A question that puzzled Marx's predecessors was, where does profit come from? When a business makes a profit, what precisely are they making? Yes, they can make a money profit, but money does not have intrinsic use-value (by definition: if you actually consume a money-thing, such as salt, it ceases to be money and becomes an ordinary commodity). What does that money represent? If a capitalist pays full value for labor and capital (ignoring land), and exchange value is just the value of the labor and capital, then where does the profit come from? Neither Smith nor Ricardo were happy with their answers to this question.
What Marx does is posit that "labor" is really composed of two things: actual labor, the amount of work that's actually done, and labor power, the amount of work necessary to keep a worker alive, able to work another day, and reproduce the next generation of laborers. So, it might take six hours of labor to grow the food, build the houses, manufacture the clothes, etc. to keep a worker alive, and this cost of labor power will allow the worker to work twelve hours the next day. Thus, the capitalist does not pay full value for labor: he pays only for labor power, which costs "six hours", and receives "twelve hours" of actual labor; his profit is thus "six hours" of labor, i.e. the surplus value of labor. Although the capitalist is obtaining six hours of "free" labor from the worker, this exchange of wages for labor power is, in capitalist terms, a "free" exchange that satisfies the Labor Theory of Value: the worker is exchanging a commodity, his labor power, which costs "six hours" of labor, for wages (representing goods) worth "six hours" of labor.
(Marx makes the point that workers are not mindless objects. A chair cannot object that someone exchanges it for its cost, but workers can and do object, sometimes violently. Therefore, workers can politically demand a price for their labor power, with a lower bound set by bare subsistence, and an upper bound set by their total amount of labor. And different categories of workers can have different political power, so the price of labor power can differ by category or sector.)
This analysis is the point of the Labor Theory of Value. It is not to predict actual market prices on a day to day basis. There are many things that can change market prices in the short term and medium term. If you're interested in price arbitrage, trying to calculate the "true" price (and arbitrage "distorted" prices), the LTV is not a particularly good tool. The LTV is a conceptual tool for understanding what capitalism is all about. Marx notes that Ricardo, Smith, and Benjamin Franklin observed that all human beings have to trade that is our own is labor; the fruits of nature are given to us for "free": we do not have to work to make the sun shine, the rain fall, plants and animals grow. Yes, people can "own" things like land or capital, and while they themselves do nothing directly productive, they can still charge people to work on it. However, what they are obtaining is the surplus labor of the people who are actually productive.
Assume my land can use a certain amount of direct labor (ignoring for the moment labor indirectly embedded in some capital) to produce a certain amount of corn. The cost of labor power, what I must give to the workers, is less than the total amount of corn I can grow. I keep the extra corn. The exchange-value of the corn I have left is precisely the difference between what the labor produces and what the labor costs. (And, in fact, the amount of labor I hire is precisely the amount at which the "last" laborer produces just the cost of labor power.)
I can exchange the extra corn I grow for an equal amount of labor embedded in other goods. If I could trade it for more labor embedded in some other good, then people would stop using labor to make the other good and start growing corn; similarly, if I could trade it only for less labor embedded in other good, then I would stop using labor to grow corn and start making the other good, and trade with other (more foolish or more efficient) producers of corn.
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