**From:** Ian Wright (*iwright@GMAIL.COM*)

**Date:** Tue Jun 08 2004 - 13:52:17 EDT

**Next message:**Paul Cockshott: "Re: on money substance and abstract labor"**Previous message:**glevy@PRATT.EDU: "(OPE-L) Re: Ajit's paper"**In reply to:**Fred Moseley: "Re: measurement of abstract labor"**Next in thread:**ajit sinha: "Re: measurement of abstract labor"**Reply:**ajit sinha: "Re: measurement of abstract labor"**Reply:**Phil Dunn: "Re: measurement of abstract labor"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hi Fred, Ajit and others I wanted to comment on: > 2. Marx assumed further that, in the production of value, > one hour of skilled labor is equivalent to (or counts as) > a multiple of one hour of simple, unskilled labor (with > different multiples for different kinds of skilled labor). (Fred) and: > Foley simply adds up various kinds of > concrete labors such as the labor of carpenters and > masons etc. to get his total direct labor, which is > what he places against the total money value of the > net output to derive the labor value of one unit of > money. It does not solve your problem of abstract > labor since the value of the money commodity is simply > based on adding up concrete labors. So I think you > need to rethink on this problem. (Ajit) and: > > Surely by adding them up one abstracts from their > > concrete type, and adds up all that remains - > > expenditure of human time. (Paul C.) >______________ > Exactly! So the abstraction has been done by the > theorist before money comes into the picture. (Ajit) I am thinking aloud, so I'm ready and willing to recognise flaws in what I write below. I also may be teaching various grandmothers to suck eggs ... apologies if so. The summary point is that the MELT is a theoretical approximation not unlike a mean-field approximation in physics. The approximation error can be directly related to the matrix of labour reduction coefficients. In the special case of homogenous reduction coefficients the MELT is an error-free measure of the value of money. The key point is to distinguish the macro-abstractions over concrete labour-types performed by the theorist and the micro-abstractions over concrete labour-types performed by the market, and the relations between them. My partial response to Ajit, therefore, is that the MELT theoretically summarises a set of micro-abstractions performed in the marketplace. The micro-abstractions are real. The question then is not whether it is legitimate to "add up concrete labours" to derive the MELT (I think it is for reasons not given), but whether the MELT is a useful representation of the average value of money. For example, the temperature of a gas is a macro-variable that summarises the energy distribution of the constituent molecules. It is a useful theoretical average -- just like the MELT. But it has definite relations to the real abstractions over concrete labour types that market exchanges induce. Consider a C-M-C simple commodity economy with non-commodity money, i.e. non-produced tokens. Assume all commodities are basic and do not require other commodities as inputs. No replacement costs, so no distinction between gross and net product. Consider that during a market period there is a set of market exchanges E = { e_{1}, e_{2}, ..., e_{n} } where each e_{i} is a pair (c_{i}, m_{i}) where c_{i} is a commodity of type 1 ... k (i.e. there are k commodity types) and m_{i} is an amount of money m_{i}>0 for all i=1...n (i.e. there are n market exchanges in this period). Each exchange pair represents an event of exchanging an instance of commodity c_{i} for an amount of money m_{i}. To simplify assume the "law" of one price, that is if c_{i}=w then for all c_{j}=w (i != j) we have m_{i} = m_{j}, for all i=1...n and for all w=1...k. In other words, instances of the commodity type w exchange for the same money price in all transactions. Let's label that price p_{w}. To simplify assume that for each commodity type w (1..k) there is at least one exchange e_{i} such that c_{i}=w. In other words, there is at least one market exchange for each commodity type. To simplify assume uniform productivity, so that the time required to produce an instance of commodity type w is the same for all producers of that commodity, and label it t_{w}. Define the exchange-value of commodity w, which we label v_{w}, as v_{w} = p_{w}/t_{w} which is measured in money-unit per concrete labour-time unit, e.g. dollars per baker-hour, dollars per tailor-hour, etc. Note that each exchange-value, v_{w}, can be considered as a "micro-MELT" because it is the monetary expression of a particular kind of concrete labour. In an economy of k commodity types there are k micro-MELTs within any market period. So at the micro-level we have: v_{1} dollars are worth 1 hour of labour type 1 (micro-MELT_{1}) v_{2} dollars are worth 1 hour of labour type 2 (micro-MELT_{2}) ... v_{k} dollars are worth 1 hour of labour type k (micro-MELT_{k}) Now dollars are commensurable but concrete labour types are not. But the commensurability of money induces an equivalence relation on the concrete labour types (e.g., Krause, "Money and Abstract Labour"). Let r_{i,j} be the reduction coefficient of concrete labour type i to type j, such that 1 unit of labour type i is equivalent to r_{i,j} units of labour type j. The equivalence relation is induced by market exchanges against money, i.e. in virtue of the respective price of the product of each labour type 1...k. In fact r_{i,j} = v_{i}/v_{j} i.e., the reduction coefficient of labour type i to j is the ratio of the respective exchange-values of their products. From the assumption