Price Differentiation and Menu Costs in Credit Card Payments

We build a model of credit card payments where the retailers are allowed to charge differential prices depending on the instrument of payment chosen by the consumer. We follow the Rochet and Wright (2010) approach, but assuming a credit card system without a no-surcharge rule or any type of price differentiation disincentive. In a Hotelling competition framework at the retailers level, the competitive equilibrium prices are computed assuming that the store credit provided by the retailer is less cost efficient than the one provided by the credit card. In accordance with the literature, we obtain that the interchange fee becomes neutral if we eliminate the no-surcharge rule, when the interchange fee loses its ability to distort the individual consumer’s decisions displacing the aggregated consumers’ welfare from its maximum. We prove that the average price obtained under price differentiation is smaller than the single retail price under the no-surcharge rule, despite the retailer’s margins being the same in both scenarios. Furthermore, we show how some cross subsidies are eliminated when price differentiation is allowed. In addition, we introduce menu costs to prove that there is a threshold value for the interchange fee such that price differentiation is equilibrium if that fee is above this value. The threshold may be interpreted as an endogenous cap for the interchange fee fixed by the credit card industry. Finally we conclude that, even with menu costs associated to price differentiation, the consumers’ welfare can be greater in the price differentiated equilibrium than in the single price equilibrium under the non-surcharge rule.