The question isn't why does this happen. The question is, why, in a free market, does the placebo have two different prices?
This is the wine story, redux. In that story, people thought that the more expensive wine tasted better than the cheaper one, even though it was actually the same exact wine. The important part of that story was that this wasn't an error: the brain actually perceived the wine as tastier.
The solution to this apparent human failing is that price itself is a part of taste, not just a marker of taste. A Hermes bag is more enjoyable than a knockoff, no matter how good the knockoff is. Ask anybody who has one.
What the JAMA article tells us is that the placebo effect can be augmented, fine tuned-- but this is the key-- with factors which are themselves not placebos.
The placebo pill itself-- sugar-- presumably has no effect; it is endowed with power by the doctor or researcher that the patient accepts as valid. But in this case, these placebos carry additional information that does not rely on the doctor at all-- price. The patient doesn't have to rely on the doctor's suggestion, he now has an externally valid guide to intuit a drug's effectiveness.
This works only if price is a reflection of value-- be it taste or efficacy. The problem is that, as I've previously written, drug prices are completely disconnected from their relative value, both against other kinds of medications (Nexium vs. tamoxifen) and of drugs within their own class (Zoloft vs. Prozac.)
The experiment in differently priced placebos is at the heart of what's wrong with our misguided obsession with "Big Pharma drives up prices." The public, in essence, cannot possibly fathom that a free market economy would allow, or generate, a pricing scheme that was uncoupled from quality; that allows the same object to carry different prices. Nor that a doctor would not see through such a phenomenon, if it existed.
The public doesn't yet know that drug prices and values are in no way connected, at all. Because it's not a free market.
And so, we erroneously conclude that meds are too expensive. They're not. They are artificially priced. The average person doesn't know that you don't have to use Lipitor, especially at $7 a pill. (BTW: this is why number needed to treat is such an important concept.) They still believe the doctor has made these value distinctions. But doctors have no incentive at all to make them. They don't have to worry about the money.
People believe that healthcare, and especially pharmaceuticals, are too important to leave to the free market. But there are unintended consequences of slapping aside the Invisible Hand. You may not see it slap you back.