MARX & MMT, PART 4 – The TSSI and Marx’s Aggregate Equalities

Differences in interpreting Marx, as we have seen, tend to come down to three key questions. The first concerns how the value of labor power is understood. This will affect the treatment of variable capital. Is its value determined by the labor embodied in wage goods or the prices of those goods? The second question concerns the value of the means of production. This pertains to constant capital. Is the value of constant capital determined by the labor embodied in inputs or the amounts paid for them? The third question concerns whether value and price determination should be considered simultaneous or temporal. It was pointed out in the previous post that Marx’s aggregate equalities stand or fall with our answers to the first two questions. His equalities hold provided constant and variable capital are assumed to depend upon the prices of inputs and wage goods rather than the labor embodied in them. This approach is taken by all single-system interpretations, whether temporal or simultaneist. For the purposes of this post, adopting any of these interpretations would have been fine. However, the choice between temporality and simultaneity will sometimes be relevant later in the series. By way of background, the present post specifically introduces the temporal single-system interpretation (TSSI).

Although the focus here will be on the TSSI, my inclination in this series is only to commit to a particular interpretation over others when such a choice is unavoidable. We can think of the exercise in terms of relaxing assumptions. For some purposes – for instance, when envisaging something akin to a short-run macro model, as was done in parts 1 and 2 of this series – all that matters is the determination of variable capital. This is because, in parts 1 and 2, we applied fairly restrictive assumptions, appropriate to a short-run focus, and confined our attention to new value added in a period. In that context, as long as the value of labor power was defined in terms of the prices paid for wage goods, there was no need to choose between any of the numerous well known interpretations that take that approach. There will still be times later in the series when the discussion will apply under this broader range of interpretations. For arguments that require Marx’s aggregate equalities to hold, it becomes necessary, as already mentioned, also to define the value of the means of production in terms of input prices. This is the purview of the present post. Later, in contexts where temporality is an issue, it will be necessary to commit specifically to the TSSI if the arguments presented are to be considered valid.

The motive for proceeding in this way is to bring out the degree of compatibility between different interpretations rather than only emphasizing their points of difference. It also means that readers who disagree with the TSSI – or single-system interpretations more generally – can still hopefully get something out of the exercise. A Marx-MMT synthesis would not necessarily have to involve one particular interpretation of Marx over others, notwithstanding the TSSI influence on this series.

Having acknowledged the influence, I need to stress that the viewpoint expressed in this series may in quite a few respects differ from that of the proponents of the TSSI. They themselves have differences among themselves. Statements of their position are provided in Freeman and Carchedi (1996), Freeman, Kliman and Wells (2004) and Kliman (2007). (Full references are provided at the end of the post.) The first of these books includes individual chapters from leading developers of the approach. The second book features dialogue between proponents of the TSSI and authors offering opposing viewpoints. The third book explains the TSSI and summarizes the history of the debate on Marx’s theory of value from that perspective.

There is one more point that I should make clear from the outset. In this post, it is assumed that a unit of the currency always represents the same amount of socially necessary labor. In other words, the MELT is assumed constant. This assumption will be dropped, at times, later in the series. Temporality modifies the formula for the MELT and this has ramifications for the macro relationships considered in parts 1 and 2 of the series.

 
Value and Price Determination in the TSSI

As the name suggests, the TSSI is above all ‘temporal’ and ‘single-system’. Being temporal, it views economic processes as dynamic and non-equilibrium in nature. Prices and values are determined sequentially, with outputs and output prices of one period functioning as inputs and input prices of the next. Being single-system, the TSSI views prices and values as mutually determinative. There is not, in this perspective, one set of forces determining values and another separate set of forces determining prices. Values and prices are thought to determine each other, but in a sequential rather than simultaneous fashion.

In what follows, I have decided to avoid matrix algebra. This makes the presentation a little more cumbersome than would otherwise be the case. The concern is that matrix algebra might be inaccessible to some, even though it is actually easier than the alternatives once you have been exposed to it. Apart from the present post, I don’t envisage employing algebra again in this series beyond an elementary level. The algebra seems necessary here to make clear the way in which the TSSI is able to replicate Marx’s aggregate equalities. For those who absolutely loathe algebra, hopefully you can still read around it okay. The next post will be almost entirely words.

