Paying for apps such as HotSchedules, Quick Appointments, or Eavesdrop is more useful to you if your friends also buy them. That makes you likely to tell your social media friends about such apps, prompting more people to purchase them.

In recent years, businesses have been tapping the internet to cheaply and simply survey a large base of potential customers.

Companies can capitalize on this network effect to sell their products—be they apps, games, toys, or operating systems—with mathematical precision, according to University of North Carolina’s Nur Sunar, Chicago Booth’s John R. Birge, and Sinit Vitavasiri of Ericsson, the phone maker. It’s even possible for a company to determine whether it shouldlaunch a product and to figure out who the optimal buyers are on the basis of their social media friends, the researchers find.

They looked at what managers call a “promote-and-exploit product-launch” strategy. Here’s how it works: suppose a product is more valuable to you if your friends also have it because it allows you to collaborate with them (think Google Docs) or track their locations (think Find My Friends). Betting on this increase in demand, thecompany can launch the product by selling first to a select group of consumers at a lower price, and raising the price once demand increases.

The study is among the first to consider together all three stages of a product launch— development, launch, and postlaunch—and to determine mathematically a company’s optimal course of action as it moves through these phases, the researchers write.

The Equation: The fastest way to promote your product

Sunar, Birge, and Vitavasiri developed a mathematical model to represent a set of customers, capture how they are connected to one another on social media, and track whether they buy the product when it’s launched. The model was designed to evolve randomly as a business develops its product before launch, much as it would in the real world, where external forces such as bad weather or a competitor’s advertising campaign might play a role in decision-making.

First, a company has to decide whether to launch a product. If it does, it identifies a launchdate, and the model incorporates a range of possible prices. The company promotes the product selectively based on the model’s insights into which customers will be most likely to buy the product and tell their social media network about it.

The model, says Birge, “gives you a process to pick out those customers whom you would really like to target, and also gives you suggestions about how to price a product and what customers to focus on.” For instance, a product developer could home in on the most likely customers and send them a coupon.