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Marx goes to some lengths in the first chapter of Capital to spell out the significance of three aspects of value - its substance, magnitude, and most unusual of all, its form. His theory would therefore seem resistant, at least, to reduction to just one such aspect, the magnitude. The substance of value is labor. The magnitude of value is the number of labor hours. The form of value is, roughly, that institutional framework within which a society's production decisions can be directed through the free exchange of commodities. This aspect of value as a social process, unexamined by Marx's predecessors in classical political economy, cannot be reduced to magnitudes.
The phrase "socially necessary", far from being an arbitary adjunct to the theory (as charged by Robert Nozick), expresses that societal perspective, radically distinct from neoclassical economics. Whereas the latter starts with the individual's perspective and exchange, Marx starts with the perspective of society as a whole. "Social production" involves a complicated and interconnected division of labor of a wide variety of people who depend on each other for their survival and prosperity. Individual labors are contributions to the whole. "Abstract" labor refers to a characteristic of commodity-producing labor that is shared by all different kinds of heterogenous (concrete) types of labor. That is, the concept abstracts from the particular characteristics of all of the labor and is akin to average labor. Socially necessary abstract labor is measured in hours of application of labor-power but can only be realized in exchange: only labor which produces a commodity that is a use-value to someone else (which they can afford and are willing to buy) counts as socially necessary.
Marx's LTV holds that the labor needed to produce a commodity includes both labor directly expended on production of the commodity and labor expended on the production of means of production used up in its production. For example, if twenty workers are used for a year to produce means of production used by twenty workers in the next year to produce a consumer good , the good embodies the labor of forty workers. (This example assumes that technology is unchanged between the two years.)
The amount of labor done by an average worker under the prevailing conditions in a society (for instance the technology and transportation in use) will produce the same amount of value regardless of the manner of that labor. Greater value can be produced by trained workers or by workers using leading-edge technologies: the increase in value is created by the training process or the work required to create the technologies.
However, a lazy or inept worker (who spends more time producing an item) does not produce more value than an industrious one. Rather, the first worker's time produces less because the value depends on what is socially necessary. That is, the value of a product is determined more by societal standards than by individual conditions.
Marx used his LTV to derive his theory of exploitation under capitalism. He assumed that all commmodities sell at prices equal to values (with both measured in the same units). In his era, this "equal exchange" represented a standard of fair exchange: an hour of labor could be used to purchase the product of an hour of labor.
In effect, he asked, "under equal exchange, how is it that a capitalist can sell commodity X at price P and make a profit?" If a boss hires labor at value and then sells the commodity at value, where does profit come from?
Unlike Ricardo or the Ricardian socialists, Marx distinguished between labor-power and labor. "Labor-power" is the ability of workers to work, given their muscles and brains. "Labor" is the actual activity of producing use values (goods and services) and value. In his examples, Marx assumed that the value of labor-power (v) was constant, determined by prevailing socioeconomic conditions. (In his time, this was seen as "subsistence.") The profit or surplus-value can arise if workers do more labor (L) than is necessary to pay the cost of hiring their labor-power.
Marx's numerical examples in volume I of Das Kapital never "prove" that capitalism always involves exploitation, i.e., that L always exceeds v. Instead, this relationship involves class struggle over the length of the working day, the intensity of labor, the use of machinery, etc. The existence of exploitation reflects the capitalists' victory (so far) in the struggle.
Instead, the "proof" that capitalism typically involves exploitation comes from his institutional and historical analysis of capitalism as a whole. One way to get L > v is to use force against the workers. But unlike other systems (such as feudalism or slavery), under capitalism the direct use of force to get workers to produce a surplus is the exception rather than the rule. To Marx, under capitalism workers are free to quit their jobs, while they are rarely beaten.
To explain the normality of L > v, Marx instead pointed to capitalism's institutional framework, in which a small minority (the capitalists) monopolize the means of production, in which the workers cannnot survive except by working for capitalists, and in which the state preserves this inequality of power. In this explanation, the normal role of force is structural, part of the usual workings of the system: the reserve army of unemployed workers continually threatens employed workers, pushing them to work hard to produce for the capitalists.
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