost fi>0).
The first term in expression (3) has strong implications on the deployment decisions of banks. For given prices, in order to provide a relatively better service, bank A can either increase its number of stand-alone ATM's (increase NA) or increase its number of overlapping ATM's (decrease NB). Either way leads to the same marginal increase in quality.
This expression spells out the impact of the own and the rival account fees on the demand for A. It also captures the impact of withdrawal pricing. By reducing its foreign fee, bank A becomes more attractive to its own depositors, because they face lower foreign withdrawal prices. Similarly, by increasing its foreign fee, bank B makes foreign withdrawals more costly for its own depositors, and loses depositors in favor of bank A.
In the third stage banks choose foreign fees (Fj) and account fees (Fj) to maximize their profits. A bank's profit sums up the revenue from banking services, the revenue (net of the interchange fee) from own customers who use foreign ATM's, and the revenue from foreign customers who use bank's own ATM network.
Then, bank A's profit is:
where x is given by (4).
The equilibrium values of the foreign and the account fees are, respectively,
for i, j=A, B and i≠j.
Notice that an increase in the foreign fee above marginal cost reduces the demand for ATM transactions and the surplus created in the ATM market. Then, banks prefer to provide foreign ATM transactions to their own customers at marginal cost in order to maximize the surplus in the ATM market. The reason is that they are able to absorb the surplus through a higher account fee. This intuition underlies the result in (5). Massoud and Bernhardt  and Croft and Spencer  report similar findings.16
Let us now examine the equilibrium account fees in (6). The first term is the level of the account fee without an ATM market. The second term represents the opportunity cost of attracting a new customer, that is, the lost ATM revenues that the customer would have generated if affiliated with the other bank. Notice that own depositors do not generate ATM revenues to the home bank, as the foreign fee equals the interchange fee (see 5). But, non-depositors generate positive expected revenues equal to a(1−a)Ni/M. With probability Ni/M a depositor of j, visits a mall with a stand-alone foreign ATM, and pays the foreign fee (equal to a) whenever her valuation of a withdrawal is high enough (with probability 1−a). The third term is related to the vertical differentiation introduced by the ATM market: a bank with a larger network can charge a higher account fee.
Finally, observe that an increase in the interchange fee pushes up the earnings per foreign transaction, but also reduces the total number of withdrawals. Consequently, in our model the account fee is non-monotonic in the interchange fee. In contrast, Padilla and Matutes  and Donze and Dubec  find that the account fees always increase in the interchange fee. Their studies of ATM deployment allow for the interchange fee, but abstract away from direct ATM fees.
Next, we analyze the second stage of the game. Each bank chooses the number of ATM's to install and their location. Recall that the cost of an ATM is k>0.
It is useful to write down the profits of firm i as a function of the number of its stand-alone ATM's (Ni), the number of its overlapping ATM's (Ci) and the total number of the rival's ATM's (Tj).
The first term in (7) gives the profits without an ATM market. The existence of an ATM market generates direct ATM revenues (second term in 7). In addition, deployment creates vertical differentiation in the deposit market and allows the banks to make extra revenues (third term in 7). Observe that the third term depends on the relative ATM network advantage (i.e., the difference in stand-alone ATM's). The last term in (7) captures the cost of deployment.
Observe that Ci=Cj. Note also that installing a stand-alone ATM is more profitable than overlapping an ATM of the competitor (∂Πi/∂Ni∂Πi/∂Ci). In terms of vertical differentiation in the banking service market, both an additional stand-alone ATM and an additional overlapping ATM generate the same marginal increase in quality (see expression 3). But, in the ATM market a stand-alone ATM generates revenues from foreign customers and increases the value of the home ATM network to the own depositors.
As the profit function of firm i is convex with respect to Ni and Ci,17 banks have only three possible optimal deployment strategies:18
a)no deployment: to install no ATM;
b)stand-alone deployment: to install an ATM in every mall without a cash dispenser;
c)full deployment: to install an ATM in every shopping mall.
This implies that there can only be three types of equilibria: no deployment, full deployment (every bank installs one ATM in every shopping mall) and stand-alone deployment (one bank installs tM ATM's, the other bank installs M−t ATM's and the ATM's do not overlap).
