The second issue limits the number of users you can serve, so that ARPU>cost is not good enough but you also need to worry about getting ARPUnew user > ARPUn-th user, with n being the number of users you can serve (with ARPUs ranked from high to low).

Do you agree that these are the conditions for your analysis to apply?

Agreed?

Thanks for taking the time to read my article and double-check my math! I really appreciate your insight.

Your response gave me a few thoughts.

First, fair point about market clearing price and CPI. How likely is it that you can hit that rate profitably, though?

Second, throttling messages isn't always possible. On Facebook, for example, user-to-user notifications, requests, and news feed items have to be sent as soon as the sender issues them. I'm thinking of the iLike story where they drove around SF picking up servers from everyone and their uncle.

Still, from a operational perspective I agree that this is probably the better solution for most people.

Third, viral growth leads can lead to demographic problems, too, which throttling doesn't address. By definition a viral process selects the users who are best at propagating, not necessarily best at monetizing. Controlling demographics with viral growth is much harder than controlling demographics with paid acquisition.

In any case it's something that needs to be understood, modeled, and tested.

Even if you don't agree that intentionally being “almost viral” is a good way to grow, I think it's important to understand the tradeoff and how the viral coefficient interacts

I couldn't find the formula I derived here anywhere else, so hopefully it helps someone!

If you can get k>1 you can always rate limit the speed at which you send notifications/invitations/whatever is your transport if you're crashing your servers. It's a lot harder to ratchet up k than ratchet it down.

Also, for almost all apps, there is an effectively infinite amount of advertising inventory to help you acquire customers if you can hit the market clearing rate of CPI. That very much depends on your ARPU.

As a result, you're better off focusing on lifting ARPU (or reducing churn) to increase LTV, and hence make sure that you can clear the market price for CPI

I guess that makes me a social media pornographer?