inyourhouse
3rd January 2010, 20:52
In my other topic, one of the issues that seemed to come up was Marxist economics. I want to make sure I understand these theories correctly, so I'm going to be reading Karl Kautsky's The Economic Doctrines of Karl Marx[1]. It does seem that Kautsky was not wholly uncontroversial (e.g. Lenin seemed to disagree with him), so maybe he doesn't give an accurate picture of Marx and/or Marxist economics. Anyway, please excuse me if the answers to my questions are obvious and point out where I have misinterpreted things. Naturally, I'll be starting with chapter one, and this post will just focus on the first part of that chapter.
The first point made by Kautsky is that all commodities must have a "use-value" - that is, a commodity must be a "useful thing". I'm interested in whether this concept of use-value is marginal, or whether it applies to an entire class of commodities, since it's not made entirely clear. In other words, is the use-value of a commodity the utility gained by having another more of a given commodity (e.g. the utility brought about by an additional 100g of butter), or is it an evaluation of entire classes of commodities (e.g. butter vs. gold)? I think Marxists made hold the latter point, because Kautsky writes that use-value is "determined by [a commodities] physical properties", which would be the same for all commodities in a given class.
If Marxists hold the marginal utility view, then the use-value (S) of a given unit of a commodity (x) can be represented by equation A, where use-value is equal to the change in utility (U) brought about by a change in the amount (n) of the commodity owned by a person. With the other view, the use-value of a given unit of a commodity can be represented by equation B, where the use-value is equal to the utility of the commodity class (some as yet unspecified function).
A: Sx = dU/dnx
B: Sx = U(x)
The next point made by Kautsky is that commodities have an "exchange-value", which is "the proportion in which a commodity exchanges with another". So, if at some time and in some place 100g of butter exchanges for 1 apple, and 100g of butter also exchanges for 2 onions, then it is reasonable to say that 1 apple would exchange for 2 onions[2]. So, would it be correct to say that the exchange-value of 1 apple is 2 onions? Mathematically, we could represent the exchange-value (E) of a given unit of a commodity (x) in terms of the amount (n) of another commodity (y) it can be exchanged for. We'll call this equation C.
C: Ex = ny
Now, Kautsky argues that for the concept of exchange-value to exist, there must be some "common property" of all commodities that allows us to equate them[3], which he terms the "value" (as distinct from the two concepts above) of a commodity. If I've understood him correctly, Kautsky is defining value as a "common property" of all commodities. The product of his investigation, then, is to answer the question of what constitutes this common property. He argues that use-value must be distinct from value because use-values (while they constitute the motive for exchange) are obviously a different (rather than a common) property of commodities, (ie. different commodities have different use-values). Let me know if I'm going wrong anywhere.
So, we can say that the use-value of a commodity doesn't constitute its value. What, then, are we left with? Kautsky says that taking away the use-value of a commodity leaves only one quality: "that of being products of labour". He then goes onto to add that as we're looking for a common property, we must also abstract from the particular kinds of labour (e.g. labour of a carpenter, labour of a butcher) that have created the commodity. As such, a commodity only has value because "homogeneous or general human labour is embodied in it". Have I got this right, so far? It seems, then, that we can mathematically represent value (V) as some function of the labour embodied in a commodity (we haven't yet specified the dimensions of this "general human labour" embodied in a commodity, so I can't yet write an equation).
A key thing that I want to note here is that this isn't a proof of the labour theory of value, per se. Kautsky reaches this result through his apparent definition of value as a common property of commodities, but if I were to define value as something else, I would get a different result. I think that a lot of the debate between Marxists and their opponents is more them talking past each other because they're using different definitions[4].
Anyway, Kautsky has said that commodities have value because of the "general labour embodied" in them, and he goes on to give us a more precise definition: the magnitude of the value of a commodity is equal to the "quantity of [...] labour contained in it". The quantity of labour is itself "measured by time". However, that isn't the same as the time "expended upon in [a commodities] production", which would imply that the product of a lazy worker is more valuable than that of a very productive worker. We are looking at "social" (rather than individual), labour. We now need to define this.
