This is an edited version of a message that I wrote in reply to a question posed by Michael Lebowitz on Michael Perelman’s listserve (on 1/15/2006) with regards to the Cambridge UK “capital critique.” While I was at the New School (1994-1996), I took the course with Anwar Shaikh titled “Ricardo, Sraffa, and Marx.” As a result, with a little help from Shaikh’s excellent lectures, I forced myself to read Piero Sraffa’s esoteric Production of Commodities by Means of Commodities (as well as his less well known 1926’s paper, “Laws of Returns under Competitive Conditions”) and Luigi Passinetti’s superb Lectures on the Theory of Production–and to almost read Piero Garegnani’s “Quantity of Capital” entry in The New Palgrave.
As I remember, the “capital critique” immediately struck me as a massive but fatally misguided effort. It clashed frontally with my own understanding of political economy and, although Anwar Shaikh didn’t appear to note it, it implied a devastating critique of Marx’s own reproduction story. This was because, in Marx’s rendition in Capital, volume 2, production is broken down into departments by using use value as the criterion: means of production in one bucket, consumption goods in the other bucket. In other words, Marx assumed a (capitalist) department 1 that produced quantities of an implied homogeneous use value, namely “means of production.” And by this Marx meant exactly the same use value that standard economic theory conceptualizes as “capital” in their specification of “technology” or “production possibilities.”
For years, I’ve been resenting myself for “allowing” so many young critical minds favorably inclined towards Marxism to be exposed to the unchallenged belief that the Cambridge “capital critique” is a quasi- if not philo-Marxist rejection of bourgeois economics. Well, if I can help it, no longer so. I haven’t had a chance to go over all that material in due form since I posted the message on PEN-L (I just cannot envision myself re-reading Sraffa or Garegnani’s writings), and I’ll probably not have that chance any time soon. But at least these thoughts will be out there exposed to public scrutiny, for whatever they may be worth. Hey, I got tenure since early this year, a degree of job security that I wish all of my class brethren also enjoyed. So, what am I afraid of? 🙂
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In standard theory, the notion of physical marginal productivity is a technical relation between inputs and outputs. There’s no (of necessity, at least) “economics” or political economy there. So, when standard theory speaks of the “marginal productivity of capital,” it means the marginal productivity of specific capital inputs (means of production). Or if one thinks that the term “productivity” should be reserved to the relation between outputs and concrete labor inputs, then call it “effectiveness of the means of production” as Marx called it. It is the same thing: a relation between physical outputs and physical inputs.
Essentially, the “capital critique” says that at an aggregate level you cannot map the technical relation from inputs to outputs, because in aggregating means of production (so-called “capital”) the weights are value notions. In standard theory, the input-output technical relation is conceptualized as the “production possibilities set” (PPS). In applications, the PPS is usually specified as a “production function” and sometimes a “well-behaved” one. In some abstract analyses, one doesn’t even need it to be a function or to be well-behaved.
But, in any case, the PPS is the technical piece of the analysis. The economic piece of the analysis is the prices and quantities of inputs and outputs. And for those who can keep in their heads the notion of technical or physical elements as content and the economic or social ones as forms, the rest is not problematic. Under partial equilibrium, one adds the utility function, assume exogenously all other prices and quantities, add a supply=demand consistency condition, and use maximization in consumption and production to pin down the equilibrium price/quantity of the item of interest. Under general equilibrium, to the production functions one adds utility functions, n-1 supplies=demands conditions plus Walras law, and uses maximization in consumption and production to simultaneously determine the equilibrium price and quantity vectors.
Now, input aggregation (implicit or explicit) is a necessity in any type of society. In a conceivable full-fledged communist society, with no markets whatsoever, given needs, people would still have to allocate their productive force of labor (stock) or their labor time (flow, “living” and “materialized”) to different uses. To avoid wasting labor, they would have to allocate it according to proportions determined by the (expected marginal) productivity of labor time in each of its different “useful, concrete” (Marx) applications. These proportions are necessarily comparisons (or ratios) of quantifiable “useful effects,” as Engels put it in Anti-Dühring in referring to socialist-planning “shadow prices,” thus prefiguring the modern conventional notions of “marginal rate of substitution” (in consumption) and “marginal rate of transformation” (in production).
What do we mean above by “useful, concrete”? Do we mean, for example, the labor required to produce shoes? Shoes seem to be pretty concrete and the labor spent producing them certainly appears concrete at first sight. But, in practice, we require all sorts of labor (“living” and “materialized”) to produce shoes? When one looks carefully, they all are very different types of labor executed by very different concrete workers. Even the labor of the “same” worker (thanks Heraclitus!) will be different from instant to instant. Narrow this down to “living” labor types and keep it simple: which labor in particular is “useful, concrete”? The labor required to glue leather pieces together? Then by “useful, concrete” we really mean only the labor that produces a particular outcome (glued leather pieces) among the many other outcomes required to produce finished shoes. The fact is that one can apply this reasoning recursively ad infinitum. But, depending on the task, communists would not want to waste much labor time splitting hairs. For various purposes, they would have to stop somewhere and deal with aggregates; say, deal with shoe-producing labor as if all the types of labor involved in shoe production were homogeneous.
