Julio Huato wrote: > ... with all due respect to Anwar and Marx, an increasing labor > productivity over time *need not* express itself in a falling L/C. > Why? Because, C is not machines, buildings, inventories, etc. (use > values), but the *value* of machines, buildings, inventories, etc. > And higher productivity means ability to produce more machines, > buildings, etc. in same labor time.
It's long been known that there's a difference between the "technical composition of capital" (a ratio of estimated use-values, perhaps using index numbers using constant prices -- or values -- as weights) and the "value composition of capital" (the value of constant capital used divided by the value of variable capital used). Since these don't always move together, Marx's "organic composition of capital" makes more sense in comparing different sectors at the same time (the cross section) than it does over time. (That is, it's role is in the discussion of the so-called transformation problem.) > There's no doubt that the technical composition of capital increases > over time as labor productivity increases. Since the physical mass of > MP tends to increase, one would be inclined to think that its value > does as well. I mean, is there any a-priori reason to expect > productivity in the production of MP to grow faster than the > productivity in the production of everything else? So Marx's belief > that, as a rule, the value composition increases over time is > consistent with the sensible assumption that, in the long run at > least, productivity across all branches of production tends to grow at > a similar pace. We must say, however, that this is just a sensible > expectation. Not an established empirical fact in the history of > capitalism. Agreed. There's a problem, however, with how the value composition of capital is measured. The most standard measure -- which Julio uses -- is C/V. In the standard math, this k = C/V shows up as determining the rate of profit (r) as follows: r = S/(C + V) = (S/V)/([C/V] + 1] = s'/(k + 1) ....(1) So that if s' (the rate of surplus value) is constant, a rise in k lowers r. We can see C/V as: k =C/V = (unit value of constant capital)*(physical amount of constant capital used) divided by (unit value of labor-power)*(physical amount of labor-power hired) The ratio of the two physical amounts is t, the technical composition of capital. I assume that rises over time. Next, the unit value of labor-power is: vLP = (real wage)/q2 = W/q2, where q2 is labor productivity in the wage-goods sector (Marx's department 2). In these terms, the unit value of constant capital is 1/q1 where q1 is labor productivity in Marx's department 1, which produces means of production. Therefore, k = (1/q1)*t/[W/q2] = t*q2/[q1*W] ...(2) To understand this, we need simplifying assumptions. First, assume that there is even growth of labor productivity in the two sectors (which, as Julio says, seems reasonable over the long term). In that case, q1/q2 is constant. Letting that ratio equal 1, so that q1 = q2 = q, we see: k = C/V = t/W ...(3) That says that C/V rises with the value composition of capital rises if the technical composition rises -- but _only_ as long as real wages don't increase faster than t. Of course, in much of volume I of CAPITAL Marx assumed that real wages were constant. If we follow that assumption, however, the rate of surplus-value rises as labor productivity in the wage-goods sector rises. That rate might be measured as: s' = S/V = 1 - [W/q2] ....(4) I'll leave the issue of whether this rise is sufficient to cancel out the rise in t for another discussion. My main point here is that the C/V measure of the value composition of capital is confusing. Let's get back to that. There's an alternative simplifying assumption. Marx sometimes assumed that the rate of surplus-value was constant, as in the discussion of equation (1) above. So assume that real wages grow with labor productivity, i.e., that the rate of surplus-value is constant, then equation (2) becomes: k = C/V = (t/q1)/(1 - s') ...(5) That says that if s' is constant, a rising t raises C/V _only if_ t rises faster than productivity in the means of production-producing sector. It doesn't matter here if there is even or uneven development of productivity between sectors. With either constant W or constant s', we shouldn't assume that rising technical composition of capital automatically leads to a risking value composition of capital. This math presents a problem: Marx treated the value composition of capital (C/V) and the rate of surplus-value (s' = S/V) as independent of each other, at least in principle. (They might and do affect each others' sizes economically, but they are seen as _theoretically_ distinct.) But in this math (equation 5), C/V depends on S/V. So some have employed an alternative measure of the value composition C/(S + V). Instead of dividing C by variable capital, in this view, we should divide it by living labor (L = C + V). That means that this measure of the value composition is mathematically independent of the rate of surplus-value. I would go further, to measure constant capital in stock terms, as K. So the value composition of capital would be z = K/(S + V) = K/L. If we also redefine the rate of profit as the profit rate on fixed capital (S/K) and the "rate of surplus value" as s" = S/(S + V) = S/L, it allows a simpler formulation of the rate of profit: r = S/K = (S/L)/(K/L) = s" * z .... (6) In that case, the two terms (s" and z) are mathematically independent of each other. That allows clearer thinking about the matter. But just as with the discussion of equation (1), if the rate of surplus-value (as measured here) is constant, a rise in the value composition (as measured here) causes a fall in the rate of profit. Even in these (clearer) terms, the idea of a rising technical composition automatically causing a rising value composition is weak. Assume again that labor productivity in department I equals q1, that gives us the value of K = (1/q1)*(the "real" value of means of production), where the "real" value (MP) would be an index number using either constant prices or constant values. Thus, z = (1/q1)(MP/L) .... (7) If t" = MP/L is the "technical composition of capital," then a rise in that ratio only causes a rise in the "value composition" (z) if t" rises faster than labor productivity in the sector producing means of production. This formulation suggests the idea that maybe C/V rises because of lagging productivity growth, likely in the early -- or maybe the decadent stages -- of capitalist development Doug asks why this matters.Well, Marx had the idea that capitalism fouls its own nest. That theory makes sense to me, even if his initial formulation wasn't so hot. -- Jim Devine / "Segui il tuo corso, e lascia dir le genti." (Go your own way and let people talk.) -- Karl, paraphrasing Dante. _______________________________________________ pen-l mailing list [email protected] https://lists.csuchico.edu/mailman/listinfo/pen-l
