Debunking Economics, Part III: “Uninformed and Inexperienced Armchair Theorisers”

Chapter 5 of Steve Keen’s Debunking Economics explores the marginalist theory of the firm. Keen first channels Piero Sraffa’s 1926 criticisms, then catalogues the neoclassical theory’s complete lack of real world corroboration – as noted in my title, a businessperson once referred to it as “the product of the itching imaginations of uninformed and inexperienced arm-chair theorisers.”

The neoclassical theory of the firm supposes that, in the short run, firms face increasing marginal costs – their costs per unit (average cost) increase as they produce more. This occurs because in the short run, the ‘amount’ of capital (and land) employed is fixed, so producing more involves squeezing more and more out of machines with more labour. The intersection of these increasing costs with how much they can gain from selling more, or their ‘marginal revenue’, constrains their size.

This homogeneous treatment of capital should strike many as silly. The neoclassical theory effectively supposes that, if we employ 9 people to dig a ditch with 9 spades, employment of the tenth will split the 9 spades into 10 slightly smaller, worse spades. However, if new labour is employed, new capital is – must be – employed simultaneously, whether it is bought or if it is taken from previously idle capacity. A taxi driver cannot do anything without his taxi; an office worker without a computer is also fairly useless.

So increasing marginal costs are unlikely to be the case with individual firms or narrowly defined industries. As Keen puts it, “engineers purposely design factories to avoid the problems economists believe force production costs to rise.” In reality, firms have excess inventories and tend to vary capital, labour and land all at once, even in the short run. They therefore face roughly constant, or falling, returns to scale.

Sraffa pointed out that it’s only really valid to treat some factor inputs as fixed if we define an industry so broadly that the factors would have to be converted from other uses. For example, if we take agriculture, and assume the country is well populated and at or close to full employment, then it’s reasonable to treat land and machinery as fixed in the short term. However, since the theory of the firm assumes that supply and demand are independent and that one ‘industry’ can be studied apart from all others, another problem appears: this situation does not lend itself well to ceteris paribus analysis. Changing wages, supply costs, and the displacement of labour from other areas will have notable impacts on the rest of the economy, such that tinkering with our curves individually cannot be deemed a proper representation of what will happen.

There are a few cases where firms or industries might fall between these two categories, but really they are the exception.

Keen cites 150 empirical surveys that found firms reporting constant or falling average costs of production. In particular he cites Eiteman and Guthrie, who found that 95% of firms out of 334 did this, whilst only 1 chose the curve that looks like the one found in textbooks. Most firms also use cost-plus pricing, rather than taking marginal considerations into account, and adopt a form of trial and error when pricing.

A flat(ish) supply curve leads us to the incredibly interesting proposition, supported by the classical economists, that supply determines price while demand determines quantity. This is, of course, a simplification ,but appears to corroborate far better with the real world than neoclassical ‘simplifications.’

In my opinion this is the strongest case against neoclassical micro as taught. Jonathan Catalan can find no objections to this section, either, and gives the story an Austrian slant. Keen says that this problem has never really been addressed by economists, but ignored, despite the clear superiority of Sraffa’s logic and the corroboration of the empirical evidence with his approach. I find it hard to believe neoclassical economists can wiggle their way out of this problem, should they ever address it.

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  1. #1 by Ron Ronson on July 14, 2012 - 6:38 pm

    I\’m not sure I see why this is such a big deal.

    I can well imagine that in most industries economies of scale would mean that in terms of pure physical output bigger is better. However as you got bigger a) your input prices would rise and b) you sale price would fall. So you keep expanding production to the point where your profit rate is at the desired level. This will look like it is cost plus markup but in reality (as you have set the price of both inputs and output by choosing your level of production) it is not really.

    The above is a simplified version of how Austrians see it but I suspect that it is not far off what most economists would believe.

    Its true that this model would not hold in perfect competition model but I suspect SK if building a straw-man if he think that by attacking a model possibly not even taught in econ 101 classes he is actually criticizing what neo-classical economists really believe.

    • #2 by Jon Finegold on July 15, 2012 - 6:22 am

      The Austrian theory of the cost plus mark-up price: Böhm-Bawerk’s cost of production theory.

    • #3 by Unlearningecon on July 15, 2012 - 8:35 pm

      Increasing marginal cost is taught in econ101, I can guarantee you that.

