Prices *might* come down if there's a huge Depression, but I doubt people would like that any better than the inflation. And of course, there are other factors involved that could keep prices going up.
The only other way I can think of it happening is an executive order saying that businesses *must* reduce their prices. I have no idea if that could even be done, but I have a better idea about how much those who bought and paid for him might react to that.