Free
Different people have different perceptions of various price points, but things with a price point of zero—free stuff—cause us to respond in distinctly strange ways, even compared to something that costs nearly nothing.
Some research indicates we perceive free things to be more valuable than an equivalent thing for which we paid (even a small amount).
It's suspected this tendency—sometimes called the "zero price effect"—is the consequence of a common heuristic by which we compare the value of things in part based on their price; what we gain versus what we exchanged for that gain.
When we're comparing things worth $100, $10, and $1, the price-differential is relatively easy to compute (orders of magnitude). We then compare and contrast the benefits offered by each thing, line them up against the opportunity costs associated with paying out the varying sums of money, and make our choice based on those comparisons.
When we compare anything to a price of zero, though, the difference between price is more likely to scale up to something like infinite.
The distinction between something that costs $100 and $0 isn't $100 according to our internal, comparison-making mechanisms: it's $100 versus the concept of nothing, which makes the free object seem like a massively better deal than the $100 option.
That same distortion of perceptual scale seems to continue all the way down to the cost of one cent.
The psychological friction of spending anything versus spending nothing is significant, and it can shift our thinking away from the world of numbers and into the world of conceptual abstraction (the concept of zero versus a more tangible, concrete figure).
This distinction has been shown to result in more positive psychological affect because we're out nothing, but we've gained (perceptually) 100% (or infinite) more of something. This, in turn, means we're more likely to feel upbeat and happy after engaging in a transaction in which the cost to us is perceptually zero.
Pricing something at zero, then, rather than utilizing a low, low price (like one dollar or even one cent) can be beneficial if you're hoping to create demand and generate interest.
More people are likely to take and try something that costs them nothing to acquire, and some research suggests they'll be more likely to enjoy that thing (in part because it was free rather than costing them something), as well—which can mean a long-term positive valence toward your brand.
The flip-side of this effect, though, is that zero-pricing a product or service can reduce our perception of its value, long-term, and can increase our sense of incidental costs associated with acquiring it in the future.
An "incidental cost," in this context, is the cost of, for instance, traveling to a distribution point where the free things are being handed out, or the perceptual risk associated with taking a pill or receiving a vaccine.
While we're primed to enjoy free things more than things that cost us any sum of money, then, we're also primed to be less willing to endure incidental costs for something we didn't pay for (and comparably more willing to pay those incidental costs when we've already invested some amount of money in a good or service).
As is often the case in mathematics, working with zero when it comes to pricing can introduce special cases into even very strict, rigid-seeming frameworks.
Zero-priced things exist outside the typical demand curve, often result in essentially nonexistent transactional costs—which reinforces the effect—and causes fewer (or zero) psychic costs, compared to other sorts of transactions after which we might experience a blip or barrage of concern related to money, scarcity, and other concerns related to the acquisition of something new.
This makes the concept of "free" useful for some types of products and services that have a very low marginal utility, or which are meant to serve as loss-leaders for something more profitable.
But it also means "free" is a leash by which we can be psychologically dragged around, if we're not careful, because we subconsciously compute this price so differently from any other monetary value which can in turn incentivize us to make irrational decisions—including those tied to a sense of reciprocity (and debt) toward the entity giving us the free thing.
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