Have you actually read Marx? If you haven't, I recommend you start with https://www.marxists.org/archive/marx/works/1865/value-price.... It'll clarify much of your confusion on basic economics.
While I am not an expert, I remember reading about it on "The Classical School: The Turbulent Birth of Economics in Twenty Extraordinary Lives", by Callum Williams. It made sense to me.
https://www.goodreads.com/en/book/show/49374783
While linking to the sources is useful, I would appreciate any argument correcting the above since, as I said, I am not an expert and it makes perfect sense to me.
This is not true; Marx's model of exploitation (known to modern economists as the Profit-Exploitation Correspondence Model (PECP)) does not concern itself with what demand and offer agree on within a labor negotiation. Marx says that workers do not sell their labor, they sell their labor-time (e.g. X units of time/goods) during which they exercise their labor-power. The discrepancy between the value of the time and the value produced during that time is where this 'exploitation' comes in.
The idea that exploitation is a matter of opinion or agreement adds a moral or justicial spin to what Marx considered to be a fact of the capitalist economy. Whether the people involved are happy with the situation or agree to it does not change this discrepancy of value or its representation in money.
Marxism is explicitly amoral, it does not concern itself with that is morally right. It is a social science that analyses the contradictions within the material world and their consequences.
> The discrepancy between the value of the time and the value produced
I am thinking how can one value this time. If it is valued by the market (how much someone is willing to pay for it) we would end up with the same problem, no?
It must be intrinsically valued, I am assuming.
The capitalist wants to pay as little as possible per hour, but will on average long term not be able to pay less than the cost of living. Capitalists pay just enough so that workers as a class reproduce themselves (so there are more workers), but less than the value the workers produce.
What is the "value"? Well, the prices cannot be explained only in terms of offer and demand (a society with an offer of 100 pens and demand for 100 pens and offer of 100 planes and demand for 100 planes still would not sell pens and planes for the same price) nor entirely because of the price of raw materials (because this only postpones the explanation: from where came the price of the raw materials?). It also cannot be explained only based on subjectivity, because there exists a number, which is a very objective measure, representing the price if you balance offer, demand, assume competition and discard several perturbations. The "value" tries to explain this basis value that later will became the price and show objectively and numerically how the wealth is produced and distributed.
This "value" is measured by Marx as the quantity of labor socially necessary to produce the product. Given a car, the value represented by a car can be measured by the mean time necessary for the workers to produce that car in the industry plus the value transferred by the machines and tools used by those workers (whose value came from the workers that produced these machines and tools). Both manual and intellectual work need to be taken into account and you can also assume that some complex tasks or more intense work can produce more value than simple tasks in the same time.
Given this, you can compare the value produced by a worker with the value of the things that the worker can buy with its salary. This is how Marx measures these things and shows the exploitation in the society.