The following proposition presents the equilibrium deployment:
Proposition 1. At equilibrium,
–if no ATM is deployed;
–if there are M stand-alone ATM's;
–if each bank deploys M overlapping ATM's.
Figure 1 depicts the threshold functions and . They divide the (a, k) space into three different regions. Above , no ATM is deployed in equilibrium (region A). Between and , there are M stand-alone ATM's (region B). Finally, below , there are 2M ATM's (region C).
Observe that in the central region there might be multiple equilibria. There is always an equilibrium in which one bank deploys M stand-alone ATM's. Whenever there are multiple equilibria, we select the one that maximizes the joint industry profits. This is the one in which one bank deploys M stand-alone ATM's.19
The remainder of this section focuses on cooperative interchange fee-setting. Given the important impact of this fee on deployment, subsection 6.1 considers alternative ways to set the interchange fee.
In the first stage, banks jointly set the interchange fee in order to maximize total profits. The interchange fee plays a crucial role in ATM deployment. For a given value of k (), by increasing the value of a, the number of ATM's increases in equilibrium, going from no deployment to M ATM's and then to full deployment (see for instance k′ in Figure 1). The joint industry profits gross of ATM costs are the same under full deployment and under no deployment. Note that under these configurations the interchange fee plays no role because there are no foreign transactions. As under no deployment banks do not incur in further costs, the worst situation for banks is full deployment. Figure 1 illustrates that no deployment can always be implemented by choosing a=0. Therefore, we only have to compare joint profits under no deployment (JPN=1) with joint profits under stand alone deployment (JPA(a)). It is straightforward that JPA(a) are maximized at . If k>0.251/M, it follows that . Then, the optimal interchange fee is a*=0. If 0.251/M, then , which implies that induces stand-alone deployment.20 As , the optimal interchange fee is . If k<0.041/M, , which implies that the highest interchange fee that induces stand-alone deployment is . As , the optimal interchange fee is . The next proposition summarizes the results.
Proposition 2. Optimal interchange fee and equilibrium deployment. The interchange fee that maximizes joint industry profits is
If k0.251/M one of the banks installs M stand-alone ATM's. Otherwise, no ATM's are deployed.
IV. THE CASE WITH SURCHARGES
Consider the same setting with the difference that a customer who uses a foreign ATM pays a surcharge (si) to the foreign bank i. The surcharge provides a new source of revenues and a strategic device which change banks' incentives to deploy ATM's. As before, in the last stage, if a customer of bank j ends up in a shopping mall with a home bank ATM, she uses that ATM. If she visits a mall with a stand-alone ATM of bank i, she uses the ATM if v>Fj+si. Observe that, with surcharges, the final ATM usage fee for the customer equals the foreign fee plus the surcharge.
In stage four, consumers choose a home bank. Proceeding as in the previous section and taking into account that the price of a foreign transaction at bank j's ATM is Fj+sj, we obtain the market share of bank A:
The impact of the account and foreign fees on the demand are essentially the same as under a surcharge ban (see (4) and the related discussion). In addition, expression (8) captures the effects of own and rival surcharges on demand. An increase in bank A's surcharge, makes foreign transactions more costly to the customers of bank B, and provides them with an incentive to open an account with A. Similarly, an increase in the surcharge of bank B, makes an account with bank A less attractive, to the extent to which A's depositors use B's ATM network.
Then, in the third stage, banks choose foreign fees (Fj), account fees (Fj) and surcharges (sj) to maximize their profits. Bank A makes profits
where x is given by (8).
As in Section 3, a bank's profit is the sum of the revenue from banking services, the net revenue from own customers who use foreign ATM's and the revenue from foreign customers who use a bank's own ATM's. But, in (8) and (9), the demand for deposits, the demand for ATM transactions and the earnings per foreign transaction also depend on the surcharges.
Expression (9) makes clear that the profit functions of the banks could be written as a function of the revenue per transaction ( and ). This is what is determined in equilibrium. An important implication of this fact is that the interchange fee plays no role in this case.
