A Quick Note On Hoarding and Scarcity: Applied Cambridge Economics

Hoarder03

Yesterday and today in the comments section to my blog there was a somewhat interesting discussion about hoarding and unemployment. One commenter claimed that hoarding only caused unemployment in a monetary economy. I have heard this a lot, but I have never thought it to be remotely true.

I laid out a simple example. Here I will give another. Imagine an economy of robots with a constant population and a zero growth rate. This economy, then, just reproduces itself day after day. In order to do this oil is needed. The robots need to consume 80 barrels of oil a day to do their work (i.e. consumption) which is wholly occupied with operating the machinery, while 20 barrels are needed to use this machinery to extract the 100 barrels needed for the economy to reproduce itself (i.e. investment).

Now, what happens if I come along and hoard, say, 10 barrels of the oil? Well, the economy will experience unemployment that day. Let’s say that the 10 barrels are taken out of ‘consumption’ because the robots know that for every 1 barrel they take out of ‘investment’ they will lose 5 barrels the next day. Well, that means that 12.5% (1/8) of the robot workforce will have to go unemployed because they cannot be paid. Let’s say they ‘shutdown’ and do not operate that day**.

Another commenter correctly pointed out that this could not happen in a marginalist model. He was entirely correct but this does not point to the unreality of the situation — this scenario is undoubtedly a real one and perfectly logically coherent — but rather the inability of mainstream models to deal with such phenomena. Due to the way mainstream models are set up — in this case, the problems arise due to assumptions of substitution; the assumption that ‘capital’ is an endowed feature that does not rely on inputs; and the assumption of timelessness — they simply cannot conceive of such problems.

But these problems are real. I am no Peak Oil theorist but I think we can all agree that if 20% of the US’s oil imports were cut off tomorrow a recession and unemployment (together with inflation) would follow. Indeed, we have a natural experiment in this regard; namely, the oils shocks of the 1970s.

During the oil shocks OPEC undertook an embargo on exports of oil to the US. This was effectively the same thing as my example of hoarding. What happened? Prices rose after each shock and a recession soon followed. You can see this in the chart below (data from FRED).

OilUnemployment

As we can see, each time the OPEC countries held back oil exports to the US the economy dipped into recession. The mainstream at the time came up with all sorts of wacko explanations for these recessions (and I want to stress that oil was not the only factor) and they also came up with wacko explanations for the inflation that accompanied them. But that was because their basic models could not incorporate such events.

Thus even in a monetary economy a withdrawal of certain key resources needed for the reproduction of the system of production will create unemployment and recession. This is intuitively obvious, of course, but economists are not the most intuitive people on the planet. Rather they are led around by the nose by their models which completely structure the way they view the world.

The model that I laid out above is, by the way, a stripped down Sraffian model. Such a model could also be derived from the work of Wassily Leontief or Karl Marx in the reproduction schemas of Volume II of Das Kapital or you can find a similar framework married to Keynesian economics in Joan Robinson’s The Accumulation of Capital, but such a model cannot be derived from marginalist theory.

What lesson should we learn from this? Simple. Different models tell us different things about different aspects of the economy. Even if you don’t think that marginalist models are complete garbage you must understand that they only produce results based on the assumptions that they make. If the initial assumptions rule out, for example, the effects that shortages of a commodity that is needed to reproduce the system of production lead to, then the model-user will not be able to understand such phenomena. They will literally suffer from a myopia that is caused by their own rigid adherence to the models that they have been told are “superior” by those who mark their exams and give them promotions.

If that is not, at the very least, a good case for economic pluralism, I don’t know what is!

_________

** Actually, it’s a little more complicated than this. If the robots were rational they would recognise that the entire workforce was required to operate the machinery. Thus, by removing some of the workforce by ‘shutting them down’ they would not get the maximum amount of oil even if they kept investment constant. Thus, they would have to balance this properly. I think that the end result comes out at about 1 barrel of investment-oil forgone and 9  barrels of consumption-oil forgone. Thus around 11.25% (9/80) of the workforce go unemployed. This will lead to a shortfall of 5 barrels the next day that will have to be distributed and so on and so on until the economy returns to full employment. But I laid it out above as I did to keep things simple. The overarching point is the same.