For those who actually enjoy algebra, a more sophisticated presentation of the material is provided in Kliman and McGlone (1999). An introductory treatment that mostly mimics a section of Kliman and McGlone’s paper is provided in a previous post. The post employs matrix algebra and works through a numerical illustration.

Notation. Unit, sectoral and aggregate magnitudes. We will begin by considering the unit price and unit value of a commodity produced in sector i, which is one of n sectors that each produce a single commodity. A superscript i is attached to variables that relate to an individual sector. The absence of a superscript indicates an aggregate variable applying to the economy as a whole. For instance, si is the surplus value associated with a single unit of sector i’s output. The total amount of surplus value created in sector i is equal to the per-unit surplus value si multiplied by the physical quantity of gross output xi produced in the sector, or sixi. The amount of surplus value s created in the economy as a whole will equal the sum of all the surplus value created at the sectoral level; that is, s = Σisixi.

Time subscripts. The production period commences at time t and ends when commodities are ready to be exchanged at time t+1. In the TSSI, the prices of inputs and wage goods that determine the values of variable and constant capital are those prevailing at time t. They carry a t subscript. The values and prices of output, in contrast, will be those prevailing at time t+1. These have a t+1 subscript. Processes that occur over the entire period (meaning period t) from time t to time t+1 should, strictly speaking, have the subscript t,t+1. Such processes include the living labor performed, the profit and surplus value generated, rates of profit and the physical output produced over the period. To make the exposition a little less clunky, these processes will have no subscript. But it will be best to keep in mind that the meaning of no time subscript is actually t,t+1.

Value and price determination. At time t, capitalists combine means of production and living labor to produce output ready for sale at time t+1. The necessary outlay for used up means of production (i.e. constant capital) depends on the prices pt of inputs prevailing at time t and the amounts at of the commodities used as inputs. Similarly, the necessary outlay for variable capital depends on the going wage rate at time t, which will purchase for workers a basket bt of wage goods at period t prices.

To produce one unit of its commodity, sector i requires the amounts of constant and variable capital shown in (1). Labor performed in excess of the amount paid for variable capital will generate surplus value for capitalists:

MMT Marx 4 Eqn 1

In words, constant capital is calculated by multiplying each input’s price by its quantity and summing the resulting products. Since many commodities won’t be used as inputs for sector i’s commodity, these input quantities will be zero. Likewise for variable capital, we multiply the price of each wage good by its quantity and sum the results. Again, any commodity that is not consumed by workers – i.e. that is not a wage good – will have a quantity of zero.

The sum of cit and vit is the ‘cost price’ and, in single-system approaches, enters both the value and price of the individual commodity. The commodity’s output value λit+1 at time t+1 will equal cost price plus surplus value. That is, λit+1 = cit + vit + si. Its output price pit+1 will equal cost price plus profit. That is, pit+1 = cit + vit + πi. So, the only difference between the value and price of the commodity is that the latter includes an amount gi = πi – si. This means that the output price can be written pit+1 = cit + vit + si + gi. Notice in (1), though, that vit + si = Li. Therefore, we can simplify the expressions for the commodity’s output value and price to λit+1 = cit + Li and pit+1 = cit + Li + gi.

The expression for constant capital in (1) can be substituted into these formulas for the value and price of the new commodity.

MMT Marx 4 Eqn 2

 
 
 
 
 
 
 
 
 
 
The mutual interdependence between value and price has two aspects under the TSSI.

One aspect relates to output values. As shown in (2), output values at time t+1 depend on period t input prices. This interdependency relates specifically to constant capital. The value of variable capital does not directly affect the value or price of the commodity because new value created equals the living labor performed, irrespective of its division into variable capital and surplus value. The definition of variable capital is still important, though, because by affecting distribution, it affects the amount of surplus value and the rate of profit.

The second aspect of value-price interdependency operates at the aggregate level and follows from Marx’s key argument that value cannot be created or lost in exchange. To be clear, this is to be understood in real terms, correcting for any inflation. (Recall, the MELT is assumed constant in this post.) What a buyer gains by buying cheaply the seller loses and so forth. This means that the price-value differences for individual commodities sum to zero in aggregate.

