Increased demand for some goods will create competition and prices will stay the same or fall. Commodity goods providers don't have pricing power so they can't raise prices without losing sales to competitors. There is also the "menu cost" which is the resistance of businesses to react in real time to economic events. A restaurant won't reprint menus everyday and the $1.99 cleaner won't change prices very often.

In addition. The total money supply isn't growing, it is being redistributed to people more likely to consume. The velocity of money will increase but the total amount won't. This will keep prices relatively stable.