of uniform productivity and one price, then r_{i,i}=1 for all i=1...k. Given k commodity types there are k^{2} reduction coefficients. For example, if the exchange-value of baking is 1$ per baker-hour, and the exchange-value of tailoring is 2$ per tailor-hour, then the reduction coefficient of baking to tailoring is 1/2. A baker-hour is valued 1/2 as much as a tailor-hour in the market etc. Note also that the reduction coefficients are the ratios of the micro-MELTs. The key point is that the abstraction from different concrete labours and their relation to a common thing, i.e. money, has been performed by the market, not by the theorist. This preamble allows us to provide a micro foundation to the MELT and maybe address some of Ajit's questions and criticisms. Note that so far there has been no "adding up of concrete labours". What is the value of money in this market period? There is already one answer -- it is the vector of micro-MELTs V = ( v_{1} ... v_{k} ) that define the value of money in terms of the k types of concrete labours. If we are content to view the economy as only a set of market exchanges at one point in time then there is not much more to say. Certainly in a C-M-C economy there is never an exchange between an amount of money and a product of abstract labour, for that does not make sense. There are only exchanges between money and products of concrete labours. So the vector of micro-MELTs is the precise representation of the value of money in this market period. But the MELT is introduced as a theoretical abstraction to construct a measure of the average value of money. This abstraction is useful if we want to know how much concrete labour-time of any type 1$ can on average buy. Under the assumptions, in particular no distinction between gross and net output, the MELT is the total market price divided by total labour expended: sum_{i=1...n} m_{i} MELT = ----------------------- sum_{i=1...n} t_{c_{i}} and has units money-unit per time-unit, e.g. dollars per abstract hour. (If you're using a viewer with proportional fonts the fraction may not format correctly). In this formula the denominator does indeed add up concrete labour-times. But this theoretical abstraction has well-defined relations to the real abstractions that take place in the market. For example, if I have 1$ in my pocket then the MELT implies that I'll be able to buy 1/MELT abstract hours. But if in fact I spend the 1$ on commodity type i then I buy 1/micro-MELT_{i} concrete hours of labour type i. This is where the error comes in, because in general: 1/MELT is not equal to 1/micro-MELT_{i} for all i=1...k The MELT equals all the micro-MELTs only in the special case that all the reduction coefficients are homogenous, in which case the value of money can be represented without error as a scalar, rather than a vector. ------ Proof: Let n_{i} be the number of market exchanges in E that satisfy c_{j}=i where j=1...n. For example, if 10 market exchanges involve commodity #2 then n_{2}=10. Then the MELT can also be written as: sum_{i=1...k} p_{i} n_{i} MELT = ------------------------- sum_{i=1...k} t_{i} n_{i} Homogenous reduction coefficients obtain when r_{i,j} = v_{i}/v_{j} = 1 for all i and j in which case p_{i}/t_{i} = a constant for all i and j (i.e., all the micro-MELTs have the same value). Call that constant C. Therefore, every p_{i} may be written as: p_{i} = C t_{i} Substitute this into the MELT equation gives: sum_{i=1...k} C t_{i} n_{i} MELT = ------------------------- sum_{i=1...k} t_{i} n_{i} Which simplifies to MELT = C and therefore all the micro-MELTs and the aggregate MELT coincide. In this special case, the value of money can be represented as a scalar not a vector. ----- So when the reduction coefficients are heterogeneous the MELT will be an approximation to the value of money for any set of concrete exchanges. That error can be measured for any commodity bundle -- the bigger and more varied the bundle the greater the sampling of the different concrete labours and -- here I wave my hands -- the smaller the error. The aggregate MELT simply considers *all* the exchanges that occur in a market period as one huge commodity bundle, and thereby provides a measure of the average value of money for the market period. The MELT is a macro-approximation to all the micro-complexity. > It does not solve your problem of abstract > labor since the value of the money commodity is simply > based on adding up concrete labors. So I think you > need to rethink on this problem. (Ajit) But the value of money is here defined by the market exchanges, and it is the market that compares concrete labours, not the theorist. Exchanges against money are needed for this. Given that the reduction coefficients are the ratios of micro-MELTs, then we can also define a reduction coefficient from concrete labour type i to abstract labour (the MELT): r_{i,abstract} = v_{i} / MELT (i=1...k) Which is related to: > 1. Marx assumed that the basic unit of measure of abstract labor, as the > substance of value", is one hour of simple, unskilled labor, of average > intensity, and using average conditions of production. (Fred) -Ian.

**Next message:**Paul Cockshott: "Re: on money substance and abstract labor"**Previous message:**glevy@PRATT.EDU: "(OPE-L) Re: Ajit's paper"**In reply to:**Fred Moseley: "Re: measurement of abstract labor"**Next in thread:**ajit sinha: "Re: measurement of abstract labor"**Reply:**ajit sinha: "Re: measurement of abstract labor"**Reply:**Phil Dunn: "Re: measurement of abstract labor"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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