Mathew Forstater wrote: > I don't know these specific arguments, but I would bet they are the > conventional one that says that, since the value rate > of profit is: > > s/(c + v) > > then it is equal to: > > (s/v)/[(c/v) + 1] > > The numerator, s/v, is the rate of surplus value, and c/v is the OCC. > > This is interpreted as implying: > >>that, in the abstract, expanded >>reproduction with a growing organic composition can go on *forever* as >>long as the surplus value rate is also allowed to increase.
That's not an argument. That's a definition of the profit rate under some strong assumptions. No. I'm talking about reproduction over time. I mean, generally speaking, what would be the condition for the expanded reproduction of social capital? This is all in value (labor time required) terms. Well, consider a simple case. Let social capital (and each of its components) grow -- say -- exponentially at a rate g. Take a representative value particle of social capital (or normalize the social capital to 1). Then the law of motion of the system is: exp(gt) = 1 + mr where m is the fraction of surplus value reinvested and r is the profit rate. Let's use your definition of r above or -- to save some typing -- put it this way: r = u/(1+h) where u = s/v is the rate of exploitation and h = (c/v)/t is the capital composition. (If one assumes, as you did above, that the turnover time of social capital t = 1, then h = c/v.) Clearly, if m = 0, then g = ln 1 = 0 -- that's the simple reproduction case. More generally though, for 0 < m <= 1 (with credit and/or foreign trade, m > 1, but let's not go there), taking logs and approximating (say by taking the turnover period to be an instant), we have: g = mr Or, if you prefer: g = m [u/(1+h)] And that's all we need for social capital to expand indefinitely along that balanced path. Note that social capital is value: homogeneous labor time. So, finite natural resources is not an issue in this context. This does not necessarily imply the expansion of stuff. It's the expansion of socially necessary labor time. How about splitting the output into use-value-defined departments and establishing proportionality conditions? Sure, split the output into n departments. The algebra will get uglier, but it can be shown that if the proportion of initial capital among the departments meets certain relationships (which can be expressed in terms of u, h, t, and m) the system can grow at g forever. What if those proportions are not met at the outset? What if you let the initial conditions to be arbitrary. Fine, but then you need some mechanism (e.g. competitive markets or an enlightened social planner) to enforce the convergence to the proportions at some point. Since the value relations linking the variables are all assumed linear (or, exponential, which is to say linear in the logs), the continuity and compactness conditions for the fixed point to exist (and be unique) are there. This is not a grand discovery. It's the Golden Rule people study in growth economics. It goes back to von Neumann, Phelps, Solow, or -- if you prefer -- Joan Robinson. > Proof of the Law of the Falling Tendency of the Rate of Profit (LFTRP) > > rmin = 0 > rmax = (L/C) > (rmax - rmin) = [(L/C) – 0] = (L/C) > > This is the profit rate band. > > If, over time, (C/L) is rising (and (L/C) is falling), then the profit rate > is being squeezed downward. > > This has nothing to do with what is happening to (S/V), because (V + S = L). > In fact, Marx thought that > the LFTRP was associated with a rising (S/V). With all due respect to Anwar, this is not a "proof" of the LFTRP. This is just a syllogism *stating* the LFTRP: *If* C/L goes up, *then* r goes to zero. Sure, but does the premise hold in the real world? That's an empirical issue. You'd have to show that -- under some space, time, and circumstance -- C/L indeed goes up. I'm not saying it doesn't. I'm just saying that it need not. It's clear to me that Marx noticed this as evidenced by his remarks on counter-tendencies. To see the point, normalize L = 1. It's all about C now. C is dead labor, the value of existing capital. It's a magnitude that depends on the state of the productive force of labor devoted to producing, say, MP. (Imagine, for simplicity, that all capital is productive: no money- or commercial capital.) Assuming the size of the social need for MP constant, C will shrink every time there's a value revolution, every time the labor producing MP becomes more productive. Accepting Anwar's framework, even if r were to approach 0 at some point (or even equaled zero), it could go back up if existing capital got de-valorized, which happens. Like, say, now. _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
