For someone who's basically an economic flat earther, you sure do have a lot of condescension to throw around. Yes, I know what empirical means. It is in fact the actual way value is determined: by observing the transactions that set the value of a product.

Transactions don't occur in a vacuum, and commodities don't spring into existence like morning dew on flower petals.

This is why, for example, there is no such thing as not being paid a fair wage. There's no correct value of labor other than what someone is willing to buy and sell it for. Therefore any wage that's paid in accordance with an employment contract is by definition a fair one.

That's absolutely correct. The price of labor power tends to sink to the average cost necessary to produce labor power.

https://www.marxists.org/archive/marx/works/1847/wage-labour/ch04.htm

This is also why the same product can be sold for different prices. How do you explain that?

Marx has a lot to say about that! There can be changes in the value of currency, there can be underproduction or overproduction of a certain commodity, there can be technical breakthroughs that suddenly produce more of a commodity for less cost, lowering the price of the previously created stockpiles. Value, in the sense of labor value, is a reflection of the socially necessary average labor needed to create a commodity at a given time, and prices tend to vary around that mean.