Multiplying the sectoral price-value deviations gi by gross physical output levels xi and summing gives the total deviation g of prices from values for the economy as a whole.

MMT Marx 4 Eqn 3

 
 
 
 
 
 
To see the significance of this, we can calculate total value TVt+1 and total price TPt+1 for the economy as a whole. Total value is calculated by multiplying each commodity’s value in (2) by its output quantity and summing the resulting products together. Total price is calculated in the same way except to apply the procedure to each commodity’s price in (3) rather than value:

MMT Marx 4 Eqn 4

 
 
 
 
 
 
 
 
 
 
 
This confirms that the first of Marx’s aggregate equalities holds under the TSSI. Namely, total value equals total price.

Rearranging (3′) shows that in aggregate:

MMT Marx 4 Eqn 5

 
 
 
 
 
This says that, apart from any inflation, the value added in price terms for the economy as a whole (total price minus constant capital) equals the amount of living labor performed. This accords with Marx’s view that all new value is created by living labor.

Marx’s other aggregate equalities also hold under the TSSI. Specifically, total surplus value equals total profit and the price rate of profit r equals the value rate of profit σ. Both rates of profit are calculated in relation to total capital Kt.

MMT Marx 4 Eqn 6

 
 
 
 
 
 
 
 
 
In the TSSI, the determination of the average rate of profit as a ratio of aggregate value magnitudes is prior to the determination of prices. The determination is prior not only logically but temporally. The average rate of profit will be the same irrespective of how prices actually distribute the surplus value already created in production.

 
Discussion. The economic processes represented by the above algebra can be summed up as follows. Each period begins with purchases of – or the application of – inputs that were produced in an earlier period and whose prices form part of the given data for the new period. There is no reason to suppose that these prices are at equilibrium levels, and in general they won’t be. Nor, in general, will prices equal values, as has already been discussed earlier in the series. But once input prices are established, it will be these prices, rather than input values, that determine the amount that must be paid to acquire the inputs necessary for production.

Since it is the price, not value, of the inputs that determines the outlay necessary for production of the commodity, the difference between the price and value of the inputs “is incorporated into the value of the new commodity as an antecedent element” (Marx 1971, p. 167). In the passage from which this brief quote comes (reproduced at greater length in the next part of this series), Marx appears to make explicit that, in his view, and consistent with the single-system position, it is input prices, not values, that enter into the values of final commodities. (Similar statements can be found elsewhere in Marx’s writings, as will also be illustrated in the next post).

A major attraction of the TSSI is that it replicates Marx’s theoretical results in a straightforward manner. In the case of Marx’s equalities, the same is true of all single-system interpretations. If in attempting to interpret a theory we can’t replicate its results, it might cause us to ponder whether we have actually interpreted the theory as it was intended to be interpreted. This is especially so if there are interpretations – single-system interpretations, in the present context – that do replicate the results without difficulty. This is an argument put forward strongly by Andrew Kliman (2007). Kliman credits the interpretative principle to George Stigler.

Being able to replicate Marx’s theoretical results does not, of course, mean that the theory is necessarily worthwhile. It would be possible, for instance, to take the view that an interpretation that fails to replicate Marx’s results might nonetheless provide the basis for a better theory. What replication does establish is internal consistency. Marx’s key results can be shown – and have been shown – to follow logically from explicitly stated premises.

Even so, a few questions may spring to mind. For one, it might be wondered why it would make sense to define the values of constant and variable capital in the single-system way. For another, it might be asked if this is an interpretation that accords with what Marx wrote on the issue. We saw a tiny snippet above of one passage that appears to lend support to the single-system view, but the question calls for a closer look. Needless to say, an even more fundamental question, which relates to all Marxist approaches to value, concerns the rationale for considering labor to be the sole creator of new value. The next part of this series offers some thoughts on the first two questions. The third, more fundamental question is left for later.

 
References

Freeman, A. and Carchedi, G. (eds.) (1996), Marx and Non-Equilibrium Economics, Cheltenham: Edward Elgar.