How would these communists add up “useful, concrete” labors that are so dissimilar in practice (sewing, gluing, painting, operating different machines, etc.) into one single measure of “useful, concrete” shoe-producing labor? They would have to use an index, an average. And the weights? The weights would have to be some measure of the “relative importance” that society assigns to each type of detailed “useful, concrete” labor. But, in a chicken-and-egg manner, under full communism (no markets here), that “relative importance” would be dictated precisely by those “definite proportions”!
In a market society, the “relative importance” concretely assigned to each labor input is given by its price (ultimately, value). But here we must distinguish the value form from its content: the technical factors that determine it. I.e., definite proportions of allocated labor, proportions that, given the concrete needs of a society, reflect the shadow “prices” of the labor inputs (i.e., the expected marginal productivity of labor in each concrete application). The Cambridge critics conflate here form and content. They say that, if one introduces “definite proportions” (shadow “prices”), then she is introducing values, in the sense of specific social relations. But, this is simply not true.
If this seems complicated when dealing with “living” labor, the complication is greater with “past” labor “embodied” in means of production (MP). In aggregating different kinds of MP (“capital inputs”), the “relative importance” of each individual input depends on its expected marginal productivity multiplied by a measure of the “relative importance” of the outputs it helps produce. But, again, one thing is that every society needs to measure the “relative importance” of different kinds of stuff and a different thing is that in some societies this “relative importance” takes the form of value and price. In a market setting, these are values indeed, but they enter here not because they are values (social forms, specific social relations), but because they are “definite proportions,” shadow “prices,” or measures of “relative importance.” And these are common to all types of society.
The neoclassicals — it is argued in ways that many Marxists have found convincing — postulate a production function relating physical inputs to physical outputs. So, clearly, “capital” here means “a physical set of MP.” Yet their aggregation of the “physical set of MP” is not merely “physical” because the weights used are the values of specific marginal productivities (e.g., Q_inputs × P_outputs), which in an ideal competitive context, equalize to the rental rates on the “capital” inputs. Then changes in “capital” can be due to changes in the composition of the individual physical inputs, which is okay. But, alternatively, they may result from changes in their marginal productivities in money terms (i.e., marginal productivities times the price of the output the inputs help produce), which is not okay because the “physical” measure is then buffeted by changes in prices (values). The effect on the measure of “capital” may not be a big deal when the two types of changes concord. But if they don’t, the neoclassicals wind up with changes in their measure of “physical capital” completely dominated by changes in the rental rates of the different types of MP. How, then, can they map one-to-one changes in the amount of individual physical inputs and their aggregate measure? They can’t! In other words, they have “reswitching”! (Or, as Michael Lebowitz puts it, the neoclassicals assume the profit rate here to determine the profit rate there and that’s tautological!)
But change the context to see through the argument: Communist plans presume that physical inputs can be mapped to physical outputs at different levels of aggregation. (I mean, let’s be Marxists here: Ultimately, the wealth we produce (say, if we take the broad view and see human history as production) is ourselves and the productive wealth with which we produce ourselves is… well, ourselves! We produce humanity by means of humanity, or productive power by means of productive power, or freedom by means of freedom! And what would be communist about it is that we’d be producing ourselves consciously, deliberately, and with a measure of social unity and mutual solidarity.) Yet their aggregation of a “physical set of MP” is not merely “physical” because the weights used are marginal productivities times other weights: measures of the “relative importance” assigned to particular outputs. But then changes in their “physical” aggregate measure of MP can result from changes in the composition of individual MP, which is okay. Or from changes in the “relative importance” of the inputs, in turn due to changes in the “relative importance” of the use values each given MP helps produce, which — according to the “capital critique” is not okay. Why? Because then the measure of “physical MP” is exposed to changes in the “relative importances.” That would not be a big deal if the two types of changes agreed. But if they don’t, the communists wind up with changes in their measure of “physical MP” completely dominated by changes in the “relative importance” of the different types of MP. Communist planners cannot map one-to-one changes in the amount of individual physical inputs and their aggregate measure. They face “reswitching”!
There you have it: reswitching plagues neoclassical economics and communist planning alike. That is because, in principle, reswitching affects any conceivable economic theory that requires aggregation (of labor power and/or means of production). Since aggregation is inescapable in making economic choices in small or large economic units under all conceivable economic arrangements, then the possibility of reswitching is practically inescapable. What any reasonable decision maker would say is, “Okay, what’s the chance of reswitching and how large is the cost involved so that I can compute an expected loss (in social labor time terms) to the best of my knowledge?” If the expected loss is large, then she’ll want to disaggregate things a little and pose the question again. Eventually, she’d reach a level of disaggregation where the expected loss involved equals the resources required to prevent it and reswitching effectively vanishes as a practical problem. “What do I care about reswitching if there are bigger fish to fry?” — she’ll think.