      I’m not sure about this, you’re basically saying reality looks a certain way but actually firms are instead conforming to a completely made up model that they themselves dismissed.

      Keen goes on to discuss what constrains expansion, and finds that most real world firms are primarily concerned with marketing and financing constraints rather than a desired rate of profit.

    • #4 by Ron Ronson on July 15, 2012 - 10:12 pm

      I should probably read Keane’s book. From your review I get the impression that he is debunking a sort of parody of neo-classical economics rather than what economists in that school actual believe.

      The view that I was presenting is as follows:

      Most firms are oligarchical which means they are big enough that they contribute to both input prices and output price. This means that they will in fact have diminishing marginal returns even if they can actually increase physical productivity as they expand. They know roughly what level of profit they wish to make and they chose the level of output that generates this level. Put these things together and you end up with “price plus markup” leading to the economy producing the right mix of goods without firms actually having to worry about “marginal costs”.

      • #5 by Unlearningecon on July 15, 2012 - 10:28 pm

        I have been taught economics and so has Keen. So has Jonathan Catalan, who finds no fault with this part at least. Keen is highly informed and frequently references the definitive PHD textbook, Mas-Colell, as well as numerous others.

        The fact is that neoclassical economics is more ridiculous than its proponents realise, so they will automatically assume Keen is attacking straw men. But he just isn’t – the only gripes I really have are perhaps is tone and the way he paints economists as more right wing than I think they are.

        Most firms are oligarchical which means they are big enough that they contribute to both input prices and output price. This means that they will in fact have diminishing marginal returns even if they can actually increase physical productivity as they expand.

        This is just a non sequitur. How does being able to contribute to input and output prices mean diminishing marginal returns? Does it not factor into your formulation at all that 95% of firms do not report diminishing marginal returns?

        They know roughly what level of profit they wish to make and they chose the level of output that generates this level.

        There’s no evidence or argument to support this view. Evidence suggests firms choose the markup they need to achieve a certain level of profit, rather than the level of output.

        Put these things together and you end up with “price plus markup” leading to the economy producing the right mix of goods without firms actually having to worry about “marginal costs”.

        What is the ‘right’ mix of goods and services? And again there is no real justification for this statement.

      • #6 by Ron Ronson on July 15, 2012 - 10:35 pm

        oligopolists not oligarchical :)

    • #7 by Ron Ronson on July 16, 2012 - 1:10 am

      I didn’t mean to annoy you with my comments, I have enjoyed your reviews of the chapters in Keen’s books – I was just trying to put your post into the context of my own views of economics. I am certainly happy to give Keen the benefit of the doubt until I have read his book (and probably the economists he is attacking).

      On diminishing marginal returns: I can see that the way I expressed this was confusing. What I take your post to be saying is that as firms increase output then the costs of production will go down not up as neo-classical theory says, I agree with that analysis. However I then went on to a case where most firms are oligopolists and their demand for input and supply of output has some effect on the prices of these things. In this case the view that cost of production falls as output rises seems less clear cut. Eventually rising input prices may cause this not to be true. However apparently the surveys show that empirically this is not the experience of firms – they do see falling costs. Is that the full story though – costs may be falling but what is happening to revenue as output rises? It is the interaction of costs and prices that lead to decisions about output – and it was this I was attempting to explore in my comment. So overall my point is “even if Keen is right and neo-classical’s are wrong on this point – does it really matter for the big picture in economics of how demand and supply end up affecting level of output” ?

      On “Evidence suggests firms choose the markup they need to achieve a certain level of profit, rather than the level of output”. So how do they chose the level of output out then ? Assuming that a firms choice of output also has some effect on input costs and sales prices (which must be true outside of perfect competition) then what you say can’t really be the whole story. Only one level of output (and corresponding prices) will achieve the markup that we both agree they may be aiming for.

      “What is the ‘right’ mix of goods and services?”: I was thinking of the level that best matches consumer demand. As firms choose the optimum level of output this will influenced by the strength of demand. A good with inelastic demand will see its price fall only slowly as firms increase output and hence the correct “markup price” will lead to much higher levels of production. (A similar argument applies relating to competition for inputs and how that affects their prices , but I’m running out of space here).

