But they didn't do the analysis all together. If they did, they would see that the economic slowdown will reduce demand and curtail the amount people are willing to spend, making it difficult or impossible to raise prices. What might end up happening is that some prices will fall, those for which the effects of decreased demand are stronger than the effects of increased costs.

I am not an economist but what I understand is that the stagflation of the Jimmy Carter era is seen as due to bad policies on the part of the central bank. Basically they had this Keynesian model where the bank could choose any point they wanted on a curve trading off unemployment and inflation. But after playing this game for long enough, people began to factor in future inflation, building it into their contracts and such, and as a result inflation no longer had the stimulative effect that it used to. Basically Keynesianism only worked if nobody knew about it. Once people caught on to the con, the jig was up. That bill came due in the stagflation era.