One shortcoming of the case with surcharges is that, for computational reasons, we need to use numerical methods to derive the equilibrium. That is, we need to calculate the equilibrium prices separately for each possible configuration of ATM's. The analysis is, to some extent, simplified by the fact that profits gross of ATM costs only depend on stand-alone ATM's (see expression (9)). Therefore, two different deployment configurations with the same number of stand-alone ATM's for banks A and B, lead to the same equilibrium prices. To reduce the number of relevant configurations, we solve the model for M=2. In this case, we need to consider only Finally, notice that the ‘no deployment’ and ‘full deployment’ lead to the standard Hotelling model. The next proposition presents the equilibrium prices and market shares for the three situations.
Proposition 3. If (NA, NB)=(2, 0) then, at equilibrium, fA=1.294, fB=0.921, sA=0.684−a, fB=a and x=0.539. If (NA, NB)=(1, 1) then fi=1.111, si=0.666−a, fi=a for all i and x=0.5. If (NA, NB)=(1, 0), then fA=1.147, fB=0.962, sA=0.675−a, fB=a and x=0.518.
Notice that when , as bank B does not deploy ATM's, bank A cannot charge a foreign fee (its customers are unable to make foreign transactions) and bank B cannot surcharge.
The account fees are determined by the opportunity cost of attracting a new depositor (i.e., by the lost ATM revenue) and by the degree of vertical differentiation. This was also the case under a surcharge ban (see expression 6). To highlight the first factor, consider a case without vertical differentiation, (NA, NB)=(1, 1). The account fee of bank i exceeds 1 (its level without an ATM market) exactly by the opportunity cost of attracting a new customer. If the depositor chose the rival bank (j), she would visit a mall with a stand-alone ATM of i with probability 1/2 and she would make a withdrawal with probability 1−si−Fj. Then, bank's i opportunity cost from attracting a new customer is Notice that, in Proposition 3, for (NA, NB)=(1, 1), the fees are Fj=a and si=0.666−a. Then the opportunity cost is exactly 0.111 and we can recover fi=1.111.
Proposition 3 allows us to study the effect of an increase in a bank's share of the ATM market on its surcharge and account fee. For instance, comparing the case (NA, NB)=(1, 1) with (NA, NB)=(2, 0), one can see that an increase in the share of the ATM market of bank A from 50% to 100%, increases both the surcharge and the account fee of bank A. The empirical study of Hannan et al. (2000) supports positive correlations between a bank's share of the ATM market and its surcharges and account fees. Massoud and Bernhardt  also report these relations when dealing with an asymmetric model. Vertical differentiation (through ATM fleet size) weakens the competition for deposit accounts. As expected, it also increases the surcharge.
Our findings imply that equilibrium surcharges are above the level that maximizes ATM revenues (i.e., 0.5−a). This indicates that surcharges are used not only to obtain ATM revenues, but also to strategically widen the incompatibility between rival ATM networks with the aim of decreasing the elasticity of the demand for banking services. Massoud and Bernhardt  and Croft and Spencer  obtain the same result, which is validated also by the applied work of Knittel and Stango . Banks can use surcharges as a business stealing device: higher surcharges make a bank more attractive in the deposit market. Strategic fee-setting underlies higher ATM prices in our model.
Finally, notice that Proposition 3 points to positive correlations between surcharges and account fees, and surcharges and deposit market shares consistent with the empirical research conducted by Knittel and Stango  and Massoud et al. , respectively.
In stage 2, banks make their ATM deployment decisions. Knowing the equilibrium prices, we can derive banks' profits. Table I presents the payoff matrix in the deployment game. Bank i chooses the total number of ATM's it deploys, Ti.
Table I. PAYOFF MATRIX IN THE DEPLOYMENT GAME
Observe that, when (TA, TB)=(1, 1), each banks installs a stand-alone ATM (that is, also (NA, NB)=(1, 1)). Installing a stand-alone ATM is more profitable than overlapping a rival ATM.
For some values of k there are multiple equilibria. In these cases, we select the equilibrium that maximizes the joint industry profits.
The following proposition summarizes the equilibrium deployment.
Proposition 4. If k<0.036, there are two overlapping ATM's at each mall. If 0.036k0.1483, each bank deploys one stand-alone ATM. If 0.1483k0.1485, one of the banks installs two stand-alone ATM's. If k>0.1485, no ATM is deployed.
