Julio,
In your last post, you did not respond to the main point of my argument about the rate of interest – that it is *taken as given*, as one component of the “price of capital”, and is not explained by marginal productivity theory. Thus marginal productivity theory takes as given what it is supposed to explain – the return to capital. It is an empty theory covered up by calculus and by vague and misleading definitions of the “price of capital”. The emperor has no clothes! This is the most important problem with marginal productivity theory, so I want to emphasize it in this post. I will respond to your other points in a subsequent post. Comradely, Fred On Mon, Jan 14, 2013 at 12:45 PM, Julio Huato <[email protected]> wrote: > Fred, > > > 1. *quantity and quality* > > I tried my best to explain my view on this, but I obviously didn't get > my point across. > > > Thus, according to marginal productivity theory, the quantity of profit > is > > independent of wages; but according to Marx’s theory, the quantity of > > profit varies inversely with wages. Thus an increase of wages has no > > effect on the quantity of profit according to marginal productivity > theory, > > but causes a reduction of profit according to Marx’s theory. > > But the marginal productivity theory cannot (repeat, *cannot*) claim > such a thing, i.e. that the quantity of profit is independent of > wages. How could it? Precisely, the cost function is the dual of the > production function (linearly transformed, just "scaled" by the input > price vector). The conditions of the class struggle are embedded in > the cost function via the production function and/or input prices > (e.g. the wage rate). > > If I say, "Let gravity acceleration be constant, then the > instantaneous speed of an object in free fall depends on the distance > from the point where it is released and the time elapsed from its > release," you cannot take this as me saying that the speed of the > object is *independent* of gravity. No. I'm assuming gravity > constant for the time being. I'm assuming that we're staying on the > surface of this planet to conduct our experiments. Similarly, the > textbooks usually say, "Let the labor market be "perfectly > competitive." Therefore, the wage rate is exogenous. Under these > conditions, competition makes the profit per unit of means of > production dependent on the marginal output generated by such unit." > This does *not* mean that the profit per unit of means of production > is *independent* of the wage rate. Obviously, if the wage rate > changes, the entire cost function shifts and, consequently, the > marginal product of "capital" goes down (under the usual assumptions > of technological convexity). Same "prediction" as Marx's. > > > I think you are conflating fixed proportions between inputs (e.g. > machines > > and labor) with fixed proportions between raw material inputs and > output. Most > > of the literature on fixed proportions is about different inputs, rather > > than raw material input and output. I don’t think there is much > > variability between machines and labor, but I think there is even less > > (i.e. little or none) between raw material inputs and output. > > I'm not sure why you're saying this. Maybe because, in my posts, I > implied that fixed proportions between inputs lead to discontinuities > in the profit function. Again, there's a mathematical duality between > the input space and the output space (the same space, if you take the > economy as a whole and, as I justified earlier, you are willing to > view society is a device by which humans reproduce themselves). If, > in the input space, you have fixed proportions between inputs, then > the marginal rates of input substitution (the pairwise ratios of > marginal outputs) are going to be undefined or flip from, say, zero to > infinity. This implies that, in the output space, the marginal rates > of transformation between outputs (the pairwise ratios of the marginal > costs) will be messed up as well. FWIW. Not sure it addresses your > point. > > By the way, some readers here will appreciate the fact that Soviet > economists contributed significantly to the modern understanding of > duality (e.g. Evgeni Slutsky, Leonid Kantorovic, etc.). > > > Michael P. mentioned Georgesen-Rogen, who is one of the few who has > > discussed raw materials in marginal productivity. In the article by GR > > that I have read (“Coefficients of Production and the Marginal > Productivity > > Theory”, *Review of Economic Studies*, 1935-36), he calls raw materials > > “limitational inputs” – by which he means that an increase of these > inputs > > is a *necessary condition* for the increase of output (i.e. fixed ratios > > between these inputs and output). And he concludes that when we take > these > > limitational inputs into account “we can no longer make use of the > concept > > of physical marginal product.” (p. 46) > > All one needs to get around GR's objection is to redefine a few > concepts. Note that we are disagreeing about the general validity of > abstractions here. We're not talking about concrete practical > applications, which -- as I said -- may require particular > modifications to the abstract models. But the same proviso applies to > any other general theory. > > Suppose you say that "home heating with an oil furnace" is the output. > It's easy to redefine output more generally as "home heating," > period, and bypass the issue. Now, the production function has as its > inputs gas, oil, electricity, and boilers powered by various > alternative energy sources, etc. There's now plenty of > substitutability between them. I imagine you objecting that there's > an oil furnace installed, "fixed" for the time being? Well, again, > extend the period of time and what may appear "fixed" starts to > "circulate." In my first hefty reply to you, I argued about how human > societies reduce all inputs and outputs to the ultimate input/output > -- the productive force of labor. If, for example, I redefine output > as "home comfort" instead of "home heating," then we can have home > heating along with many other substitutable inputs (e.g. sweaters, > etc.) as the arguments in this redefined production function. > > > Julio, please explain in further detail how an increase in the working > day > > shifts the production function and how it affects the quantity of profit > > produced. > > Okay. Arbitrary example: Let "labor" be a variable input in some > apple production function, measured in worker-day units, with working > days defined as 8 hours/day. If L = 1 worker-day, Q = 16 apples. > Technology, etc. are all fixed. Now, change the working day to 10 > hours/day. With L = 1 worker-day, say, Q = 20 apples (or 18 with > decreasing returns to labor hours). Etc. The entire production > function shifts upwards. Similarly, if the intensity of labor > increases. > > > So Clark was wrong about his own theory and you are right