This is where things become kind of tricky, because Kaustky quotes Marx and we are introduced to the concept of "labour-power", which seems to mean the productivity of labour. I'm assuming that this is defined in terms of exchange-value. Marx defines a few different types of labour-power. The labour-power of the community is the total productivity of labour (ie. what all individuals in the community can produce), while the labour-power of an individual is the productivity of that particular individual. The "social average labour-power" is thus the average productivity of labour in a community. One thing I'm confused about here is the definition of an "individual" in a community. Does the term refer to every person in a community, or does it apply to only workers (both employed/unemployed), or only employed workers?
Anyway, given some definition of "individual", we can make represent these concepts mathematically. The labour-power of an individual (lp) can be represented by equation D as the amount (n) of a commodity (x) produced by an individual multiplied by the exchange-value (E) of a unit of that commodity, over a given period of time (t). The labour-power of the community (Lp) can be represented by equation E as the sum of the labour-power of all individuals in that community. Social average labour-power (A) can be represented by equation F as the labour-power of the community divided by the number of individuals (i) in that community. Is this correct?
D: lp = nx*Ex/t
E: Lp = Σ(nx*Ex)/t
F: A = Σ(nx*Ex)/(i*t)
Now we're introduced to Marx's "labour-time" concept, which seems to mean the amount of time spent producing a good. Marx then talks about "average labour-time" and "socially-necessary labour-time", which seem to be the same thing: the average amount of labour-time necessary to produce a commodity with a given use-value and a given production process (e.g. labour intensity).
Mathematically, then, we can represent "socially-necessary labour-time" as the sum of the labour-time of individuals (lt), divided by the total amount (n) of a commodity (x) produced by all individuals multiplied by the exchange-value (E) of that commodity. We'll call this equation G.
G: Lt = lt/(nx*Ex)
Now, going back to measuring value, Kautsky seems to be saying that the magnitude of the value (V) of a commodity (x) is equal to the socially-necessary labour-time embodied in that commodity (Lt), which can be represented mathematically with equation H:
H: Vx = lt/(nx*Ex)
I'll pause here and allow for comments before I go on to read the rest of the chapter in a few days. I hope the link between labour-power and labour-time is explored, because there doesn't seem to be a link at the moment. Also, a question: is "socially-necessary labour-time" an economy-wide concept, or does it differ for each commodity? The same question applies to "social average labour-power".
[1] marxists.org/archive/kautsky/1903/economic/index.htm
[2] Ignoring the problem of double coincidence of wants inherent in barter for the sake of example
[3] I don't actually agree with this, but I'm only interested in understanding Marxism here
[4] Interestingly, this could be evidence of Kuhn's theory of incommensurability between paradigms
The first point made by Kautsky is that all commodities must have a "use-value" - that is, a commodity must be a "useful thing". I'm interested in whether this concept of use-value is marginal, or whether it applies to an entire class of commodities, since it's not made entirely clear. In other words, is the use-value of a commodity the utility gained by having another more of a given commodity (e.g. the utility brought about by an additional 100g of butter), or is it an evaluation of entire classes of commodities (e.g. butter vs. gold)? I think Marxists made hold the latter point, because Kautsky writes that use-value is "determined by [a commodities] physical properties", which would be the same for all commodities in a given class.
If Marxists hold the marginal utility view, then the use-value (S) of a given unit of a commodity (x) can be represented by equation A, where use-value is equal to the change in utility (U) brought about by a change in the amount (n) of the commodity owned by a person. With the other view, the use-value of a given unit of a commodity can be represented by equation B, where the use-value is equal to the utility of the commodity class (some as yet unspecified function).
A: Sx = dU/dnx
B: Sx = U(x)
The next point made by Kautsky is that commodities have an "exchange-value", which is "the proportion in which a commodity exchanges with another". So, if at some time and in some place 100g of butter exchanges for 1 apple, and 100g of butter also exchanges for 2 onions, then it is reasonable to say that 1 apple would exchange for 2 onions[2]. So, would it be correct to say that the exchange-value of 1 apple is 2 onions? Mathematically, we could represent the exchange-value (E) of a given unit of a commodity (x) in terms of the amount (n) of another commodity (y) it can be exchanged for. We'll call this equation C.
C: Ex = ny
Now, Kautsky argues that for the concept of exchange-value to exist, there must be some "common property" of all commodities that allows us to equate them[3], which he terms the "value" (as distinct from the two concepts above) of a commodity. If I've understood him correctly, Kautsky is defining value as a "common property" of all commodities. The product of his investigation, then, is to answer the question of what constitutes this common property. He argues that use-value must be distinct from value because use-values (while they constitute the motive for exchange) are obviously a different (rather than a common) property of commodities, (ie. different commodities have different use-values). Let me know if I'm going wrong anywhere.
