On Thu, 15 Jun 1995 [EMAIL PROTECTED] wrote: > But the point still holds: if one replaces Marx's simplifying > assumption with a demonstrably market-relevant condition (long-run > wages constant at the subsistence level), there is no "tendency" for > the rate of profit to fall--and this is a useful result. Gil Gil, apparently we have a somewhat different reading of this section of the third volume of Capital. The only place I find Marx suggesting that technical change is itself a causative agent of falling profits is in a brief passage in his supplementary remarks at the end of the section. Here, Marx makes it quite clear that the effects of technical change on profits cannot be understood outside of the changes they create in prices and quantities, which Okishio entirely fails to do. In any event, this passage (which I don't think is true in as much generality as Marx stated it -- but more on that later) was not central to Marx's exposition of the "law," during most of which technical change is listed as a counteracting factor either through the more intense exploitation of labor or through the cheapening of the elements of constant capital. To my mind, the most straight-forward justification for the fall in the rate of profit is this: "If we further assume now that this gradual change in the composition of capital [from variable toward constant capital -- TB] does not just characterize certain individual spheres of production, but occurs in more or less all spheres, or at least the decisive ones, and that it therefore involves changes in the average organic composition _of the total capital belonging to a given society_, [my emphasis -- TB] then this gradual growth in the constant capital, in relation to the variable, must necessarily result in a _gradual fall in the general rate of profit_, [e.a.i.o.] given that the rate of surplus value, or the level of exploitation of labor by capital, remains the same." [this is the third paragraph of the "part." I'm using the 1981 Vintage edition.] Marx then proceeds to say about ten sentences later (same paragraph,as is his habit :) ) that the fall "is just another expression for the progressive development for the social producitivity of labor, which is shown by the way that the growing use of machinery and fixed capital generally enables more raw and ancillary materials to be transformed into products in the same time by the same number of workers, i.e., with less labor." I think this may be where the excessive attention to technical change comes from; however, note that there is nothing in this passage (nor the few subsequent passages in this section making similar claims) that Marx is actually talking about an individual capitalist coming up with a new technique. He purposefully uses the phrase "social productivity of labor" (I'd be curious to know what the German is. Justin?) and, in the passage I just quoted before this, in the clause that I emphasized, refers to the increase in constant capital belonging to a total society. In other words, these are social phenomena and do not necessarily reflect CU-LS productivity enhancements by individual capitalists, even if these may be the type of enhancements most commonly made. Rather, the phenomenon is that: (1) capitalists accumulate capital, and most of this capital is reinvested. This creates an increase in the social capital stock. (2) Marx then goes through a number of examples that demonstrate the effects of diminishing marginal returns to capital (he doesn't use the word anywhere, but I think the shoe fits pretty well) under various assumptions about the rate of expolitation. Basically, diminishing marginal returns, assuming a constant rate of exploitation (or even a constant real wage, or even a zero wage for that matter, as an example will illustrate below, though Marx never shows this), mean that the additional capital investments yield less surplus value than their predecessors, thereby also bringing down the average rate of return, i.e., the average profit. [Someone may argue that the concept of "marginal returns" requires institutional assumptions about the value of factors, but it's pretty clear to me that these assumptions are made once either the wage or the rate of exploitation is assumed constant and a production function is specified.] During all this, of course, labor is becoming more productive because it has more and more capital to work with. Needless to say, this is not the same thing as technological change. In the next chapter, Marx goes through the various reasons why profits do not in fact always fall, arguing that technical improvements will offset the fall through increased exploitation and commodity cheapening. I see Okishio's theorem as largely consistent with Marx, particularly when Marx states (this is actually in the third chapter, a bit into section two, page 356 in my edition): "A rise in productivity... can increase the magnitude of the capital only if it increases the part of the annual profit that is transformed back into capital, by raising the rate of profit. In so far as labor productivity is concerned, this can come about (since this productivity is not directly relevant to the _value_ of the existing capital) only in so far as it involves either a rise in relative surplus value or else reduces the value of constant capital, in other words cheapens the commodities that go into the reproduction of labor-power or the elements of constant capital." Of course the assumptions here are different: constant rate of surplus value (i.e., wages growing at the rate of productivity) in Marx's case vs. constant real wage in Okishio's. However, a constant real wage does not preclude falling profits. Let me turn around and go totally neoclassical for a minute, in order to illustrate this with a particular example. Suppose aggregate production is described by a Cobb Douglas function, f=k^a * l^(1-a). Suppose labor supply is fixed at 1. Suppose there is a capitalist class that owns capital stock k(0) at time zero and that profits get reinvested into the capital stock. Suppose k(0) = 1. Then, assuming the silly old marginal product laws, labor gets paid (1-a) * k(t)^a, i.e., a constant fraction (1-a)/l of output. Therefore this is consistent with a constant rate of exploitation even if it's not the best justification for it. Capital accumulates according to the differential equation dk = a*k(t)^a, which I'm sure is simple but I don't feel like solving it right now. In any event, it's always positive and total capital is always increasing. The profit rate at any given point, from marginal conditions, is equal to a*k(t)^(a-1), which goes to zero as k(t) increases to infinity. On the other hand, assuming a constant real wage, capital accumulates