"Free" is a price. Research has shown that "free" is an especially powerful price or label, changing behavior more dramatically than most other factors. Synonyms currently in vogue for "free" include "open" and "public." It's unclear if these terms have the same market power as "free."

Providing free content to readers has been a disruptive pricing model on the Internet. If you want evidence of this, ask a newspaper publisher -- assuming you can find time with them as they scramble to put the "free" genie back in the bottle. "Free" drained newspaper coffers, caused newspapers to collapse, led to the layoffs of hundreds of journalists, and shifted the news market toward new funding approaches.

The initial hope of "free" newspaper content -- the business gamble -- was that advertising payments would balloon in pursuit of the huge audiences "free" would spawn, thereby surpassing the value of subscriber payments, and leading to a big payoff. That didn't work, and now newspapers are busy building and refining paywalls for the networked economy.

In any case, because traffic is the lifeblood of any online business model, we now face click-bait headlines everywhere, today's equivalent of the "yellow journalism" of the early 20th century -- lurid, distasteful, and hard to ignore.

Other "free" content sources also have business models working behind the veneer of "free," and they are just as dependent on traffic.

Wikipedia is free to use, yet it has a successful business model -- fundraising. In its 2014-15 fiscal year, the Wikimedia Foundation (the parent) raised $75 million, its best year ever. The majority of these funds -- more than 60% -- came from the United States. Donations were smaller per donor, but more people donated. Of course, fundraising is a legitimate and time-tested business model, as NPR can attest. Because Wikipedia depends on individual donors, traffic is a key variable to its fundraising success.

"Free" has a few odd qualities. For instance, it is a condition enjoyed by as few as one party in the exchange of value. For NPR listeners who donate, NPR is not free. It could be that everyone who listens to NPR has donated, all save one person. This serves to illustrate that NPR is only free to those listeners who do not donate. The same goes for Wikipedia and its users. I've donated multiple times to both, so NPR and Wikipedia will never again be strictly "free" to me. I'm part of their paid base.

Similarly, in academic publishing, a Gold OA journal is no longer "free" to the authors of a paper published in that journal. In the same way that NPR is now never free to me because I frequently donate, OA journals are never strictly "free" to any author who has paid an APC. For a mega-journal like PLoS ONE or Scientific Reports, the journal can never be strictly "free" for thousands of researchers.

Granted, the share of costs for NPR for which I'm responsible are trivial, and constantly eroding, but they only approach zero and cannot mathematically attain zero. It is a Zeno's paradox of payments -- the tortoise and Achilles of cash.

This paradox is the same one that all business models possess at their heart, and why acquiring new customers is so critical for long-term success. Without the subscription model, publishers seeking to earn money have to move to the retail model -- asking for customers to purchase something occasionally at a point of sale. And traffic is key to this retail model, which NPR, Wikipedia, online newspapers, and more journals participate in.

For OA publishers, acquiring authors at a sufficient pace to maintain cash flows is their main financial challenge as retail publishers. They offer author services, which compete on price, convenience, and reputation. Authors shop these outlets, a retail experience. PeerJ attempted to move away from a retail model with a membership model, but it has since added a more customary per-paper APC model, signaling a move back into retail.

The subscription and membership models solve this retail paradox to a large degree through renewals. NPR strives to solve it by getting donors on monthly payment plans, and Wikipedia tries to solve it by optimizing their donation forms via A/B testing and other approaches.

New models of publishing, which have more in common with retailing, may want to look at how former retail outlets for information and services -- Amazon, Netflix, iTunes, Sam's Club, Costco, and others -- have solved the payment paradox. Blunting the pressures of full-on retailing may be a major reason the subscription model is more popular, and being utilized by more businesses, than ever.