Update: I actually ran through the simulation properly in the comments. What we actually get is a permanent unemployment equilibrium. Here I quote my comment from below:

In the period in question — call it Period t — demand is 100 (but 10 are essentially disposed of). The inputs needed to cater for this demand come from Period t-1. These were produced in a full employment economy. The robots then decide how to distribute these 100 inputs, minus the 10 extracted by the hoarder (imagine these disappear), in line with how best to produce inputs in Period t+1. The best way to do this is to “shut down” 19 of the robots and have the rest work.

In Period t-1: 80 units of labour (at subsistence wage) and 20 units of (circulating) capital produce 100 units of output. The labour:capital ratio here is 4:1. For every 4 units of labour, 1 unit of capital is used. Together each “coupling” produces 5 units of output, so 100 units.

In Period t: 10 units disappear (hoarded). Leaving the economy with 90 units. These are divided up in line with the previous ratio (4:1). So, that means that 72 units of labour are thrown together with 18 units of circulating capital (again, 4:1, the optimal ratio). The rest of the labour force remain unemployed because they are in “shutdown” and cannot be reactivated without more output. This system again reproduces itself. It produces 90 units of oil.

Now that I actually work through it what we get is a permanent unemployment equilibrium ala Keynes in the General Theory. Wow! Very interesting!

About pilkingtonphil

Philip Pilkington is a London-based economist and member of the Political Economy Research Group (PERG) at Kingston University. You can follow him on Twitter at @pilkingtonphil.
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30 Responses to A Quick Note On Hoarding and Scarcity: Applied Cambridge Economics

  1. dansullivan0 says:

    The article comes so close to seeing the difference between finite natural resources and labor products, and never quite gets there. Clearly, however, if his hoarder had been stockpiling silicon chips, the economy would obviously just make that many extra silicon chips.

    Even a shortage of oil would not stop employment unless something else was at play. Heck, people were more fully employed in the United States before there was oil than afterward, and there is no significant unemployment among the Amish, who are quite prosperous and spurn the use of oil products.

    People are idle because land and natural resources are idle, and the motivating force behind land and natural resources idle is that people will pay money to get the hoarder to let go of them. Classical economists have understood this at least as far back as John Locke, who wrote,

    “Sec. 50. But since gold and silver, being little useful to the life of man in proportion to food, raiment, and carriage, has its value only from the consent of men, whereof labour yet makes, in great part, the measure, it is plain, that men have agreed to a disproportionate and unequal possession of the earth, they having, by a tacit and voluntary consent, found out, a way how a man may fairly possess more land than he himself can use the product of, by receiving in exchange for the overplus gold and silver, which may be hoarded up without injury to any one; these metals not spoiling or decaying in the hands of the possessor. This partage of things in an inequality of private possessions, men have made practicable out of the bounds of society, and without compact, only by putting a value on gold and silver, and tacitly agreeing in the use of money: for in governments, the laws regulate the right of property, and the possession of land is determined by positive constitutions.

    “Sec. 51. And thus, I think, it is very easy to conceive, without any difficulty, how labour could at first begin a title of property in the common things of nature, and how the spending it upon our uses bounded it. So that there could then be no reason of quarrelling about title, nor any doubt about the largeness of possession it gave. Right and conveniency went together; for as a man had a right to all he could employ his labour upon, so he had no temptation to labour for more than he could make use of. This left no room for controversy about the title, nor for encroachment on the right of others; what portion a man carved to himself, was easily seen; and it was useless, as well as dishonest, to carve himself too much, or take more than he needed.”

    What Locke is saying here is that, before money, there was no point in hoarding land, but after money, there was. And the more land is hoarded and held back from the public, the more desperate people will become and the more they will pay for access to that land.

