It could, at least temporarily. But there is no reason to belive it won't stabilise again.
Increased demand without increased production will increase prices. But then producers will follow, and production will increase, and prices will stabilise.
Increased tax on the rich and distributing it to poor moves a tiny bit of the combined 'voting power' we have over production as consumers to the poor, so there will be slightly less luxury cars produced and slight more food.
Why would they produce more if they could? It must meet the demand at the current price point. More money goes to poor people, more demand for food at the current price. That will increase the price, which will increase production. Short term the price might go up a lot, but then new production will come online, and the prices will fall back to today+delta.