So, we can say that the use-value of a commodity doesn't constitute its value. What, then, are we left with? Kautsky says that taking away the use-value of a commodity leaves only one quality: "that of being products of labour". He then goes onto to add that as we're looking for a common property, we must also abstract from the particular kinds of labour (e.g. labour of a carpenter, labour of a butcher) that have created the commodity. As such, a commodity only has value because "homogeneous or general human labour is embodied in it". Have I got this right, so far? It seems, then, that we can mathematically represent value (V) as some function of the labour embodied in a commodity (we haven't yet specified the dimensions of this "general human labour" embodied in a commodity, so I can't yet write an equation).
A key thing that I want to note here is that this isn't a proof of the labour theory of value, per se. Kautsky reaches this result through his apparent definition of value as a common property of commodities, but if I were to define value as something else, I would get a different result. I think that a lot of the debate between Marxists and their opponents is more them talking past each other because they're using different definitions[4].
Anyway, Kautsky has said that commodities have value because of the "general labour embodied" in them, and he goes on to give us a more precise definition: the magnitude of the value of a commodity is equal to the "quantity of [...] labour contained in it". The quantity of labour is itself "measured by time". However, that isn't the same as the time "expended upon in [a commodities] production", which would imply that the product of a lazy worker is more valuable than that of a very productive worker. We are looking at "social" (rather than individual), labour. We now need to define this.
This is where things become kind of tricky, because Kaustky quotes Marx and we are introduced to the concept of "labour-power", which seems to mean the productivity of labour. I'm assuming that this is defined in terms of exchange-value. Marx defines a few different types of labour-power. The labour-power of the community is the total productivity of labour (ie. what all individuals in the community can produce), while the labour-power of an individual is the productivity of that particular individual. The "social average labour-power" is thus the average productivity of labour in a community. One thing I'm confused about here is the definition of an "individual" in a community. Does the term refer to every person in a community, or does it apply to only workers (both employed/unemployed), or only employed workers?
Anyway, given some definition of "individual", we can make represent these concepts mathematically. The labour-power of an individual (lp) can be represented by equation D as the amount (n) of a commodity (x) produced by an individual multiplied by the exchange-value (E) of a unit of that commodity, over a given period of time (t). The labour-power of the community (Lp) can be represented by equation E as the sum of the labour-power of all individuals in that community. Social average labour-power (A) can be represented by equation F as the labour-power of the community divided by the number of individuals (i) in that community. Is this correct?
D: lp = nx*Ex/t
E: Lp = Σ(nx*Ex)/t
F: A = Σ(nx*Ex)/(i*t)
Now we're introduced to Marx's "labour-time" concept, which seems to mean the amount of time spent producing a good. Marx then talks about "average labour-time" and "socially-necessary labour-time", which seem to be the same thing: the average amount of labour-time necessary to produce a commodity with a given use-value and a given production process (e.g. labour intensity).
Mathematically, then, we can represent "socially-necessary labour-time" as the sum of the labour-time of individuals (lt), divided by the total amount (n) of a commodity (x) produced by all individuals multiplied by the exchange-value (E) of that commodity. We'll call this equation G.
G: Lt = lt/(nx*Ex)
Now, going back to measuring value, Kautsky seems to be saying that the magnitude of the value (V) of a commodity (x) is equal to the socially-necessary labour-time embodied in that commodity (Lt), which can be represented mathematically with equation H:
H: Vx = lt/(nx*Ex)
I'll pause here and allow for comments before I go on to read the rest of the chapter in a few days. I hope the link between labour-power and labour-time is explored, because there doesn't seem to be a link at the moment. Also, a question: is "socially-necessary labour-time" an economy-wide concept, or does it differ for each commodity? The same question applies to "social average labour-power".
[1] marxists.org/archive/kautsky/1903/economic/index.htm
[2] Ignoring the problem of double coincidence of wants inherent in barter for the sake of example
[3] I don't actually agree with this, but I'm only interested in understanding Marxism here
[4] Interestingly, this could be evidence of Kuhn's theory of incommensurability between paradigms