  2. ivansml says:

    “Now, what happens if I come along and hoard, say, 10 barrels of the oil? Well, the economy will experience unemployment that day.”

    Does it now? Let’s say yes. So employment decreases by 10/80 = 12.5%. But production of oil requires (robot) labor, and assuming a linear fixed-coefficient technology (like all Sraffian models do), that means total production also decreases by 12.5%, to 87.5 barrels. Now robots want to consume 70 barrels, but there’s actually only 57.5 barrels left after hoarding and investment takes place, so there’s still disequilibrium. That means we need to decrease employment by another 12.5/87.5 = 18%. And so and so it goes, until the economy collapses and output is zero. Where did the robots make a mistake, I wonder?

    Exercise for the reader – what would happen if it was the wage, instead of employment, that decreased by 12.5% in the first step?

    Exercise for the reader # 2 (warning – requires math): Rewrite the example in terms of neoclassical production sets embedded in a dynamic Arrow-Debreu model (c.f. Mas-Collel et al.: Microeconomic theory, chapter 20), discuss the set of feasible allocation sequences and characterize stationary steady states. Discuss how a steady state is related to the notion of “self-reproducing” economy. Finally, and in light of your previous results, evaluate the following statement “Due to the way mainstream models are set up […] the assumption that ‘capital’ is an endowed feature […] and the assumption of timelessness — they simply cannot conceive of such problems.”

    “The mainstream at the time came up with all sorts of wacko explanations for these recessions (and I want to stress that oil was not the only factor) and they also came up with wacko explanations for the inflation that accompanied them. […] If that is not, at the very least, a good case for economic pluralism, I don’t know what is!”

    I don’t know what mainstream did at the time, as I was not alive back then. But in these days, the example of 1970’s oil crisis as a negative supply shock, with its effects illustrated through simple AS-AD model, is covered in (approximately) every undergraduate macro textbook on Earth. There even exist economists who spend large part of their career studying effects of oil shocks, and hundreds of scholarly papers on the topic (I know – who would have thought?). You may want to have a little of that pluralistic education yourself, mate.

    • (1) Did you see the footnote perchance? I don’t think it operates like you say. The robots — let’s say that they’re a collective, like the Borg, and they communicate the best plan to one another — optimize by shutting down a certain number of robots and retracting a little bit of investment oil. That’s all. You don’t need to divide by zero or whatever it is that you’re doing.

      (2) Assume that the wage is paid daily. So either the robots “turn on” and work or they don’t. This is not wholly unrealistic as it shows that such things do not adjust by the nanosecond. Besides, the alternative is the same. If the oil-wage reduction is spread over the whole population the robots simply work shorter hours. The “unemployment” is identical, it is just redistributed through “work-sharing”. (Mathematically, if wN is total consumption, in the case where employment adjusts N falls and in the case where wages adjust w falls; the actual effects are the same on total labour hours).

      (3) You’re going to have to make your own case here if you want me to engage with what you’re saying.

      (4) The mainstream came up with monetarist explanations of the 1970s stagflation. If you are not aware of this then please read a book on the history of economic ideas. Also, a supply shock in an AS-AD model will cause inflation, not unemployment!

      • ivansml says:

        1) 2) Output is linear in labor. If some part of robots shut down, then output will decrease proportionately, and you solution doesn’t reflect that.

        3) If you’re unfamiliar with what I wrote, no problem. But in such case you may want to refrain from repeating half-century old criticisms that have been addressed long time ago. The “mainstream” model easily allows to incorporate dynamics, intertemporal accumulation of capital, “reproducibility” and all that stuff.

        4) No, it will decrease output and increase inflation, unless the short-run aggregate supply curve is vertical. Just open the textbook or Wikipedia, will you?

      • 1)2) Again, read the footnote. I was simplifying for the sake of readability.

