Nothing will "happen" to the price. I mean, it's not a chemical process, or a physics process, or a mathematical process. It's not automatic at all.
A price doesn't change until a human person DECIDES to change it, and then changes it.
If gasoline becomes scarce, or if people THINK gasoline is scarce, then the companies that sell gasoline are in a powerful position. They can simply say to everyone:
"Hey people ! Gas is scarce. There's not enough to go around to everybody who wants it. So we're going to raise the price. THAT way, there will be some people who don't want to pay the higher price, or CAN'T pay the higher price, so they'll buy less gas. Then PRESTO, there'll be plenty left for everybody who's OK with the new price. Bwa-ha-ha-ha !"
And THEY raise the price of gas.
Then everybody says "The price of gas went up." but if we're very careful, we realize that's not exactly what happened. What happened was the companies that SELL us the gas RAISED the prices.
To me, that's a different thing.