# Decision to make one side of a multisided platform the subsidy side

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?

Yes. For example, in Armstrong (2006), a monopoly platform sets the price for side 1, $p_1$, such that

$$\frac{p_1-f_1+n_2\alpha_2}{p_1}=\frac{1}{\eta_1}$$

where $f_1$ is the unit cost on side 1, $n_2$ is the number of consumers on side 2, $\alpha_2$ is the cross-side externality created by each side 1 consumer, and $\eta_1$ is the conditional price elasticity of demand on side 1.

Thus, side 1 consumers get subsidised (i.e. $p_1<f_1$) if

1. their demand is very elastic
2. they create a big externality for the other side.

That's the basic principle. Subsidise the guys who create a lot of value and who would run away if the price were high.

Thus, for example, nightclubs offer free entry to females rather than males if the owners believe that females are more price sensitive and that men care more than women about meeting members of the opposite sex (I let you decide for yourself whether that's true or not).

By the way, we can compere this equation to the one a normal monopolist would use:

$$\frac{p-f}{p}=\frac{1}{\eta}.$$

The reduction in price to internalise the network externality can clearly be seen.