        3) Make the case in the face of the above example if you can. I don’t think you can. I think what those models did was they assumed away these problems through various arbitrary assumptions. But if you’re confident in what you’re saying you should be able to “solve” the above model for full employment. I doubt you can.

        4) Oh right yeah, sorry. Thinking it through you’re right. Anyway, the response in the 1970s was monetarism. Not AS-AD. It does seem, however, that your endorsements of AS-AD are at odds with your endorsements of Arrow-Debreu…

      • ivansml says:

        1), 2) Your footnote still doesn’t solve the problem:
        demand: 71 consumption + 19 investment + 10 hoarding = 100
        output: 100 * (71/80) = 88.5

        3) Sorry, got better things to do. Just as a teaser, here’s how one would represent mathematically production side of the robot economy:

        // capital now = investment one period ago
        K_{t} = I_{t-1}
        // Leontieff prod. fun. in capital and labor
        Y_{t} = min{K_{t}/a, L_{t}/b}
        // output consumed or invested
        Y_{t} = I_{t} + C_{t}

        Except for production function, it’s exactly isomorphic to Solow growth model (with full depreciation of capital in one period).

      • 1)2) I think that we’re having a problem of communication here. And by that I mean that you are making assumptions that I am not making and then pretending that this is a mathematical mistake. Demand is, as you say it is. In the period in question — call it Period t — it is 100 (but 10 are essentially disposed of). The inputs needed to cater for this demand come from Period t-1. These were produced in a full employment economy. The robots then decide how to distribute these 100 inputs, minus the 10 extracted by the hoarder (imagine these disappear), in line with how best to produce inputs in Period t+1. The best way to do this is to “shut down” some of the robots and have the rest work.

        I don’t even know what you’re doing. Your demand equation makes sense. But your output equation does not. Here, I’ll try to be clearer and do the maths less roughly.

        In Period t-1: 80 units of labour (at subsistence wage) and 20 units of (circulating) capital produce 100 units of output. The labour:capital ratio here is 4:1. For every 4 units of labour, 1 unit of capital is used. Together each “coupling” produces 5 units of output, so 100 units.

        In Period t: 10 units disappear (hoarded). Leaving the economy with 90 units. These are divided up in line with the previous ratio (4:1). So, that means that 72 units of labour are thrown together with 18 units of circulating capital (again, 4:1, the optimal ratio). The rest of the labour force remain unemployed because they are in “shutdown” and cannot be reactivated without more output. This system again reproduces itself. It produces 90 units of oil.

        Now that I actually work through it what we get is a permanent unemployment equilibrium ala Keynes in the General Theory. Wow! Very interesting!

        (3) This is an assertion. Not an argument. Make the case properly. If it actually makes sense.

      • ivansml says:

        So robots consume stuff produced one period before. My timing assumption was pretty standard (used e.g. by Sraffa, as far as I know), but OK, yours can work too. Still, there’s no particular reason why robots should react the way you say – they could just keep working 80 units of labor, using 20 barrels for investment and consuming the remaining 70. In decentralized economy, this could be achieved e.g. by decrease in wage.

        If you mean that each robots needs to consume 1 barrel just to be able to work, then effectively you’re assuming that wage is fixed and cannot adjust, so naturally you can get unemployment.

        You have chosen numbers so that if robots maximize output in each period, they will just be able to reproduce their inputs. In other words, Y_{t+1} = Y_{t} (plus any shocks between periods t and t+1), output is a random walk. With just slightly different numbers you’d get positive or negative growth, Y_{t+1} = c*Y_{t} with c more or less than 1. Not particularly enlightening, in my opinion.

      • I did not assume that each robot consumed 1 barrel. But I did assume a subsistence wage. In that sense, the wage must be fixed otherwise workers will literally not get the calorie/oil intake to be able to work. This is a standard Sraffian/Ricardian/Marxian assumption.

        Is this reasonable? In the example given above: yes! I am trying to show a case where a hoarding of a very important input in the economy (oil) has effects on the production structure and doesn’t allow the economy to reproduce.

