CORRECTION: An earlier version of this story incorrectly attributed a comment detailing the factors that go into the retail costs of brand-name drugs. Author Mick Kolassa said the active ingredient in a drug is not what drives costs. The text has been corrected.

If you took an Ambien or similar kind of drug last night to fall sleep, the FDA thinks it still might be making you drowsy this morning — that’s a safety concern. The agency is requiring pharmaceutical companies to cut in half the amount of active ingredient it puts in each dose. So half the dose means half the price, right?

Mick Kolassa wrote the book on how pharmaceutical pricing works — really. It’s called Elements of Pharmaceutical Pricing. I asked him if cutting in half a pill’s active ingredient translates into a cheaper drug.

“The short answer to that is, ‘No’,” says Kolassa.

According to Kolassa, we’re almost never paying for the active ingredient to begin with.

But studies say we do pay a lot for research, development, and marketing.

“If you look at the price of generic Ambien, you can get an idea of what the ingredient cost might be,” Kolassa says.

The generic runs as little as $10 a month, compared to $200+ for the name brand. While consumers may not see a savings from a weaker dose, Harvard’s Dan Carpenter says drug makers could actually see a loss in the short term.

“The key effect is the publicity,” says Carpenter.

He says the FDA’s announcement might cause some patients to switch to a different drug, or quit taking sleep aids all together. In a statement, Ambien’s manufacturer — Sanofi — says it is working with the FDA, and stands behind the drug’s safety.