Freeman, A., Kliman, A. and Wells, J. (eds.) (2004), The New Value Controversy and the Foundations of Economics, Cheltenham: Edward Elgar.

Kliman, A. (2007), Reclaiming Marx’s “Capital”: A Refutation of the Myth of Inconsistency, Lanham: Lexington.

Kliman, A. and McGlone, T. (1999), ‘A Temporal Single-system Interpretation of Marx’s Value Theory’, Review of Political Economy, Vol. 11, No. 1, pp. 33-59.

Marx, K. (1971), Theories of Surplus Value, Vol. III, Moscow: Progress Publishers.

12 thoughts on “MARX & MMT, PART 4 – The TSSI and Marx’s Aggregate Equalities

  1. Pete,

    Thanks for another great post.

    Sorry if I’m going too slowly and making silly questions. Please bear with me.

    In (1) both constant capital (c) and variable capital (v) have a time subindex (t). However, surplus value (s) and labour (L) have no time subindexes. The same applies to the equations following immediately (profit — pi — as well, has no time subindex).

    Why not?

    ———-

    As I further read the post, I noticed that equations (2) and (3) define parallel hyperplanes for the time period t,t+1. For instance, if n=2 then we have parallel planes in 3D space, separated by g^i.

  2. Hi Magpie. The variables without subscripts would have the subscript t,t+1 to indicate that we are referring to processes that occur over the entire period, from time t to time t+1. For these variables, I left out the subscripts, but they should be thought of as t,t+1. (I tried to explain this in the notation section.)

    As examples, L is living labor performed over the period. s is the surplus labor performed over the period. x is the output produced over the period.

    In contrast, the input prices are the prices that prevail specifically at time t. The output prices and output values are the prices and values that prevail at time t+1.

    Similarly, the amounts paid for c and v depend on prices at time t.

  3. Pete,

    I have one observation and one question.

    First, the observation, which is related to this:

    A major attraction of the TSSI is that it replicates Marx’s theoretical results in a straightforward manner. In the case of Marx’s equalities, the same is true of all single-system interpretations. If in attempting to interpret a theory we can’t replicate its results, it might cause us to ponder whether we have actually interpreted the theory as it was intended to be interpreted. This is especially so if there are interpretations – single-system interpretations, in the present context – that do replicate the results without difficulty. This is an argument put forward strongly by Andrew Kliman (2007). Kliman credits the interpretative principle to George Stigler.

    For what it might be worth, I agree with Prof. Kliman on that. One, however, does not need to trace that principle back to Stigler (although tracing it to him is delightfully ironic): it’s a matter of common sense.

    Marx wasn’t a mathematician (not that the maths involved are exceedingly complicated), was writing under extremely difficult circumstances, in the 19th century, in German. He never finished Capital. If someone deserves the benefit of the doubt (a benefit others, much less deserving, are regularly given) is him.

    An example to argue this point is Fermat’s last theorem.

    In 1637 Fermat left a hand-written note at the margin of an old maths book, saying that he had found a proof (too large to fit the margin) for the following proposition: no 3 positive integers a, b, c, satisfy the equation a^n + b^n = c^n (for n positive integer larger than 2).

    For over 3 centuries, mathematician after mathematician — professional and amateur alike — failed to prove it formally. And it wasn’t that nobody ever tried: the Guinness Book of World Records describes it as the world’s most difficult mathematical problem, having generated thousands of failed attempts to solve. It would be reasonable to assume it could not be proved (therefore, it was false, Fermat was mistaken) and leave things at that (basically what his critics claim with respect to Marx’s three aggregate equalities).

    And then, Fermat’s last theorem was proved (in 1994). The man was right, after all.

    This is where the analogy with Marx breaks: after a proof of Marx’s claim is offered, Marxist economists refuse to conclude what mathematicians had no problem concluding.

    ———-

    The question:

    Correct me if I am mistaken, but I believe Marx’s three aggregate equalities seem to depend critically on g = 0; as a consequence, perhaps one should be extra-careful in this point. Apart from Marx’s own argument, why should one accept that g = 0? Can you elaborate on this in your own words, or offer an illustration?

    Thanks!