      • #8 by Roman P. on July 16, 2012 - 5:09 am

        Ron,
        But what if the firms whose outputs are your inputs also experience decreasing MC? If so, then buying more inputs will lead to the lower average price of inputs too! For example, buying just a gallon of H2SO4 will likely cost you a lot, but buying a million of them will likely cost neither acid-producer nor acid-user as much.
        (To Unlearningecon: sorry, previous comment was a glitch)

      • #9 by Ron Ronson on July 16, 2012 - 1:50 pm

        But eventually as firms expand they would all will be competing for the same pool of labor and other resources and the price should rise (at least in my model), which is why I am a little skeptical that the results from those surveys can be taken 100% at face value.

      • #10 by Unlearningecon on July 16, 2012 - 2:05 pm

        You have not annoyed me with your comments at all and I encourage comments from either ‘side.’ I was just having trouble discerning exactly what you mean.

        I see you are referring to the case where firms have a sufficient degree of market power that CP analysis is not appropriate. I agree – I would say that to have a ‘flat’ supply curve but stick with classic supply-demand analysis, we would have to define an industry narrowly enough for this not to be a problem.

        However your argument against a flat supply curve appears to rest on the assumption that a supply curve is not flat, and increased demand for factor inputs will increase the price of those same inputs. If anything I think this is the opposite: as firms grow bigger and have more market power, they will be able to get lower costs. This is a fairly standard ‘economies of scale’ argument that is taught in economics courses, and appears to corroborate well with the evidence.

        You almost answer your question from the penultimate paragraph in the final one: firms choose the level of output in response to demand! In modern economies they have to ‘create’ this demand with marketing & advertising, and financial constraints also hold them back. They then work out total average costs and stick often a fairly arbitrary markup on it based on their aims/what they can get away with.

      • #11 by Ron Ronson on July 16, 2012 - 4:26 pm

        Your model seems to include the following attributes:
        – Firms face flat or even downward sloping supply curves for their inputs. This plus economies of scales mean the more they produce the lower their average costs
        – They create their own demand via advertising
        – They set prices based on costs plus a self-selected markup

        I believe that these assumptions ignore scarcity and competition. If these assumptions were true for all firms then the only thing that would prevent us all living lives enjoying unlimited and very cheap luxury goods would be the failure of marketing people to generate sufficient demand for them.

        However competition between firms means they cannot create their own demand curves or set their own rate of profit. Competition for scare resources needed for production must mean that the supply curve for inputs has to slope upwards at some point as output expands.

        I agree that many firms may be setting their output and prices based on a desired rate of profit. But what they may not be aware of is that by the very act of doing this they are changing the equilibrium levels for themselves and other firms for these variables.

      • #12 by Unlearningecon on July 17, 2012 - 11:36 am

        You forgot financing constraints, which I also mentioned! I don’t think this means the supply curve starts to slope upwards, however; I simply think it restricts supply past a certain point.

  2. #13 by Dallas Wood on July 14, 2012 - 6:54 pm

    Thank you for blogging Keen’s book. It has made for some interesting reading. But I am very confused by your most recent post. On the whole, I’m not quite sure what point you’re driving at here. Here are 3 specific complaints/comments that might help me better understand what you’re saying, if you have time to address them.

    #1) I don’t believe the following sentence is an accurate representation of production with a fixed input:

    “The neoclassical theory effectively supposes that, if we employ 9 people to dig a ditch with 9 spades, employment of the tenth will split the 9 spades into 10 slightly smaller, worse spades.”

    Adding another unit of labor does not change the number of units of capital (# of spades). The fixed capital just means that each worker you add to your production process is less productive than the one before it.

    ——————-

    #2) You seem to be saying that all production processes are best described by a fixed proportions production function (e.g. 1 man & 1 shovel are required to dig Y holes per day). I don’t believe this accurately describes the production of most products, but even if it did I’m not sure what that brings to the discussion. If one input is fixed, you still don’t get constant marginal costs over all ranges of production even with fixed proportions. Here’s an example.

    Say 1 man with 1 shovel can dig 1 hole per day. Your firm has 9 shovels and you can hire an infinite amount of workers for $10 per hour. Your MC for the 1st hole will be $10, your MC for the second hole will be $10, and so on, but the MC for the 10th hole will be infinity.

    ——————–

    #3) But maybe your point is that no input is ever fixed? That you can always vary any input in the production process (land, capital, what ever). In other words, that we always live in the “long run”. If that is what you are saying, then I think that is more of an argument about the physical state of the world and not inherent flaws in neoclassical economics.

