The math doesn't support this. There is great confusion about this point. Imagine, for example, that there are people that want to buy one unit of a product made by a monopoly that is a greedy corporation trying to maximize profits. And to keep things simple, make everything discreet in dollars.
10 people are willing to pay $2
5 people are willing to pay $3
1 person is willing to pay $4
and no one is able or willing to pay more than $4
So this would be the demand curve.
Now, let's do the supply curve. Keep it simple and assume a constant cost of production equal to $1 per unit.
The question is, if you are a greedy corporation, then how much should you charge to maximize your profits?
You should charge $2.
At that price, you will make $10 selling to the poors, $5 selling to the middle, and $1 selling to the rich. $16 bucks in profit for the greedy corporation.
If you charged $3, you would make $10 in profit selling to the middle, and $2 in profit selling to the rich, for only $12 in profit.
12 If you charged $4, you would make only $3 in profit.
3 In other words, it is profit maximization + law of demand + law of one price that drives down prices in the face of a demand curve.
People get this all wrong, they think that it requires perfect competition or some set of unobtainable market assumptions to make stuff affordable, it does not. It's just the law of demand (charge more and you get fewer customers) plus the law of one price (everyone pays the same amount).
This is why things like government subsidies to the poor to help them buy stuff actually drives prices up. It's why businesses wage an eternal war to be able to price discriminate. Health care, for example, would be much more affordable if hospitals had to post their prices and could not charge different rates to different people based on what they could squeeze from their insurance or based on how much money they had. It's why programs to help the poor by giving them more cash to buy stuff end up making things unaffordable for everyone else. It's why section 8 rental subsidies drive up rents. It's why during the covid subsidies, the new car price index went up from 147 to 188, but after the imposition of tariffs, it didn't change at all. So much of the world is explained just by some simple math, the law of one price, and the law of demand.
Because the companies are already charging the most to maximize their profits. They are not charities. Whenever a business says "if I have to pay this extra tax, it will just drive up prices", then ask them "Are you a charity? If you could charge more, then why aren't you charging more now? If you can't charge more now, why do you think you will be able to charge more tomorrow?"
Now, I'm not saying that there is no relationship between costs and prices, and that everything is set purely by demand and the law of one price. To get supply in there, you need more assumptions about the type of competition and the cost curve. But in general, supply only enters into the picture in that if you raise a firm's costs, then some firms go out of business because they can't pay the higher costs, and for the firms that are left, there is less competition, and it is this reduced competition that allows (some) of the increase costs to be passed on to consumers.
Always remember -- firms are already charging the most they can possibly charge in order to maximize total profits. That's the normal state of affairs, and it is what drives prices lower. Whether you are modeling a monopoly, or monopolistic competition, or an oligopoly, or perfect competition, it does not matter. They always charge the most they can possibly charge, and the law of demand, working with the law of one price, drives prices down.