Notice that for 0.039k0.037 there are two equilibria: one in which each bank deploys two overlapping ATM's and another one in which each bank deploys one stand-alone ATM. For 0.037k0.1483 there are also two equilibria: one in which each bank deploys one stand-alone ATM and one in which only one bank installs two stand-alone ATM's. In both cases, we select the equilibrium where each bank deploys one stand-alone ATM because it generates higher joint industry profits.
V. THE EFFECT OF SURCHARGES ON DEPLOYMENT AND WELFARE
This section contrasts the market outcomes with and without surcharges in order to identify the effect of surcharging on social welfare. Surcharges affect both banks' incentives to deploy ATM's and the pricing of foreign ATM transactions.
Figure 2 illustrates equilibrium deployment with and without surcharges as a function of k.
Clearly, banks install (weakly) more ATM's when surcharges are allowed. Surcharging allows the banks to unilaterally determine their earnings per foreign transaction. Our previous results indicate that banks use surcharges strategically to increase the cost of foreign transactions and become more attractive in the deposit market. That is, surcharging allows a bank to better exploit any ATM network advantage. Then, when banks make deployment decisions, surcharging gives them incentives to create an ATM network advantage by deploying more ATM's.
We can also use Figure 2 to follow the evolution of foreign ATM transaction prices. In particular, for 0.036<k<0.125 in one of the regions where deployment is the same with and without surcharges, ATM prices are higher with surcharges (si+Fj=0.666) than without surcharges ( fi=a*=0.507).
Thus, a surcharge allowance has two conflicting effects on welfare. On the one hand, surcharges stimulate deployment and increase welfare. On the other hand, for a given deployment, surcharges push up ATM prices and harm consumers. The following proposition presents the outcome of this trade-off.
Proposition 5. If k0.031 or 0.125k0.1485 welfare and consumer surplus are higher with surcharges. If 0.031k0.125, welfare and consumer surplus are higher without surcharges. If k>0.1485, both regimes yield the same surplus as no ATM is deployed.
Our result points to a non-monotonic relationship between the deployment costs and the impact of surcharging on welfare. In our setting, the equilibrium deployment pattern is sensitive to changes in the ATM cost, k. In this case, the effect of surcharging on welfare, which crucially depends on deployment, is written in terms of the ATM cost. Below, for different ranges of k we explain the interactions which underlie Proposition 5.
For k0.036, under surcharging there is full deployment, while without surcharges there are two stand alone ATM's. The surcharges maximize the surplus in the ATM market because withdrawals are priced at marginal cost, and lead to higher consumer surplus. At the same time, surcharging duplicates deployment costs. It follows that, surcharging (full deployment) leads to higher welfare whenever the deployment cost is low enough (that is, for k0.031).
For 0.036<k<0.125, regardless of the surcharging regime, there is stand-alone deployment. In this region, the strategic effect of surcharging leads to higher ATM prices (0.666 vs. 0.507). Consequently, welfare and consumer surplus are higher without surcharges.
For 0.125k0.1485, under surcharging there is stand-alone deployment and without surcharges there is no deployment. The benefits associated with the creation of an ATM market exceed its cost. It turns out that welfare and consumer surplus are higher under surcharging.
To summarize, in a model in which both ATM prices and deployment are endogenous, we find instances where surcharging enhances welfare. The increase in total surplus generated by the larger ATM networks completely compensates for the harm to consumers caused by the higher transaction prices. The empirical study of Knittel and Stango  supports our findings.21 These results inform the policy debate in ATM markets: to correctly assess the impact of surcharging, both their effect on prices and ATM deployment need to be taken into account.
VI(i). Alternative Criteria for the Choice of the Interchange Fee
So far we have assumed that the interchange fee is set to maximize joint industry profits.22 Antitrust cases involving major EFT networks in U.S. and Europe support the relevance of this supposition.23 Still, some networks (for instance, LINK) do use cost surveys in interchange fee-setting. Whether banks choose the interchange fee to maximize profits, or just to recover network/ATM costs is an open policy question.
For this reason, we consider in this extension alternative interchange fee-setting. The exercises we present below show that different interchange fee-setting regimes only change the range of deployment costs for which surcharges increase welfare.