    But even in that world where any input can be varied, you won’t necessarily get the flat(ish) supply curves you discuss at the end of your post. That’s true even if we believe all production processes can be described by fixed proportion production functions. Returning the hole digging example, say you can always buy more shovels at anytime for $10. Then the marginal cost for digging the 1st hole, 10th hole, or 100000th hole will be $20 ($10 per person + $10 per shovel). Flat marginal cost, right? But look at what you’re assuming. You’re assuming that no matter how many people you employ, the wage is always $10. And no matter how many shovels you buy, the cost is always $10. Why should we believe this always holds true for an entire industry?

    • #14 by Jon Finegold on July 15, 2012 - 6:29 am

      1. Right, that’s why Keen says that the 9 spades will be divided among 10 workers.

      2. The entire point is that there are rarely “fixed inputs,” and usually firms will have excess capacity to be able to expand output.

      3. Keen doesn’t assume that for an entire industry. Sraffa suggests that the costs of inputs will change as demand for them changes; but, with regards to the costs of production of a single firm this isn’t necessarily true. Firms within an industry will compete for market share, rather than infinitely expand output. They will also vary the pattern of inputs (a similar idea, even if not exactly the same, as Hayek’s ricardo effect).

      • #15 by Dallas on July 15, 2012 - 5:28 pm

        1. “Right, that’s why Keen says that the 9 spades will be divided among 10 workers.” If that’s what Keen says, fine. But Unlearningecon says 9 spades becomes 10 worse spades (as I quoted). I still think that would be incorrect.

        2. Like I say in 3, I thought that was the point Unlearningecon was driving at. But I am still note sure why his post detours onto a discussion about how labor and capital must always be combined for production to expand. It seems beside the point, because even if it were true it doesn’t change what happens when one of those inputs is fixed. And, again, if his primary argument is that “no input is ever really fixed”, then that really isn’t an argument about neoclassical producer theory per se (since it deals just fine with varying all inputs).

        3. I don’t know what Keen assumes. I only know that if you want the flat industry supply curve that unlearningecon describes, then input prices cannot increase as industry output increases.

    • #16 by Unlearningecon on July 15, 2012 - 8:23 pm

      Dallas,

      1. If you employ people to dig a ditch, they need a spade. The only way you can hold the capital employed fixed but add another ditch digger is if the spades are made of some sort of homogeneous glob called ‘capital’ and can reassemble themselves terminator 2 style.

      Alternatively, I guess the person could dig with their hands.

      2. I think you are confusing how much capital the firm owns with how much it employs. In your example the firm does not follow the neoclassical theory by squeezing more and more out of a fixed amount of capital, but instead employs extra capital when labour is employed.

      3. Inputs are only fixed in a broadly defined industry, but then we run into the same problems outlined above.

      Keen elaborates on a better theory of production later in this chapter. He talks about how what constrains firms employment and growth are mainly financing and marketing considerations.

      The primary reason to believe cost curves are flat or falling is, of course, that this is what firms actually report!

      • #17 by Dallas on July 16, 2012 - 1:52 am

        UE,

        Thanks for responding. Here are some final thoughts from me before we all head back to work tomorrow.

        1. I’m glad you liked my example of the 10th person digging with their hands. :) I honestly think that is a better interpretation in this example. Though, if you really believed that a person can’t dig a hole without a shovel (that production was described by fixed proportions), then the 10th person would actually contribute nothing to production. He would just stand there doing nothing.

        Anyways, I know where you are coming from with this homogeneous capital thing. It is a common complaint of mainstream macro, where big-K capital is an aggregate of shovels, trucks, and what have you. But this is a micro situation! Your example is a very specific production process. There is no reason to lump all non-labor inputs into mysterious quantities of “capital”. If you wanted, you could create a production function that explicitly includes shovels, trucks, land, whatever. So I don’t think the whole “ homogeneous capital” complaint applies.

        2. Then I guess don’t fully understand your example. In your example, I thought you were saying that the firm **owns** a fixed number of shovels (9). If that is the case, the firm doesn’t need to employ all 9 shovels at all times nor would neoclassical producer theory require him to.

        Suppose that we are still dealing with a situation where 1 man with 1 shovel can dig 1 hole. This production process could be described using a fixed proportion (or Leontief) production function–y=min(K,L). Again, you have 9 shovels (K=9) and you employ 1 person (L=1). How many holes can you dig? 1 because min(9,1)=1. Now let’s say you employ 2 people. How many holes can you dig? 2 because min(9,2)=2.

