Julio, replies below. On Wed, Jan 16, 2013 at 11:07 AM, Julio Huato <[email protected]> wrote:
> Fred, > > Let me limit this post to clarifications and direct responses to your > direct inquiries: > > > 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”. > > Here's what I wrote early on about it: > > "Re. (4), if you state that (a) y = 1 + 2 x, that (b) z = 4 - x and > that (c) y = z, you are not necessarily contradicting yourself. In > general, obviously, y cannot be equal to z: (a) and (b) are very > different equations. But, you can certainly find particular values of > x, y, and z such that all these equations hold just fine, i.e. x*=1 > and y*=z*=3. Again, this is not in general, but in particular -- at a > "point," so to speak. So, no, you are *not* allowed to argue that > equations (a) and (b) "assume" x while the point of the theory is to > determine the particular values of x (i.e. x*) that reconcile the > system. If you do, then the logical contradiction is yours." > > And also this note, where I refer back to the paragraph above: > > "Marginal productivity theory takes the rate of interest as given in > order to derive the demand condition. There's nothing wrong with > that. What is derived is a rule or function, which has to be > reconciled with the supply side. I explained in a previous post why > this procedure is perfectly proper." > > Let me put it more generally: How can you derive any conclusion about > something if that something is not stipulated in the premises of your > reasoning? Similarly: How can you determine the particular solution > (value or set of values) of the endogenous variable in your theory if > this variable does not appear as an argument in the equations that you > intend to solve for your particular solution? > > You seem to be arguing that the MPT reasoning is a plain tautology like > this: > > Premise 1: the return on K is x. > Premise 2: the return on K is x. > Conclusion: x=x. > > But that is *not* the MPT reasoning. Instead, it goes something like this: > > Premise 1: the return on K must satisfy demand conditions, namely > x(K)=MPK, nontrivial (i.e. independent of y), > Premise 2: the return on K must satisfy supply conditions, namely > y(K)=i (given) nontrivial (i.e. independent of x), > Premise 3: competition enforces x(K) = y(K). (This implies that x(.) > and y(.) are not, in general, equal.) > Conclusion: Under competitive conditions, MPK* = i* = r*(K). > > You may not agree with it, but this reasoning is logically consistent. > Julio, I think you are confusing the price of capital and the rate of interest. The price variable that is determined in marginal productivity theory is the *price of capital*, not the rate of interest. The rate of interest is one component of the price of capital, along with a depreciation component, and in disequilibrium an entrepreneur’s profit component (= 0 in LR equilibrium). The independent variable in the Kd function is the price of capital (PK); i.e. Kd = f (PK). The Kd function is derived by varying PK. But as PKvaries, the rate of interest stays the same, as an exogenous given. What changes as PK changes is the disequilibrium profit component, not the interest rate (the “opportunity cost”) component. Assume for now that the Kd function can be derived in this way – letting go for now the impossibility of defining the MPK in all the cases in which production involves raw materials (or other intermediate inputs) (as Georgesen-Rogen acknowledged). Now Kd has to be combined with Ks in order to determine PK. What is the theory of Ks? I know of no such satisfactory theory in print. (Julio, if you know of one, please send me the reference.) Such a theory would presumably have to do with “capital goods rental firms”, i.e. firms that rent machines to other firms (another very unrealistic assumption of this theory; Julio, the unreality is not that the rental firms’ earnings are called rent, but that it is assumed that firms *rent *their machines rather than *purchase *them). In any case, even if a satisfactory theory of Ks could be provided, Kd and Ks together would determine *PK*, not the rate of interest. The rate of interest would still be taken as given, an exogenous variable. That is why I say that marginal productivity theory is *empty* – because it does not provide an explanation of the determination of the rate of interest, which is the return to capital. The reasoning behind this theory may be “logically consistent” (ignoring all the problems with defining marginal products that I have discussed and the lack of the theory of Ks), but it is still empty because it does not explain the return to capital. > > In Marx’s theory, on the other hand, the amount of profit depends on the > > difference between the new-value produced by workers and the wages paid. > New > > value in turn depends on the product of the MELT and the quantity of > > SNLT. That > > is: > > > > Profit = (MELT)(SNLT) – wages > > > > Thus an increase of wages results in a $ for $ reduction of profit. > > > > So I spoke too strongly when I said that MPK is independent of wages. > The > > MPK does vary inversely on wages, but is a completely different way from > > the relation between profit and wages in Marx’s theory. > > Of course it is different (seemingly so), because the assumptions > about SNLT are different. In your equation, SNLT depends (I suppose, > following Marx) on the level of the productive force of labor and the > size of the social need for that commodity, two things you take as > given. In other words, SNLT is *exogenous* in explaining the > magnitude of surplus value. On the other hand, in the "neoclassical" > story, SNLT is *endogenous*, as the size of the social need expands > and contracts depending on prices (although, like in Marx, the > productive force of labor is also taken as given). So, the > "neoclassical" story accounts also for the feedback effect of wage > changes on profit via the adjustment of SNLT. However, if you're > willing to assume continuity, the effect in both stories turns out to > be the same, at the margin. This follows directly from the envelope > theorem: > > profit*(SNLT) = profit(wages, SNLT), where wages = wages(SNLT): > d profit*/d SNLT = d profit/d SNLT | wages=wages*(SNLT) > I don’t understand this argument at all. What is required to be proved is that the neoclassical MPK (aphysical characteristic of the production function) is equal to the Marxian [(MELT)(SNLT) – wages]. Where is the MPK in these equations? Where is the MELT? Please explain these equations in words – not what a derivative is, but how these equations prove that the neoclassical MPK is equal to the Marxian [(MELT)(SNLT) – wages]. I also don’t see how these equations are an application of the envelope theorem. The envelope theorem shows how the optimal value of a function with a parameter changes as the parameter changes. What is the parametized function in these equations and how does this function relate to the needed proof? > > > How does Q increase if both L and K remain the same? Magic? If L is > > measured in terms of worker-days, then an increase in the hours in a > > working day has no effect on the number of working days. K/L remains the > > same and thus profit/wage remains the same. Which is contrary to Marx’s > > theory, according to which an increase of the working day increases SNLT > > and therefore increases the new-value produced and profit. > > > > On the other hand, if L were measured in hours in marginal productivity > > theory, then capital inputs should also be measured in hours, so that an > > increase in the working day would increase K and L by the same proportion > > and thus would have no effect on K/L and profit/wages. > > Fred, > > You asked what happened to the production function if the working day > increased. If the production function is in hours, then (obviously) > nothing happens. The question is valid only if the input units are in > working days, in which case the production function shifts upward > altogether. Under the usual assumptions, if you use workers for 10 > hours/day, then you are likely to produce more output that if you use > them for 8 hours/day. So Q increases. > > Now, you say, expanding the working day from 8 hours to 10 hours > entails that K also expands proportionally. Why? Aren't you > smuggling again the notion of fixed proportions? Not warranted. > A production function is a technical relation between inputs and outputs. A production function shifts only if there is a change of technology. An increase of hours in the working day is not a change of technology; it is more labor with more of the same old technology. Thus there is no justification for your “upward shift” in the production function. Although you measure L in terms of days, and there is no increase of L according to this measure, in fact in the real world there is an increase of L, along with an increase of K (the same technology), and that is why Q increases. Fred
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