Let us first assume that the interchange fee is set to recover the marginal cost of providing ATM services to foreign customers. As we supposed that these costs are negligible, we have to compare welfare with and without surcharges for a=0. Figure 1 illustrates that, without surcharges, when a=0 there is no deployment in equilibrium regardless of the deployment cost (k). Then, whenever surcharging supports the existence of an ATM market (that is, for k<0.1485), it also enhances total welfare. Notice that the intuition in our benchmark model applies: surcharges increase welfare because they stimulate deployment.
Next, we suppose that the banks choose the interchange fee to maximize joint ATM market profits rather than joint industry profits. Below we present the interchange fee that maximizes joint ATM profits in the case without surcharges.
Proposition 6. The interchange fee that maximizes joint ATM profits is
If k0.060, one bank installs two stand-alone ATM's. Otherwise, no ATM's are deployed.
There is less deployment in this case than in the benchmark model (where the interchange fee is set to maximize joint profits). The reason is that ATM's not only generate direct revenues, but also lead to higher profits in the banking service market. This highlights the strategic effect of ATM's. Comparing welfare with and without surcharges under joint ATM profits maximization, we conclude that surcharges are welfare enhancing if k0.027 and 0.060<k<0.1485. Again surcharges increase welfare, because they stimulate deployment.
Finally, let us consider the interchange fee chosen by a social planner to maximize total welfare. To draw our conclusions, we inspect Figure 1 for M=2. When k>0.151, there is no deployment regardless of a. Hence, we focus on k0.151. A low interchange fee leads to no deployment, an intermediate one induces stand-alone deployment, and a high interchange fee results in full deployment. Welfare depends on the interchange fee only under stand-alone deployment. In this case, a social planner would choose the lowest interchange fee which implements stand-alone deployment, that is .
The cooperative choice of the interchange fee is not a necessary condition for surcharges to increase welfare. Surcharges may lead to higher total surplus because they change banks' incentives to deploy ATM's through the mechanism spelled out in our benchmark model. As the business stealing effect does not depend on the interchange fee, we expect our result to be qualitatively robust to any interchange fee-setting regime.
VI(ii). A Model without Commitment to ATM Pricing
Our benchmark model reveals a non-monotonic relationship between deployment costs and the surcharge/welfare interaction. We stressed the strategic effect of surcharging as an important factor leading to this relationship. We devote this subsection to the following related questions. Which is the impact of surcharging on welfare if we rule out the strategic effect of surcharging? Does the non-monotonic relationship between ATM cost and the impact of surcharges on welfare depend on the strategic effect?
To answer these questions we consider an alternative timing for the game. In this variant of the model, the prices of ATM transactions (surcharges, if allowed, and foreign fees) are set in stage 5 after consumers have chosen a home bank (in stage 4) and before deciding upon ATM use at a shopping mall (stage 6). We discuss below this model for M=2.24
Besides allowing us to clarify the forces behind our results, the new timing has empirical relevance for markets with low menu costs (where prices can be easily changed in the short run) and with large switching costs (where depositors do not shift away when ATM fees increase).
In this variant of the model, banks cannot commit to ATM prices. This rules out strategic fee setting which is a key element in our benchmark model. There banks have incentives to increase the surcharge in order to gain deposit market share. In the model without commitment to ATM prices, surcharges benefit banks only as a source of direct revenue.
Similar to the benchmark model, under a surcharge ban, ATM prices depend on the interchange fee. Then, when the banks set the interchange fee collusively, they use it to restrict deployment and competition for deposits. Under surcharging, the interchange fee is still neutral with the new timing. Consequently, it turns out that deployment is weakly higher under a surcharge allowance than under a surcharge ban. Figure 3 presents ATM deployment with and without surcharging with the alternative timing for M=2.
Without commitment to ATM prices, the surcharges do not affect depositors' decisions on where to open an account. As there is no business stealing, the incentives to increase the surcharge are lower than in the benchmark model. This leads to an important difference in the model without strategic fee-setting: The cost to the consumer of a foreign transaction with surcharges (foreign fee plus surcharge) is lower than the cost of a foreign transaction without surcharges (foreign fee).
