As the other two answers put it, I dont think there is any way you can make a logical increasing percentage per timeframe, due to scarcity being illogical to normal life. (specifically for westernized, more developed countries in our world)
What I would suggest is look at real life examples of what happens when the brown stuff hits a fan.
examples - The current (July 2021) water scarcity in Iran, the current problems being faced in Cuba, as mentioned by @o.m. the great toilet paper crisis of 2020, and any number of other times that humans have been even mildly inconvenienced by famine, plague and war.
It is in human nature that we all want what is best for ourselves, and who among us can honestly say that when it is a matter of life and death, we would not screw over the next guy if it gives even the hope of something better for yourself and family?
The examples I am most familiar with, as they occurred in my country, are the great cigarette shortage, the alcohol shortage, and the current KZN crisis.
The first two occurred when covid first hit, and the gov ordered lockdowns for two weeks. To go with this, was a complete ban on the sale of alcohol and cigarettes. As there was no legal way to get these things, people had to go to illegal traders, who could charge what they wanted. for comparison, a packet of 20 cigs costs about R35 on average, about \$2.40, and a bottle of beer is around R20, \$1.37. once the ban came into effect, traders were selling cigarettes for anywhere between R100-R200, \$6.87 - \$13.75, and a bottle of beer for about R75, \$5.
After two weeks, when the lockdown and the ban was extended by a further month, the prices increased overnight, with some traders selling up to R650, \$44,68 for cigarettes and about R200 for beer, about \$13.
I use only beer as the example because it would be to long if I went into the price of spirits, wines etc.
With the current KZN crisis, some stuff happened in the country that I am not going to get into, but basically rioters stole and burned a couple of trucks on the main highway between the port in the province of KZN and the economic heart of the country in Gauteng, effectively blocking it. They and other looters then began attacking shops and shopping centers, with a fair amount of the usual looting Tvs, fridges etc, but also burning down entire shopping centers, wholesale markets etc. Within literally 2 days, the price of food had increased about 1000%, and that was just for basics like bread. About R15, \$1 for a loaf beforehand, was now selling for close to R100, \$7
in 2 days.
There are many other examples as stated above from around the world, So again, I would say look into some of those, and see how it would play out in your world.
What is produced and available locally, what would people be willing to pay for something before they say nah, what would smugglers be willing to risk for the rewards. There is a whole plethora of things that can have an effect on what becomes sought after.
Who would have thought it would be toilet paper?