        Is this assumption reasonable in other circumstances? Maybe, maybe not. We can discuss each of them as they come. But my example is an economy where a key input is hoarded. In order to get an idea of this we must use a classical subsistence wage model.

        Again, I stress: different models work for different things. A Sraffian model can show that a restriction in a vital input-commodity can cause the economy to be unable to grow at the same rate. A typical marginalist model cannot do this. (AS-AD can’t because it doesn’t have a labour market. Thus when output contracts it is not clear how this affects unemployment and wages. Also the AS-AD framework functions by a contraction of the money supply relative to prices, but that is not what I am trying to show here. In the AS-AD an expansion of the money supply would reduce unemployment. If you monetised the above model an expansion of the money supply would not reduce unemployment).

        Anyway, the point stands: hoarding in a non-monetary economy of a good that is vital for the reproduction of that economy will cause unemployment. And even in a monetary economy such a restriction can cause unemployment if it is a vital element of the wage-basket and thus, in a sense, non-negotiable.

    • **(4) Actually the AS-AD model implicitly assumes higher employment, or at least higher investment, in a supply-shock due to lower real wages. This is a major flaw in the model that I used to annoy my poor macro lecturer with. In fact, I can make a fairly good case that an AS-AD model produces a hyperinflationary spiral in the face of a supply-shock. But that is for another day, perhaps.

  3. Pontus says:

    Phil, you are modelling a supply shock.

    “Now, what happens if I come along and hoard, say, 10 barrels of the oil?”

    This is a deus ex machina that comes along a simply removes 10 barrels of oil. Not even Prescott would dream such a neoclassical event up. And of course, if you cripple supply you cripple employment. What’s the novelty? And why is this not in mainstream models? It’s actually the most textbook case that all students are protesting about.

    If we abstract from the deus ex machina, and assume that the robots decide not to consume 10 barrels, and not to invest them either. Then I can see how this would create a recession. In the same way as people in a coordinated event all decided to go on a hunger strike.

    Do you seriously think this is progress?

    • Well, Pontus, you didn’t say that when you commented on the last post.😉

      Anyway, what the above example shows — and what more sophisticated Sraffian/Leontieffian models show much better — is that certain inputs are more important than others to the structure of production. When I was discussing this with you, your working assumption was that all inputs were identical. That is why you wrote:

      If a good is hoarded, there is still demand for it (if I buy wheat but don’t eat it, I still bought it). And if it is a produced good, it is still produced. In the OPEC case, not producing oil means not utilising the labour force. This contrasts with hoarding of oil, in which the labour force is used. Guess which one will lead to underemployment?

      Also, if the oil plant shuts down the aggregate demand shortfall from the laid off workers would balance with the aggregate supply shortfall. That is also incorrect if oil is a more important input than others and will have further knock-on effects.

      If you dropped the arrogant, spiteful attitude you might actually learn something you know…

      • Pontus says:

        “If you dropped the arrogant, spiteful attitude you might actually learn something you know…”

        Lol. From you? The Dunning-Kruger effect strikes again!🙂

        And of course I didn’t say so. I honestly didn’t think someone was stupid enough to bring up an example where a commodity that delivers 500% return AND is vital for individual consumption, which in turn is vital for production, is neither invested nor eaten. But I was wrong.

        Your argument is basically the following: Suppose output is produced according to y=f(h), where h is hoarding and f(.) is some heterodox thing which relates negatively to h. Then hoarding leads to a fall in output! QED!1!!! HAHAHAHAHAAH!1!!11! You are all wrong stupid mainstream economists.

        Assuming the solution is normally not a very progressive way forward. I am sure that you can come up with a heterodox model in which the economy shits unicorn. But just because you can come up with such a model doesn’t mean the economy shits unicorns. Just FYI.