Recall that in the model with strategic fee-setting, surcharges lead to an increase in the cost of a foreign transaction. Then, surcharging is welfare decreasing over the range of ATM costs where stand-alone deployment is independent of the surcharging regime. In contrast, in the model with no commitment, surcharges decrease ATM prices. As they also weakly increase deployment, without strategic fee-setting, surcharging always increases welfare and consumer surplus, and reduces profits. Then, the non-monotonic relationship between deployment costs and the surcharge/welfare interaction we identified in our benchmark model is indeed driven by the strategic effect of surcharging.
A comparison of Figures 2 and 3 shows that, under surcharging, deployment is weakly higher in the model with strategic fee-setting. For instance, when 0.093<k<0.148, there is no deployment under the alternative timing, but there is stand-alone deployment when surcharges have a strategic effect. Also, the range of deployment costs that lead to full deployment is wider under strategic fee-setting (k<0.036 vs. k<0.035).
In this paper we assess the impact of ATM surcharging on welfare. We compare a surcharge allowance and a surcharge ban in a simple framework which captures the interplay between the ATM and the banking service markets, and allows for strategic fee-setting. Our setting endogenizes all prices involved in a foreign transaction (surcharges, if allowed, foreign fees and the interchange fee), and also ATM deployment.
Surcharging has two conflicting effects on welfare. It increases foreign transaction prices, so it harms consumers, but it also stimulates deployment which is welfare enhancing. Our results reveal a non-monotonic relation between deployment costs and the impact of surcharges on welfare. For low deployment costs, surcharges increase social welfare and consumer surplus. For intermediate ATM costs, surcharging reduces welfare and consumer surplus. And, for high deployment costs, surcharging is once again beneficial to consumers and to society.
Our finding that surcharges may be welfare increasing matches the observed data and points to the fact that a correct assessment of surcharging needs to account both for its direct effect on prices and its impact on ATM deployment.
For tractability, our analysis leaves out several important features of real ATM markets. We focus on competition between depository institutions, but a surcharging allows non-bank deployers to enter the ATM market. By assuming ex-ante symmetry, we ignore banks attempts to extend market power from the deposit to the ATM market. Our model exaggerates the transportation costs within the ATM market, and does not consider the effects of alternative payment methods (e.g., card or online payments) on the demand for withdrawals.
A.I. Proof of Proposition 1
First, ‘no deployment’ is a best response to ‘no deployment’ only when
which occurs whenever .
Second, ‘full deployment’ is a best response to ‘full deployment’ for the competitor only if
which occurs whenever . Notice that .
When (10) holds, no deployment is an equilibrium. Full deployment is not an equilibrium, because (11) does not hold.
The existence of a stand-alone equilibrium depends on k. Consider a candidate equilibrium in which one bank installs t ATM's and the other bank installs M−t ATM's. Then, optimality of the chosen strategy requires that
This is the case whenever . However, condition (12) is incompatible with condition (10), because . Then, if , there is no stand-alone equilibrium.
When (11) holds, full deployment is an equilibrium. No deployment is not an equilibrium because (10) does not hold. Existence of a stand-alone equilibrium depends on k. It should be the case that the bank prefers to install M−t ATM's to full deployment:
This is the case whenever . However, condition (11) and condition (13) are incompatible, because . Then, if , there is no stand-alone equilibrium.
For , by construction, one bank monopolizing the ATM services in all shopping malls is an equilibrium. There may be other equilibria, but in all of them there are M stand-alone ATM's.
A.II. Proof of Proposition 3
We start with case (1, 1). The only solution to the FOC's is the one presented in the proposition. Next we verify that the second order condition for bank i (i=1, 2) holds given the equilibrium prices of bank j. Let be the profit function of bank i evaluated at the equilibrium prices of bank j. We check that is positive (negative) whenever . This implies that the optimal prices lie in the hyperplane . Then FOC's are sufficient, because is globally concave on ( fi, si).
For the remaining cases, i.e. (2, 0) and (2, 1) (or (1, 0)) the same logic applies. The key point is that the derivative of profits with respect to the account fee is linear in the account fee which allows us to focus on the hyperplane where this derivative is equal to zero. Then, we show that, on this hyperplane, the profits are a concave function of the remaining variables.
