|Here's an edited snippet of a chapter I'm writing for someone else's book.
> ... the cost of hiring LP (ω) [the cost of hiring an hour of labor-power to the capitalist] differs from the hourly payment (v) actually received by its sellers [workers], so that S [the surplus-product] may be positive [unlike in a neoclassical world]. The difference (s = ω – v ≥ 0) is the surplus product created per hour of E hired; it can also be described as "normal" profit per hour [a.k.a. the "opportunity cost of capital"]. In the NC [neoclassical] case, s = 0.
> Though it has not yet been justified, stipulate that s > 0. Before turning to the economic nature of s, examine its mathematical connection to λ [the intensity of labor]. The total surplus product (S = s•E [where E is the number of hours of labor-power hired]) equals the residual received after paying for inputs (Q – (1 – α)∙Q – v•E) [in this silly model]. Therefore,
s = (α•Q/E) – v = MPE – v = λ∙MPL – v
[MPE = marginal product of an hour of labor-power hired, while MPL =
the marginal product of an erg of labor actually done. λ = the
intensity of labor = ergs of labor done per hour of labor-power
> Thus, s > 0 if and only if MPE > v, i.e., that [Joan] Robinsonian exploitation characterizes all of society. [The marginal product of hiring labor-power must exceed the explicit cost of paying for it.] Alternatively, s > 0 if and only if λ > v/MPL: labor done per hour of LP hired must exceed the explicit marginal cost of hiring it (measured in ergs per hour). I read (6) from right to left, saying that rising λ (more intense work) causes increasing s, ceteris paribus.
> What s means depends on one’s perspective. The RF ["Moneybags," a capitalist representing the class as a whole in a competitive world] has a totally micro frame of reference: because all firms reap these profits, s is seen as "normal" profits that must be obtained to justify staying in business and hiring LP. That is, since this income is forgone when a firm does not operate in other lines of business, it must earn s in order to justify staying in its current line. It is an “implicit cost” of operating there and hiring LP. So to the RF, ω is the total opportunity cost of hiring LP, while v is only the explicit cost of its doing so.
> Individual workers may or may not agree with this perspective. But from a class or macro perspective, workers purchase the right to work for their own livelihood by paying for it with surplus labor (λ – v/MPL). [before the math, it's a paraphrase of Marx] Not being due to monopsony or monopoly, workers must do surplus labor no matter who hires them. It is like a per-hour tax paid to the capitalist class as a whole; similar to a payroll tax, this “tax” on the number of hours hired is shifted to employees. It is the capitalists’ reward for their societal power, as if the state, by protecting property rights in K [capital goods or means of production], delegates to each the ability to collect this tax.
> ... Breaking briefly from the RF [representative firm, meaning that a single capitalist represents the class] model, let capitalists be heterogeneous. They receive “tax” revenues according to their individual traits, which may have little connection to the labor that their workers do: market processes dole it out in proportion to the amount of K they own, adjusted for any special advantages they have in competition (scarcity rents, patent monopolies, etc.), risks taken successfully, and the like. Many receive above- or below-normal profits. Under perfect competition with no lasting rents, however, such abnormal profits and losses disappear. But given our stipulation, positive normal profits persist. <