The Proportional Fee, Transaction Fee and Membership Fee

There are in general three types of fees used by platforms: the fixed membership fee, transaction fee and proportional fee. In real-life, all three fees are used by different platforms. Often, the fee charged by the market maker is a combination of the fixed, transaction and proportional fees. We try to offer a rationale for the usage of these fee structures. Compared with the transaction fee, the profit for the platform is higher under the proportional fee. If the consumption value is high enough, then the profit under the membership fee is the lowest. If the value is low enough, then the profit under the membership fee is the highest. If the value is in the middle, then the profit under the membership fee is in the middle as well. However, when we allow free entry of merchants, results are different. The profit of the card network could be lower under the proportional fee than the transaction fee with free entry of merchants. Equilibrium under the proportional fee and the membership fee is the same. Consumer surplus is lower under the transaction fee than the proportional fee and the membership fee. But social welfare could be higher under the transaction fee. We also consider regulation of the fee structure and the optimal fee.