according to the function dk/dt = k(t)^a*l^(1-a) - wl (= k(t)^a - wl), which again is always increasing. Here, the profit rate is equal to [k(t)^a*l^(1-a) - wl]/k(t), i.e., it's converges asymptotically to k(t)^a-1, which is larger than in theMP case only by a constant factor and goes to zero as the capital stock increases. It would not be hard to show, in this example, that if productivity were growing at the same rate as capital (whatever the solution to that damned diff eq is in front of the other coefficients) that the profit rate would be constant. This merely illustrates the one side of the story of technical change and accumulation that Okishio considers. Of course the above example is of fairly limited relevance to actual accumulation, (1) because it doesn't take into account the effects of wages on consumption and (2) because the innovations are both Harrod- and Hicks-neutral, which don't seem, in general, to describe the real world. I'm not going to address (1) now, but I think Marx does provide an important response to (2), which was followed up on By Shaikh in respnse to Okishio [Marx does also provide a good response to (1) that I think is very under-studied, but it would double the length of this post to discuss it and I'm already eating up time and bandwidth. I think the question of CU-LS technical changes creating lower profits is usually justified from the following passage: "No capitalist voluntarily applies a new method of production, no matter how much more productive it may be or how much it might raise the rate of surplus value, if it reduces the rate of profit. But every new method of this kind makes commodities cheaper. At first, therefore, he can sell them above their prices of production, above their value. He pockets the difference between their costs of production and the market price of other commodities, which are produced at higher production costts. This is possible because the average socially necessary labor time required to produce these latter commodities is greater than the labor time required with the new method of production. His production procedure is ahead of the social average. But competition makes the new procedure universal and subjects it to the general law. A fall in the profit rate then ensues..." The general story, then, is that the capitalist adopts the new method of production that creates higher profits than before during, say, period 1, and then lower profits than before during, say, period 2. I think there are a number of expectational considerations in determining whether or not the capitalist would want to do this. Taking the individual capitalist as the sole agent, this could only happen by way of accident, since it's hard to believe that an entrepreneur would undertake an activity that would lower the expected future profits or else be fooled persistently into thinking those profits were higher than they actually were. On the other hand, looking at interactive behavior, things could go either way depending on expectations (i.e., dynamic strategies), for which the Folk Theorem says pretty much anything interesting goes. Successfully choosing not to make an innovation might happen in more mature markets where entrepreneurs are more sure of their competitors' profits versus newer markets (e.g., computers) where somebody is bound to enter the market with the new technology fairly soon. In any event, in the latter case (which I would argue is probably more the norm; few markets are entirely fixed from entry) I think it's pretty straight forward to illustrate Shaikh's response to Okishio with a Cournot example (for which Shaikh with his aversion to anything vaguely neoclassical would be none too happy). I'm trying to use "reasonable" numbers here. Suppose two firms face a demand function p = 10 - q and two possible technologies with constant marginal costs 5 and 2.5. Ignore sunk costs for a second. The Cournot equilibrium for the first technology is q = 5/3 for each firm, p = 6 2/3, and each firm has profits 2 7/9. In the second case, q = 2 1/2, p = 5, and each firm has profits 6 1/4. (the "reasonableness" so far is that the price elasticity of demand at the relevant point is just over 1, which is a little high but actually then only underscores the point since a lower elasticity would strengthen the effect. The thing I like about the two-player Cournot example is that it puts the individual firm's elasticity at about twice that of the aggregate elasticity, which seems ballpark right to me though I don't know of studies of this kind of stuff). Now, back to the sunk costs: Suppose all marginal costs are labor and all sunk costs are capital (it doesn't really matter for the Marxian questions since they are, by definition, variable and constant capital). Each firm would be willing to just over double its capital costs in order to maintain the same profit rate. Given that each firm raises its output by fifty percent, this seems excessive but not too excessive. I'm sure moving the elasticity up would create a 1-1 increase or even less in the break-even case. I do think this kind of game is a lot more reasonable than the typical neoclassical functions that Okishio considers for a couple of reasons: (1) innovations more typically involve larger sunk costs and smaller marginal costs and (2) firms have a bit of room to manoever their prices as well as get into price wars or not get into them. The point is not that changes under these conditions _always_ lower the profit rate, but that under very reasonable specifications they may. Either way, it illustrates Marx's point pretty well: I leave it to the reader :) :) to show that in the break-even case (i.e., the same profit rate in the two scenarios), the firm that stays with the higher-MC technology while the other one switches will get really screwed. I haven't done the math but it seems pretty intuitive and not hard to compute just annoying. If a firm believes that it can switch technologies a "period" before its competitors do anyway, then the incentives will be that much greater. So expectational considerations can go a long way toward lowering the profit rate. In any event, I don't think this is the main justification for falling profits. Technical change seems to be correlated with higher profits, though I don't know of studies of this on a firm-level basis, with 3-5 year lags and using more "Marxian" estimates of these variables. But it does raise serious questions about the relevance of Okishio's theorem, even within the one side of the story of accumulation that it does address. Added to this, Gil, if there is no tendency of the profit rate to fall, why has it been on a downward trend for the last 25 years or so? Yours for the squabble after the revolution, Tavis