about his > theory? > > Seems unlikely to me. > > Yes, Clark was wrong about his own theory. It happens often. It's > not just me saying it, but even if it were only me, that would not > make him any righter. The earlier interpretations of marginal > productivity theory have been amended in various ways since Clark's > times. And not only Clark's belief that each class gets its "natural" > desert. Also the original confusion about zero profits deemed general > but shown since to be limited to "linearly homogenous" production > functions ("constant returns to scale"). Etc. > > > I don’t understand what a theory of deserts has to do with a theory of > > profit. > > With all due respect, Fred, but it's you who mixed things up. Cf. > your papers. You frame the marginal productivity theory as a theory > of deserts, as the argument that workers deserve to be exploited, etc. > I am the one who's tried to show that this is totally unwarranted on > the theory's premises. And I believe this is not the way any serious > conventional economist todays interprets the theory. Cf. any > advanced micro textbook. > > > I am criticizing how Krugman and other neoclassical economists interpret > > marginal productivity theory, because that is the dominant interpretation > > and it is an invalid theory and an ideological weapon. > > Not really. You premised your criticism of Krugman on marginal > products, production functions, etc. being "illegitimate" concepts, > etc. But if you're wrong and these concepts are "legitimate," then > your criticism of Krugman lacks substance. > > > An empirical test of marginal productivity theory is not possible because > > marginal products are not observable separately from the prices of labor > > and capital. That is one of the main problems with this theory and my > > first criticism of Krugman in my post on the Economist’s View blog. > > Obviously, I have failed to convince you that it is *not* the prices > of labor and capital as *social forms* that are involved, but instead > the *material contents* of such forms: material "quantitatively > specified proportions" or "essential determinations of value," which > Marx in Capital (for the most part) postulated as given. I can only > advise you and other readers to re-read what I wrote on my blog re. > the CCC and to think about it carefully. > > > This is an important point, which I would like to emphasize. The price > > variable that is supposed to be determined by the marginal productivity > > theory of capital is the *price of capital*, i.e. the price of capital > > goods – sometimes call the “rental rate” because it is usually assumed > that > > firms *rent *their capital goods rather than purchase them (another very > > unrealistic assumption of this theory). > > How do you believe that the price of machines is determined in a > capitalist society? Do you think that it has nothing to do with the > capitalist demand for machines? If, like Marx, you believe that the > *necessity* of social labor time devoted to machine production depends > (on the one hand) on the magnitude of the (capitalist) "social need" > for machines, then you need to specify what drives capitalist > acquisition of machines, what makes the (capitalist) social need for > machines to increase or decrease. Here's a hint: Capitalists do not > care about machines for their own sake. Machines are simply devices > for them to extract unpaid labor from workers. Competition will make > the capitalists acquire machines only insofar as their spending on > them yields a return at least equal (or, approximately so, adjusting > for the lumpiness of machines regarded at a certain scale) to the > return on other inputs. If the return on the machines is greater, > then they will acquire machines. If not, they will favor other > inputs. > > Now, I don't see why the "rent" part puzzles you and seems unrealistic > to you. Doesn't Marx explain "land" price as capitalized rent (the > "discounted present value" of land rents)? Where does Marx get his > discount rate? What is his argument? Landlords in a capitalist > society view holding land like they would regard holding machines or > any other type of productive wealth. Holding it only makes sense to > them if the return on their land (the "rental rate") is the same they > would get by holding the land price as loaned capital. (And, of > course, if the land comes along with other goodies, you have to take > into consideration the "depreciation," "depletion," or "amortization" > of said goodies. (An understanding of this is also in Marx, by the > way: cf. Capital 3, part 6. The "land" rental rate = interest rate. > Opportunity cost. And I use quotation marks, because "land" here is > -- again -- shorthand for any type of owned wealth under capitalism. > Yes, the interest (as opposed to the "profit of enterprise") is a > rent. > > I could go on and on. This is Marx's volume 3, and many of his > arguments were not completely settled. I am no Marx, but I believe > that we can do better with hindsight. But I'll leave that discussion > for later. > > > The price of capital (goods) (*PK*) consists of two components: an > > explicit *depreciation *component (this period’s cost of the capital > goods) > > and an implicit *interest *component, which is the “opportunity cost” o > the > > rental firms of investing in these capital goods, rather than in > > alternative investments. The depreciation component is equal to the > > product of the price of the capital goods when purchased (*PG*) and the > > depreciation rate of these capital goods (*d*), and the interest > component > > (the “opportunity cost”) is equal to the product of the price of the > > capital goods when purchased and the rate of interest prevailing in the > > economy (*r*). Algebraically: > > > > *PK** *= *dPG* + *rPG* > > > > Thus we can see that the "price of capital" (goods) is not an actual > market > > price, but is instead a hypothetical price constructed with the > assumption > > of an implicit “opportunity cost” of the capital goods rental firms. It > is > > not clear why anyone would want to explain this unreal price, which no > one > > ever observes in capitalist economies. > > Why would anyone want to explain value (an "unreal price"), which no > one ever observes in capitalist economies? Goose and gander. This is > just to show how some of your arguments are tantamount to rejecting > abstractions because they cannot fully account for the concrete. > > > The emperor has no clothes! > > The last word on this discussion should be yours, Fred. > > Comradely. > > PS re. this thread: Michael Perelman, if that's okay, please cc me > your comments or post them on the list for everybody to read. I > cannot find them on the archives. > _______________________________________________ > pen-l mailing list > [email protected] > https://lists.csuchico.edu/mailman/listinfo/pen-l >
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