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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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 (revised in November 2014).