        That’s the math. Intuitively, you could read this as saying you will never use more shovels than you have people. But since you have a fixed number of shovels, you will never be able to dig more than 9 holes. For example, say you have 10 workers. min(9,10)=9.

        So, I am indeed employing extra capital as you increase the number workers. But only to a point. The amount of capital you own is fixed. So you cannot employ more than 9 units of capital (9 shovels).

        THIS is what I thought you were saying. Are you instead saying that you must *employ* 9 shovels regardless of the number of workers you employ? So, for example, 1 person would have to use 9 shovels?

        If we were talking about a production process where there was substitutability between inputs (maybe a process described by a cobb-douglas production function), then I think it would make sense to talk about having 9 fixed units of capital that must always be employed. But I don’t think the example you gave really works like that. Digging ditches seems best described by a fixed proportion production function and that means 0 substitutability between inputs.

        Maybe you’re trying too hard to design an example that makes neoclassical production theory sound silly?

        3. I don’t think your response really gets at my comment, which was that if you want a flat supply curve, you will need to assume that the price of inputs is constant regardless how many inputs an industry employees. I don’t think that assumption always makes sense.

        Anyways, thanks for the discussion!

      • #18 by Unlearningecon on July 16, 2012 - 1:55 pm

        Look at this.

        This isn’t about how much capital a firm has spare, but how much it employs. The capital input stays at ‘1’ and we are not told what units this is measured in. As more labourers are added to squeeze more out of the capital, the production goes down. Maybe the digger does dig with his hands; maybe capital is made out of the same stuff a terminators. I am not required to make the theory sound silly, it does this itself.

        As Robert Vienneau notes, I’m not talking about Leontif production functions. I’m also not suggesting 1 worker will ever use 9 shovels – all I’m saying is, contra the story of fixed capital and rising marginal cost, the ‘amount’ of capital employed will have a roughly linear relationship with the amount of labour employed, rather than being fixed.

        I don’t see that the price of inputs being constant or falling is a problematic assumption?

      • #19 by Dallas on July 16, 2012 - 2:54 pm

        I don’t want to be rude by not responding so here are some quick responses. But this might have to be my last contribution to the discussion since I am going to be in & out all week. Hopefully these comments are helpful!

        First, I don’t think there is anything wrong with the example in cliff notes and it helps me better see what you are trying to say. But I don’t think it really addresses my confusions. First, saying that a firm must employ 1 unit of capital (or 9 or whatever) makes sense if you have a production process where you can substitute labor and capital (like if it were described by a cobb-douglas production function).

        But in your previous post, you said that a man needs a spade to dig a hole. If you need 1 man with 1 shovel to dig 1 hole, that is a fixed proportion production function anyway you slice it (even though you now say that isn’t what you have in mind). So if you employ 1 person, that person will only use 1 shovel and leave the rest sitting there. This is not inconsistent with the example in cliff notes. They are just using a different production function (though they explicitly say what it is).

        Though I guess if you really wanted to stick with the notion that 9 shovels must be employed, you could imagine the 1 worker using each of the 9 shovels in turn. But the fact would remain that he would only produce as much as he would if he just used 1 shovel (the production function is still y=min(K,L)). It is really just a question of what story you want to tell to make the production function more intuitive. Although I don’t know why one would choose to imagine 1 worker taking turns with 9 shovels when a simple image is 1 worker using 1 shovel and leaving the other 8 alone.

        Now, judging from your most recent post you are NOT saying that 1 worker must use 9 shovels. BUT you are still insisting that that 9 “units of capital” must always be employed, even if you hire 1 person. Are you are sticking with this idea that all man-made inputs must be aggregated into this malable goo called “capital”? So I guess the 9 units of capital somehow turn into 1 really nice shovel when you only employ 1 person?

        Well, I just have to repeat that you really don’t need to do that! Like I said before, the homogeneous capital complaint makes sense in macroeconomic model where all capital is aggregated. But this a microeconomic example! There is no need to aggregate or pretend capital has magic properties at all. You could easily write a production function that includes any number of inputs! So why pretend you must have this mysterious input called “capital”?

        Now, in the cliff-notes link, you point out that they just include a generic input called “capital” that is combined with labor to make a product. But I hope you’re not implying they had to it that way. I mean, it is cliff notes for crying out loud! ;) The point is to provide an introduction to economic concepts as simply as possible.