      • You’re right, it is rather obvious. Strange that you got it wrong in the comments section of the last post.😉

      • Pontus says:

        Oh, Phil, you’re reading comprehension is suffering too. I didn’t get it wrong. I just excluded the possibility that someone was that stupid. But as I said, I was wrong: someone actually is that stupid. Let’s not mention any names.

      • Of course, you did Pontus, of course you did… no really… we all believe you… we really do!😉

      • Pontus says:

        Who are we?

        But yes, of course I was arguing that if f(h) relates negatively to h, then an increase in h does not lead to a decrease in f(h). Of course I was.

      • Oh there’s a few people who get laughs from your antics on here, Pontus. Keep dancing monkey. Keep dancing.

  4. Pontus says:

    Phil: “[A] supply shock in an AS-AD model will cause inflation, not unemployment!”

    Ivansml: “No, it will decrease output and increase inflation, unless the short-run aggregate supply curve is vertical. Just open the textbook or Wikipedia, will you?”

    Phil: “Oh right yeah, sorry. Thinking it through you’re right. Anyway, the response in the 1970s was monetarism. Not AS-AD. It does seem, however, that your endorsements of AS-AD are at odds with your endorsements of Arrow-Debreu…”

    Beautiful! Phil cannot even get first year undergraduate stuff right! It’s really sad. As I said before, with friends like these, the heterodox don’t need any enemies.

    • More classiness from Cambridge’s classiest economist!😀

      You might want to read the rest of the comments, Pontus. The transmission mechanism in AS-AD is wrong.

    • Pontus says:

      Does that change the fact that you had absolutely no idea what you were talking about? In fact, it almost makes me think that there might be other areas where you have no damn clue, but still let your yapping mouth go loose. Funny that.

      • Do you feel better after that little cathartic episode, Pontus? Will you need another release tomorrow? Give me your address and I’ll send you a punch-bag… or perhaps an inflatable doll might be more appropriate?😀

      • Pontus says:

        “or perhaps an inflatable doll might be more appropriate?”

        Slow clap. Stay beautiful Phil. Stay beautiful. What finesse!

      • Well, I’m just trying to understand what emotional void you’re filling on here, dude.

      • Pontus says:

        Touche Phil! You are really nailing it today. You’re an acquired taste. Refined.

      • Oh, I’m entirely serious. You’re a pretty weird dude. I mean think about it. You follow blogs of people you consider stupid and then attack them in the comments section with a mix of crude insults and criticisms. I mean, you actually spend your time doing this. It’s really sad. It’s obvious that you’re trying to prove something to yourself. You’re quite transparent.

      • Pontus says:

        Woah! Check this out. Just replace “blogs of people” with “mainstream economists” and “the comments section” with “a blog and articles”, and you describe your entire career! Now THAT’S sad.

      • Yes, yes, of course. But I’m not focused on the person. I think that many of the people I criticise are very smart. When I speak to them in person I’m courteous. You, on the other hand, try to make things personal. You have a boiling need to attack people. You see the difference? Your activities reek of insecurity and self-doubt.

      • Pontus says:

        So you’re saying that when you are suggesting that I need an “inflatable doll”, or when you call me a dancing monkey, you are being courteous? And that it’s not personal, and doesn’t reek of insecurity and self-doubt?

        Seriously?

        Just as a reality check for you Phil: Very very few people think of you as “courteous”. On the contrary, you are making quite a name for yourself as being one of the rudest, insecure, and incompetent wannabe economists around. I tough on you, yes. But for the only reason that you’re being such a dick to everyone around you. You can thank me later.

      • Yes, I know that some of the mainstream guys don’t like me much. But again: it’s not personal. I just think their ideas are bad. As people, I have no problem with them. That’s why I’m not on their blogs all the time trying to attack them as people. That’s not my style. That’s just sad.

        Oh but that’s the only way to deal with people like you. You’d find rather quickly that if you stopped commenting on here and on Syll’s blog I’d quickly fall off your radar. You see, I have no desire to engage with you, follow you on the internet and so forth. It’s you that comes to me, not vice versa (you should think hard about that by the way).

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