  4. Excellent question, Magpie. No, I cannot prove this point. I do think it is a reasonable position, and personally I find it the most plausible starting point, but I can’t prove it.

    In a single-system setting, the answer to your question “Must g be zero?” comes down to the question, “Is it true to say that value is created only in production?”

    For Marx it is true because, in his theory, labor is the sole creator of new value, and the labor process occurs in production, prior to exchange. (It is possible to agree that g must be zero and that value is only created in production and yet disagree with the view that labor is the sole creator of new value, but that would not be Marx’s position.)

    As you know, in Marx’s view commodities already have their values prior to entering into exchange. In real terms, whatever happens in exchange cannot alter the total amount of value already created. If a commodity sells cheaper than otherwise, the buyer gains what the seller loses, and so on. Overall, the amount of total value is unaffected.

    In a sense, it might seem self-evident that value is created solely in production, not exchange, but of course we are talking here, not about physical output, but value. Even so, in a single-system setting, I find it hard to see how commodity value in real terms – as opposed to nominal terms – could come out of anything other than the production process. I’m not sure many critics of single-system interpretations would quibble over g = 0 given the single-system definitions of c and v. Instead, they would take issue with the definitions of c and v. But, as you know, Marx had in mind the “vulgar economists” of his day when dismissing exchange as a possible source of value.

    If we accept Marx’s view that value can only be created in production, and that it cannot be added to or subtracted from in exchange, then under single-system assumptions it follows that total price must equal total value. This implies that g must be zero. And this then also ensures, logically, that the other equalities will all hold as well.

    Note that in a dual-system framework, this is not true. Even if total price is taken arbitrarily to equal total value (as an invariance postulate), this will not logically imply that the other equalities hold.

    Example

    The purpose of this example is to illustrate the way in which Marx’s equalities hold, in a single-system setting, if we grant that value is only created in production. So, this doesn’t prove the fundamental point. It just illustrates what happens once it is accepted that total value is unaffected, in real terms, by exchange.

    Consider an economy with only two sectors. Rather than considering unit prices and values, we will simply deal with the sum of prices and sum of values for each sector. There is no fixed capital. The MELT is constant and equal to $1/hr. In other words, an hour of labor equates to $1 of value.

    Subscripts here are used purely to distinguish sectors. I’ve left out the time subscripts. Really, c and v should have time subscript t. The time subscript for L, s, π and r should be t,t+1. And the output prices and values should have time subscript t+1.

    For sector 1, c1 = 10, v1 = 10, s1 = 10.
    For sector 2, c2 = 50, v2 = 10, s2 = 10.

    Total value for the economy as a whole is c + v + s = 100. If we accept Marx’s argument that, in aggregate, no value can be gained or lost in exchange, total price must also equal 100. This implies that the price-value differences must sum to zero. That is, g = 0. Otherwise, total price would differ from total value, and some value would have been gained or lost in exchange.

    The average rate of profit for the economy as a whole is

    r = (s + g)/(c + v)

    Since we are accepting, at least for the sake of the example, that g = 0, it follows that the average rate of profit can be calculated as

    r = s/(c + v) = 0.25

    The ‘price sums’ for the two sectors are:

    p1 = λ1 + g1 = 30 + g1
    p2 = λ2 + g2 = 70 + g2

    We can derive expressions for g1 and g2 from the expressions for the rate of profit. Since

    r1 = (s1 + g1)/(c1 + v1)

    it follows (rearranging the expression) that

    g1 = r1 (c1 + v1) – s1

    And similarly

    g2 = r2 (c2 + v2) – s2

    To simplify further, assume that each sector receives its price of production. In that case, both sectors are subject to the same rate of profit, the average one r. That is,

    r = r1 = r2 = 0.25

    Therefore

    g1 = r(c1 + v1) – s1
    g2 = r(c2 + v2) – s2

    Substituting in what we know:

    g1 = (0.25)(20) – 10 = –5
    g2 = (0.25)(60) – 10 = +5

    As expected, g = g1 + g2 = 0.