        Second, as far as your assumption of constant price of inputs, I don’t think it is always a bad assumption. But there are cases where it might be. And I think it is worth making that explicit. I mean, think about it from your own perspective as a provider of labor services. If you’re getting paid $20 per hour for 40 hours, would you still charge $20 for your 41st hour? Or would you start charging more as the opportunity cost of your time rises? Just something to think about.

      • #20 by Unlearningecon on July 19, 2012 - 5:44 pm

        makes sense if you have a production process where you can substitute labor and capital

        Where does this happen?? I can think of some examples of specific capital replacing specific labour but really, overall you need some combination of both if you are to produce anything.

        This is not inconsistent with the example in cliff notes.

        It is inconsistent because the extra people in cliff notes result in slightly higher production. I mean, OK, maybe they can cheer the guy on and get him stuff, but you and I both know this isn’t what they mean. What is happening is more productivity is being ‘squeezed’ out of the same amount of capital.

        I really feel, as I said below, that this is entering ‘how many angels can dance on a pinhead?’ territory. But I’ll bite anyway. If a company has 9 shovels and employs 1 labourer, it is only employing one shovel. The rest of the capital is idle; I am not insisting it is employed. The example from cliffnotes may just be for beginners but I think it is fundamentally misleading and quite plainly wrong. If you turned ‘capital’ into any recognisable form of capital then even a beginner would see that it is a silly example. Add the fact that real world evidence doesn’t support it and how can it be justified?

        As a seller of labour, in the real world, I would take whatever was given to me unquestioningly because it is incredibly difficult to get a job at the moment. This changes for highly skilled people but is not true for the majority. Furthermore, suppliers actually tend to decrease costs when their customers order more.

  3. #21 by Mick Brown on July 14, 2012 - 7:01 pm

    Having dropped out at 17 in the 1960s of the education and social system that goes with being brought up by a Cambridge economist (and never being told anything about economics) I spent the next 45 years working mainly for small firms in all sorts of jobs.

    The most ever I heard said about pricing was “double the price of materials and add 50%” or the like.

    (Of course there was an awareness of what other companies might charge.)

    At no time during those years did I ever hear the word ‘marginal’ apart from when I took an OU course and a half in Economics when I was 50 plus.

    I spent the following 15 years getting my head round all the microeconomic theory in relation to my own experiences, model by model.

    Then when I thought it was all over, I read Steve Keen’s book.

    Will it ever end?

    I hope not.

    • #22 by Unlearningecon on July 15, 2012 - 8:29 pm

      I often ask business owners I know about marginal cost etc. and the common response is “what the hell are you talking about?” They simply work out the costs and then stick on as much as they can get away with/need to live/think is reasonable.

  4. #23 by Robert on July 15, 2012 - 9:47 am

    Dallas Wood is confused. The ditch-digging example does not assume fixed proportions. Each of the 10 slightly smaller, slightly worse spades are a different kind of capital good than the 9 spades. As such, 10 of one might cost the same as 9 of the other. Some sort of homogeneous, ghostly capital is what is assumed to be fixed. This “capital” is measured in units of American dollars or British pounds or Euros or what have you.

    The example may sound silly. But the neoclassical theory of the firm in the short run is silly. (So is the neoclassical theory in the long run, but that is not the point of the example.)

    I think the example dates back to Dennis Robertson.

    • #24 by Unlearningecon on July 15, 2012 - 1:21 pm

      It sounds so ridiculous that people from all sides would immediately assume it was a straw man. But it isn’t.

      Also, the example wasn’t in Keen. I think I got it from the anarchist FAQ.

    • #25 by Dallas on July 15, 2012 - 5:53 pm

      Well, I don’t want to spend the entire discussion on the first bullet point, especially since #2 and #3 are more directly about me trying to understand the point of the post. I know the folks that comment on this blog have their own ideas about capital theory and I am not going to try to change anyone’s mind. So here are my final thoughts on the first bullet.

      I think a more faithful interpretation of a production function like the one described in the OP might involve the 10th worker digging with his hands. Or only digging when one of his fellow workers takes a break and he can use their spade? Either way, capital remains fixed and production exhibits diminishing marginal returns (the 10th worker will be digging much fewer holes than the 9th worker).

      Robert, if you have any links that describe your point in more detail, please feel free to post. I would be interested in reading them. Have a good day!

