Could I get [an English PhD student] to explain coherently the labor theory of value, please? Or if not explain it, point me to a reliable way of identifying the value of labor as opposed to the value of capital across all the production processes that exist today (under my naive assumption that incentives matter so there probably has to be some return to capital if we're hoping to deploy it in a way that serves us all well)?I'm not an English PhD student (and I probably won't be a Political Science/Economics PhD student for some years). And I don't know if I can explain the labor theory of value, or even Marx's theory. I think I can, however, explain a reasonably coherent labor theory of value.
As I see it, my labor theory of value is an ideal theory, in the sense of a partial explanation excluding certain distorting or complicating conditions. In much the same sense, the theory of gravity is — on the surface of the Earth — an ideal theory that ignores, however ubiquitous, the complicating conditions of aerodynamics. Even though it's obviously not the case that airplanes actually fall towards the surface of the Earth accelerating at 10m/s2, gravity and gravity alone does indeed exert a force or the airplane that must somehow be counteracted.
The ideal theory is that absent complicating factors, commodities produced for exchange will trade according to the total amount of socially necessary abstract labor time consumed in their production.
The abstract labor time is actual physical human time spent creating the commodity modified by subjective and objective factors. The subjective factors discuss the "inherent undesirability" of a particular task: an hour spent cleaning a sewer or doing manual labor in the hot sun is generally considered more inherently undesirable than sitting in an air conditioned office typing at a keyboard. The objective factors discuss the "intensity" of the work: if everything else being equal Alice can create twice as many widgets as Bob in an hour's time, then Alice is putting in twice as many hours as Bob of abstract labor time.
It is typically the case (with notable exceptions) that many different firms (or individuals) act as suppliers of a commodity in a non-trivial market. These individuals will typically produce the same or similar goods by consuming different amounts of abstract labor time. The socially necessary labor time is a statistical property of the individual labor times, specifically the labor time actually used by the least efficient firm producing the commodity at the market clearing price. Firms which produce the commodity more efficiently receive something of a premium; firms which would produce the commodity less efficiently go bankrupt and are eliminated.
The total amount of socially necessary labor time is simply the sum of all the socially necessary abstract labor time consumed in producing the good, including all time spent creating capital and performing lower- or higher-level managerial and administrative tasks, including transaction costs. We consume labor time to create factories and equipment; we consume labor time to train and educate skilled workers, managers and administrators. It is not the case (at least under my labor theory of value) that we make a distinction between the value of capital and labor: capital requires labor to produce and has the value of the labor used to provide the capital. The distinction is more precisely captured by contrasting the value labor with the value of the ownership of capital, independently of its (labor) cost of creation.
The labor theory of value is most important, I think, when looking at the dichotomy between labor and labor power, i.e. the difference between the total amount of socially necessary labor time required to create a commodity vs. the total socially necessary labor time required to create labor time, i.e. the difference between the amount of labor necessary to create a commodity vs. the amount of labor necessary to feed, clothe, house, etc. a worker. We see a surplus economic growth when the cost of labor power is lower than the labor produced by that cost.
As I noted at the beginning, my labor theory of value is an ideal theory, and it might be the case that complicating factors are not merely ubiquitous but actually desirable — analogously, airplanes cannot fly without the "complicating factor" of aerodynamics.
Specifically, we must make decisions about how much labor to allocate directly to the production of commodities that will be directly consumed in the short term, and how much labor to allocate to investment and creation of capital to improve productivity in the medium and long term. I suspect that absent these complicating factors, a market based exclusively or ideally on the trade of socially necessary would "naturally" invest very little in future productivity.