    We can now calculate the price sums for the two sectors

    p1 = 30 + g1 = 25
    p2 = 70 + g2 = 75

    the profit for the two sectors

    π1 = p1 – (c1 + v1) = 25 – 20 = 5
    π2 = p2 – (c2 + v2) = 75 – 60 = 15

    and, finally, check our working by calculating the rates of profit:

    r1 = π1/( c1 + v1) = 5/20 = 0.25
    r2 = π2/( c2 + v2) = 15/60 = 0.25

  5. Pete,

    Before going back to business, let me say this first: reading you it’s a refreshing experience. You are not only knowledgeable, but you are also an honest, down to earth man. Frankly, there is no comparison between you and the pompous poseurs that populate the internet. It’s funny how the two extremes manage to co-exist.

    I thank you, my friend, for that. But enough of this.

    Regarding this:

    “No, I cannot prove this point. I do think it is a reasonable position, and personally I find it the most plausible starting point, but I can’t prove it.”

    Well, I suppose it is up to us to do that; after all, there is nobody else. And it may not be that difficult, either. The key, I suspect, is in accounting. And, as you may have noticed, I tend to put thought on my pet theories.

    I found this, however, intriguing:

    “It is possible to agree that g must be zero and that value is only created in production and yet disagree with the view that labor is the sole creator of new value, but that would not be Marx’s position.”

    Who believes that “value is only created in production and yet disagree with the view that labor is the sole creator of new value”? Mainstream economists (and on this I include all Keynesians, regardless of prefixes) believe that value is created in exchange (some go as far as believing it is a matter of “flow of funds”, only) and, at any rate, that labour and capital (plus, land, human capital, social capital, gender capital) adds value.

    I am not sure about Sraffians, but I do believe they also accept that value is created in production, by labour.

    So, I can’t really see who fits that description. Who is it you have in mind?

  6. So, I can’t really see who fits that description. Who is it you have in mind?

    It must be my imaginary enemies and the paranoia getting to me. 🙂

    I was initially going to write in the previous comment that the question of whether g = 0 comes down to whether labor is the sole creator of value. Then I thought there was a logical possibility I was missing — i.e. that maybe someone could think that value was solely due to production but not labor.

    The key, I suspect, is in accounting.

    Very intriguing idea, Magpie. I’m not sure exactly what you have in mind, but you’ve got me curious.

    I tend to think of labor as value in terms of human effort, similar perhaps to this well known passage from Smith:

    The real price of everything, what everything really costs to the man who wants to acquire it, is the toil and trouble of acquiring it. What everything is really worth to the man who has acquired it, and who wants to dispose of it for something else, is the toil and trouble which it can save to himself, and which it can impose upon other people. What is bought with money or with goods is purchased by labour as much as what we acquire by the toil of our own body. (Wealth of Nations, ch. 5, book 1)

    Basically, I would say that value is human effort. If effort must be expended, then those who appropriate the surplus results of that effort (the capitalists) have possession of something (value) that cannot be replicated without human effort. If, to the contrary, everything could be produced without any human effort – nature creating machines that create other machines that produce output without any intervention at all by humans – it makes sense to me that values, in Marx’s sense, would be zero.

  7. This seems like a good start:

    Basically, I would say that value is human effort. If effort must be expended, then those who appropriate the surplus results of that effort (the capitalists) have possession of something (value) that cannot be replicated without human effort. If, to the contrary, everything could be produced without any human effort – nature creating machines that create other machines that produce output without any intervention at all by humans – it makes sense to me that values, in Marx’s sense, would be zero.

    Under competitive conditions, prices would also likely be zero. The state could give them positive prices by imposing exogenous taxes on owners, payable only in the state’s currency, and then issuing currency to non-owners with which to purchase the goods and services produced without human effort. But, under competitive conditions, no revenue would be left over for owners after taxes had been paid.

    You probably do not remember my post on Krugman and robots[*], but prices would be zero without human effort, if for no other reason, because — in a simple, non government economy — nobody would have money to pay for the output (new value). If no income is available, output cannot be sold and so its market price would be nil.

    I had time to re-read the discussion back then and I think there were mistakes both in my defense of the whole idea and in the criticism it received.