  5. #26 by Blue Aurora on July 16, 2012 - 1:37 am

    Regarding the concept of homogenous and heterogenous capital…

    Of course no one denies that capital is in practice, heterogenous. However, Keynes himself didn’t use any partial derivatives in the General Theory. Hayes’s guide to Keynes’s magnum opus depicts him using partial derivatives, when Keynes does not use them. See the following links.

    http://cje.oxfordjournals.org/content/31/5/741.short

    http://cje.oxfordjournals.org/content/32/5/815.extract

    http://cje.oxfordjournals.org/content/32/5/811.extract

    http://www.kof.ethz.ch/en/publications/p/kof-working-papers/282/

    • #27 by Unlearningecon on July 17, 2012 - 11:35 am

      One of the great things about Keynes is that his theories actually seem to work better when further heterodox insights are incorporated.

      I haven’t read TGT carefully enough to know whether Keynes uses partial derivatives or not, but there seems to be a lot of debate over it. I’l look into it.

      • #28 by Blue Aurora on July 18, 2012 - 6:11 am

        Heterogenous capital or homogenous capital, no partial derivatives appear in the General Theory. I don’t own an original MacMillian copy of the book, but I do own the 1964 paperback Harcourt and World edition. Only total derivatives appear in the book. If there were, Keynes would have specified two inputs instead of just one input.

  6. #29 by Robert on July 16, 2012 - 4:24 am

    Dallas still does not understand the hole-digging example is not one of fixed proportions, a Leontief production function, or whatever.

    Dennis Robertson suggested that perhaps the hole would be too crowded to employ the 10th man. Instead we would get 9 worse shovels and a bucket for the 10th man to fetch beer. The example, apparently, comes from Dennis Robertson’s article, “Wage Grumbles”. Another article of the same period making a similar point is Shove’s review of Hicks’ book, “The Theory of Wages”. I quote from Shove here: http://robertvienneau.blogspot.com/2007/01/nothing-is-new-under-sun.html

    Ron Ronson doesn’t seem to know that the neoclassical theories of monopolistic competition and of monopoly supposedly imply that less will be produced than in “perfect competition”. And the firm in these theories will be operating in conditions of decreasing marginal cost, not increasing marginal cost.

    By the way, Keen switched the order, between the two editions, of the chapters, “Size does matter” and “The price of everything and the value of nothing”.

    • #30 by Ron Ronson on July 16, 2012 - 2:03 pm

      ‘Ron Ronson doesn’t seem to know that the neoclassical theories of monopolistic competition and of monopoly supposedly imply that less will be produced than in “perfect competition’
      In fact I did know this – having both learned it and seen it refuted on this very blog a week or so ago.

      “And the firm in these theories will be operating in conditions of decreasing marginal cost, not increasing marginal cost.”
      I didn’t know that – it seems inconsistent with what is said about neo-classical theory in the post.

  7. #31 by Derek R on July 16, 2012 - 8:30 pm

    Men working with shovels get hungry, tired and thirsty while digging and recover when they are allowed a break. If we have 10 men working with 9 shovels for 8 hours per day, we will indeed dig more holes in a given number of days than if we have 9 men working with 9 shovels for 8 hours per day because the 10th man need merely wait until one of the other 9 goes home for the day before starting to dig. So at the very least we will get 8 more hours of production per day by adding a 10th man to the 9 shovels.

    Even in the case where we have 27 men with 9 shovels giving round-the-clock digging, a 28th man will give a little more production since men are more productive at the beginning of the shift than after 8 hours. Therefore the 28th man can replace the weakest of the other 27 at some point during his shift.

    There is no need to split the shovels or replace them.

    • #32 by Unlearningecon on July 16, 2012 - 8:59 pm

      This really is getting into ‘how many angels can dance on a pinhead?’ territory. The fact is that real firms employ capital and labour simultaneously. They just do. They rarely ‘hold capital fixed’ and employ more, expect perhaps when hours are split, but that kind of thing is simply not discussed in economics classes, and is a special case anyway.

      EDIT: Just realised your example would not generate increasing marginal costs.

  8. #33 by Sean Fernyhough (@Sean_Fernyhough) on July 22, 2012 - 1:45 am

    It’s worth remarking that the Sraffa article from 1926 is available freely online. The article and Keen’s chapter makes it clearer why Sraffa made his comment about economies of scale in the introduction to commodities.

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