So, both the labor theory of value and “supply and demand” can both coexist in Marx’s framework. They are compatible ideas. On the most basic level, cloth from a loom has a “use value.” I can take the cloth and use it as a towel or a wash-cloth. Or, I can take the cloth, cut it up, and sew it together into a shirt, pants, etc. This “use value” is what basically determines the “demand” part of supply and demand. The “supply” part of supply and demand is basically determined by the labor that goes into making a thing. Someone has to plant the cotton, pick it, put it on the loom, dye it, transport it, sell it at the market, etc.

So, the higher a “use value” is, the higher the demand can be. And the more labor that has to go into making something, the lower the “supply” will be. This is a big, big oversimplification, of course. But to continue the cloth example, if you look at high-quality, durable blue jeans vs. a simple washcloth, the blue jeans have more “use value” to you as a consumer, so they can have a higher demand, increasing their price. You can then take the basic “use value” of the blue jeans and find its “exchange value” by looking at all sort of different things, including advertising, artificial scarcity, etc., which affect demand, and things like labor laws, monopolization, transportation infrastructure, etc. which affect supply.

The main difference between “exchange value” and price is that “exchange value” is independent of many complicating factors affecting price, like currency exchange rates, geographical differences in standard of living, etc. For example, the same blue jeans, with the exact same “use value” and “exchange value,” might be sold at a higher price in New York City than Boise, Idaho, because people there are willing to pay more money for the same jeans. In a more online example, the exact same video game is sold at wildly different prices in different countries with different currencies. Discounts and sales affect prices even more drastically. But the existence of a coupon/discount does not change the “use value” of a game, or even its abstract “exchange value,” just the price you pay for it.

This is actually a very subtle issue, with a lot of complicated details to work through. Here an entry about it from the literal “Encyclopedia of Marxism:”

Exchange-value differs from “price” in two ways: firstly, price is the actualisation of exchange-value, differing from one exchange to the next in response to a myriad of factors affecting the activity of exchange; secondly, price is the specific value-form, measuring the value of the commodity against money.

https://www.marxists.org/glossary/terms/e/x.htm#:~:text=Exchange-value differs from “price,of the commodity against money.

But to sum it up, Marx does believe in “supply and demand,” which is perfectly compatible with the labor theory of value. It’s just that labor determines the “supply” side of supply and demand. Because it is laborers who are ultimately “supplying” the raw materials, and the labor that goes into turning those raw materials into usable commodities. Hope this helps!

Edit: the other answer is better, but I’m going to leave this up in the hope someone can either confirm or deny what I said in the last paragraph.

Likewise with the loom example, the powered loom devalues the labor value but it could also be understood as an increase in supply per unit labor.

(I can take a stab at this one, but someone please correct me if I am wrong.)

What you describe is whats happening. If the necessary labor time to produce one yard of linen is cut in half, one unit of labour produces 2x the use-value/material wealth compared to yesterday’s hand loom, but is now worth 1/2 per unit produced in exchange. So the material wealth increases, but at the same time the value of each yard of linen diminishes.

If I’m understanding this, this is the way the dual character of labor relates and forms the dual character of the commodity-form. I. E. Concrete labor as production of use value (and material wealth) and abstract labor as the amount of average necessary labor time (and thus value).