A.III. Proof of Proposition 5
The welfare function is the sum of consumers' gross utility from banking services (V), consumer surplus derived from ATM services (CSATM), bank revenues generated by ATM transactions (RATM), minus costs of ATM deployment (CATM) and transportation cost incurred by consumers when choosing the bank (TC):
Consumer surplus from ATM services is affected both by ATM deployment and surcharging:
Recall that when surcharges are banned fi=a and si=0 for all i. Under surcharging, Proposition 3 gives the prices corresponding to the relevant deployment scenarios.
Joint bank revenues from ATM services are given by:
Observe that only stand-alone ATM's generate revenues.
The transportation cost TC is
when the indifferent consumer is located at distance x from bank A. Obviously, the location of the indifferent consumer depends on equilibrium prices and deployment.
By evaluating (14) in the two scenarios (with and without surcharges), taking into account the different deployment regions given in Propositions 2 and 4, we get the result.
A.IV. Proof of Proposition 6
First of all, observe that we have ATM revenues only when there is stand-alone deployment . Revenues are maximized at a=0.479. The different regions in the Proposition are explained by the fact that if k<0.018 and if k>0.060, deployment costs (2k) are higher than ATM revenues.
1 For example, in the U.K., the three prices cannot be charged in the same transaction. This is due to an imposition by LINK, the network that operates all the ATM's in the U.K.. In fact, typically, the only price involved in the transaction is the interchange fee. However, there are banks that use foreign fees, and non-bank institutions that surcharge.
3Knittel and Stango  find empirical evidence that greater deployment often completely offsets the harm from higher fees. They estimate a structural model of consumer demand for bank accounts as a function of account fees, ATM fees and ATM deployment.
4 Actual data from Australia points to an average fraction of foreign withdrawals of about 46% between 2002-2008. See RBA PSB Report .
5Donze and Dubec  provide complementary intuition. They consider both a concentrated shopping space (with low travel costs) and a dispersed one (with high travel costs). Their results in the latter case are consistent with ours.
6 Currently, in the U.S., the typical price of the machine ranges between $5,000-$10,000. The variation can stem from differences in the capacity to hold cash, in the quality of the material used, or in the safety features. The operating costs include, for instance, phone line, power, professional cash loading service, replacement receipt paper.
7 Our results also indicate positive correlations between surcharges and account fees, and surcharges and deposit market shares.
8Knittel and Stango  find that surcharges strengthen the positive correlation between number of own ATM's and deposit fee.
9 In a model with exogeneous deployment, Croft and Spencer  report that surcharging neutralizes the collusive effect of the interchange fee.
10 In 2006, the Italian Competition Authority started an investigation of the Italian Banking Association (ABI) and its electronic banking unit (Co.Ge.Ban.). One of the allegations was that the cooperative determination of the interchange fee could prevent competition and violate Art. 81 of the EC Treaty. In 2004, Lieff Cabraser Heimann & Bernstein, LLP, filed suit against major ATM networks in the U.S. alleging that defendants had fixed the interchange fee and contending that this practice was a per se violation of the Sherman Act.
11 In effect, their ‘no surcharging’ game corresponds to a situation in which banks use a uniform price both for affiliated and non-affiliated users.
12 However, bank competition and strategic fee setting are only considered in an extension of their study which mainly focuses on bank/nonbank competition (one institution provides only ATM services) and depositor lock-in.
13Donze and Dubec  analyze ATM deployment decisions when the interchange is fixed collusively and there are no direct ATM fees. Focusing on the pervasive effect of the interchange on competition for deposits, they report overdeployment if there are many banks or consumer reservation prices are high.
14 As less than 1% of banks impose ‘on-us’ fees on home transactions, we assume that home transactions are free.
15 We assume that V is high enough so that the market is covered in equilibrium.
16 However, the first article focuses on ‘on-us’ fees rather than foreign fees.
17 Notice that the profit function is also convex in standard Hotelling models when firms invest in quality.
18 The fourth corner Ni=0 and Ci=Tj cannot be optimal, because . Observe that for the particular case a=0, we have But, in this case, by making use of , we know that if overlapping an ATM is optimal, installing a stand-alone ATM is also profitable.
19 Notice that our welfare results in Section 5 do not depend on this supposition.
20 Note that and as well as . An explicit expression for cannot be obtained.