I'm reading Matchmakers: The New Economics of Multisided Platforms by economists David S. Evans and Richard Schmalensee.
They describe how businesses often make a rational choice to allow one side of their "matchmaking" business to be the "subsidy side", i.e. the side paying a negative price, and the other side to be the "money side", as in the side that pays fees to the business. Here "matchmaking" means serving as an intermediary that lowers the transaction cost of connecting 2 or more populations, such as Visa connecting shoppers and retailers.
For example, PayPal pays (or used to pay) consumers for signing up for the service, so they're the subsidy side. Businesses typically pay the fees and are thus the "money side".
Is there an equation, formula, or inequality that describes how the business chooses which side to treat as the subsidy or money side?