    Take this initial criticism by K101:

    “I don’t think that the lack of consumer demand would be the biggest issue in a fully-automated economy. Capitalists have their own investment demand for productive inputs and this investment demand makes up a great deal of the economy. (and this is why a crisis can’t be the result of underconsumption…)”

    I can agree with everything — or almost everything — K101 says above. It’s true that capitalists have their own investment demand for productive inputs, as true as the fact the Moon orbits Earth every 28 days or so. But it’s irrelevant to the way GDP is calculated; as irrelevant as the fact of Moon’s orbits: GDP calculated by value added by definition excludes “investment demand for productive inputs”. Period.

    GDP to all effects and purposes would be 0, even though the quantities produced would be positive. This forces prices to zero. There is no way around. (Incidentally, this would prove my basic point that “labour is the source of all value”, as GDP by added value is GOP + COE: COE vanishes and this causes GOP to vanish)

    The problem — as I have concluded since — is that K101 is referring to total output; and I am speaking of GDP. As you know, they are not the same thing: total output is $c+$s+%v; GDP is $s+$v.

    His argument — unless I badly misunderstood him — seems to be that total output would not be zero, because capitalists could still trade between themselves (Incidentally, he apparently has no problem with the GDP = 0 bit).

    By implication, for K101, capitalist’s “investment demand for productive inputs” (aka intermediate demand) is independent of final demand.

    Only that it ain’t.

    My counter argument was that why would capitalists keep trading between themselves? Say, General Motors can no longer sell cars to the public (and by hypothesis, there is no government): there is no final demand for cars. But US Steel could still attempt to produce steel and sell it to General Motors (if GM bought that steel, that would be intermediate demand; this is what K101 seems to believe could still happen).

    But if GM purchases steel, it would not be able to sell the cars made from it: so, why would they buy? I think it pretty safe to conclude that they wouldn’t.

    After GM ceased producing cars, soon enough US Steel would stop producing steel.

    Moreover, once US Steel ceased producing steel, that would mean the end of the line for coal miners and iron ore producers, as much as GM closing doors meant the end of the line for US Steel.

    The only way capitalists could keep operating is if US Steel produces shovels, so that the coal miners and iron ore producers can mine stuff and sell it to US Steel, to produce shovels to mine stuff, to produce shovels to … But even in this case, there’s no profit: every single dollar goes to pay for constant capital. We have only $c in an endless cycle.

    [*] Krugman, Robots and Exchange Value.
    http://aussiemagpie.blogspot.com/2012/12/krugman-robots-and-exchange-value.html

  8. By the way, I should add something.

    Even if — for the sake of the argument — we were to concede K101’s objection:

    “I don’t think that the lack of consumer demand would be the biggest issue in a fully-automated economy. Capitalists have their own investment demand for productive inputs and this investment demand makes up a great deal of the economy.”

    That would still be irrelevant to my demonstration. If K101’s case is accepted, total output falls not to 0, but to $c. But that has no bearing whatsoever on the fact that new value is nil.

    Variable capital went to zero, and that caused profits to drop to zero (because surplus value was not realized). QED.

  9. Pete,

    On second thoughts, I think there is a flaw in my reasoning and I may have spoken way too soon. GDP doesn’t need to go to absolute zero immediately as a consequence of automation, although this should still affect a lot of economic activity.

    However, there might still persist some economic activity, not much, but at least more than the rather absurd “shovel and stuff” scenario.

    I’ll have to re-think the whole thing. Sorry.

  10. No worries, Magpie. Interesting thoughts, in any case. I do remember that post and the discussion.

    FWIW, Marx wrote (Capital, Vol. III, ch. 18):

    [A]s we have seen (Book 2, Part III), continuous circulation takes place between constant capital and constant capital (even regardless of accelerated accumulation). It is at first independent of individual consumption because it never enters the latter. But this consumption definitely limits it nevertheless, since constant capital is never produced for its own sake but solely because more of it is needed in spheres of production whose products go into individual consumption.

    I tend to think that final investment demand, too, is always, at least ultimately, derived demand. If there is no individual consumption at the end of the chain, no matter how indirectly, the investment goods won’t get produced IMO.

    Capitalists, of course, are also a small source of consumption demand.

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