David A. Price and Zhu Wang
Why do debit card networks base their fees on a percentage of transaction amounts when the marginal cost of executing a transaction does not vary by amount? Research suggests that this type of fee structure, a linear ad valorem fee, maximizes profits for card networks by allowing price discrimination. Also, because percentage fees make card usage more economical for lower-value transactions, such a fee structure tends to increase social welfare.
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Mead, Tim, Renee Haltom, and Margaretta Blackwell, "The Role of Interchange Fees on Debit and Credit Card Transactions in the Payments System," Federal Reserve Bank of Richmond Economic Brief, No. 11-05, May 2011.
Shy, Oz, and Zhu Wang, “Why Do Payment Card Networks Charge Proportional Fees?” American Economic Review, June 2011, vol. 101, no. 4, pp. 1,575–1,590. (A working paper version is available online.)
Wang, Zhu, and Julian Wright, "Ad-Valorem Platform Fees and Efficient Price Discrimination," Federal Reserve Bank of Richmond Working Paper No. 12-08, November 2012.