Economists prove that the earth is flat

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…and in doing so, miss important factors affecting unemployment.

Consider the curve in the diagram below:

Now imagine a man traversing this curve from left to right in small steps of width W. Let us label the exact height (Y) of each foot as YL and YT (L stands for “leading” T stands for “trailing”). The difference in height will clearly depend on the width of the step and the gradient (G) of the slope. This can be expressed as:

 YL = YT + (W x G)

If we now consider smaller and smaller step sizes, in the limit as W approaches zero, YL becomes closer and closer to being equal to YT. If both the gradients and the step sizes are small, a poorly trained mathematician may sloppily pronounce that:

YL = YT        (warning, this equation is wrong)

Hopefully you can see that this statement is wrong, and if taken too seriously could erroneously lead people to believe that “slopes are impossible” and that therefore “the earth is flat”!

So what has this all got to do with economics?

The answer is that many economists have made the same mistake as our proverbial bad mathematician. There is an equation in economics textbooks that states:

aggregate expenditure = aggregate income*

In this case the “leading foot” is aggregate income and the “trailing foot” is aggregate expenditure. This may need some clarification:

The idea that aggregate income equals aggregate expenditure emerges from a simple model of the economy in which all the money that is earned by people is then spent on stuff that was made by people. Or to put it more precisely, the sum total of all the money earned by everyone in the country, per small unit of time (call this unit T), equals the total cost of everything purchased by everyone during that same unit of time. At this point alarm bells should be ringing because you will notice that my explanation of the meaning of the equation involved time, while the equation itself makes no mention of it. Just like the bad mathematician’s equation makes no mention of W. The economists have just said to themselves, “if we make T small enough, we can ignore its effects”. But just like ignoring W, ignoring T, does not allow for any change in the income or expenditure.

So lets see if we can fix this. Looking back at the (correct) equation for the height of the man’s two feet as he traverses x, we should expect the correct form of the expenditure & income equation to have something of the form

aggregate expenditure (at end of interval T) = aggregate income (at start of interval T) + changes in the money supply during T

Anyone that has a clear grasp of our monetary system** will know that loans create money and repayments destroy money. This means that the true state of affairs is as follows:

aggregate expenditure (at end of interval T)  = aggregate income (at start of interval T) + new loans taken out (during past T) - existing loans repaid(during past T)

So what if the original, crude version of the equation is a bit wrong, what problems may this cause?

Answer: you may miss out on the fact that a constantly falling money supply will cause a lack of demand. Aggregate expenditure may be maintained at a level just marginally less than aggregate income for perhaps months or even years.

How does a changing money supply affect the economy?

One way you can reasonably model an economy is to imagine that all the buying and selling happens at discreet intervals of duration T, with all the “sellers” of goods doing their selling at one time step and then, being newly armed with money, become buyers at the next step. This is shown in the diagram below for a scenario in which there is a constant money supply. Note the (aggregated) comments made by the parties on each side (click on image for larger version):

Under these circumstances, we can say:

aggregate expenditure (at end of interval T)  = aggregate income (at start of interval T)

Now consider what will happen in a rising money supply environment in which new money will occasionally be loaned into existence. See the following diagram. Note the comments as well as the additional money shown on the left hand side.

Under these circumstances, we can say:

aggregate expenditure (at end of interval T)  > aggregate income (at start of interval T)

And now by contrast, consider a falling money supply environment in which money will occasionally expire out of existence due to loan repayments. Note the comments as well as the disappearing money shown on the left hand side.


Under these circumstances, we can say:

aggregate expenditure (at end of interval T)  < aggregate income (at start of interval T)

A falling money supply environment is thus likely to be a miserable economic environment with high unemployment. This is why we have all these unconventional money creation schemes (like QE) going on right now. These schemes tend to be described by the media as simply “money printing”, but sadly they are not. Instead they  are all variations of “borrowing money into existence” with a consequence of raising debt levels. So economists and politicians are presenting the public with a false choice between either rising debt or a falling money supply. If economists would consider truly printing money (debt free), then we could have a rising money supply without greater debt.

There are actually alternate versions of this equation which add in factors like investment and foreign trade, but none of these alter the fundamental problem, so I will stick to analysing this most basic version of the equation for the rest of this article. My criticism equally applies to more complex versions of this equation you commonly see in textbooks.
** if you don’t then watch this video.

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  • João Granchinho

    Very good article, Reiss. Keep up the good work.

  • Conrad Jones

    Great article as usual. Clearly explains that a Rising or Falling Money Supply does affect the Economy.

    Now seems obvious.

    Unfortunately it doesn’t seem obvious to the CBI who stated today:

    “The CBI
    and the British Chambers of Commerce (BCC) want tens of thousands of new homes to be built to create new jobs and provide affordable homes.”

    Yes – it would create new Jobs, but the statement seems to suggest that we have a shortage of Homes and not an over supply of Credit Money in the Housing Market.

    House prices were in the “Rising Money Supply” category, but are now stagnating in the “Falling Money Supply” category.

    The Mainstream Media, the Government, Financial and Business Sectors have always maintained that the “Falling Money Supply” category for Housing is “BAD”.

    But unaffordable housing is also bad which suggests that “Rising Money Supply” category for Housing must also be “BAD”.

    Their solution is to flood the Housing Market with “affordable” houses. But this would then reduce the price of exisitng Home Owners property which would then cause another House Price Crash? Unless the “affordable houses” were only for FTBs and were of a very poor construction – Houses built to last only twenty years perhaps, and so would reduce the effect on exisitng older better built Homes.

    The Government’s solution (both Labour and Conservative) was to flood the FTB Market with Money in Shared Equity and other schemes. From the diagrams above it is easy for non-economists to see how these schemes may have actually made things worse for FTBs.

    • Voice of Treason

      I absolutely agree with you that the housing market is deeply dysfunctional. The way we buy houses, by creating new credit (i.e. mortgages) to purchase already existing assets is totally insane. In fact it has become the main driver of our ever-increasing supply of debt-money and it has to stop. It is self-defeating, since it only results in housing bubbles, followed by inevitable crashes. It just turns property into a speculative punt and drives prices so high that we all become lifelong debt slaves.

      However, I do think we should be building new (energy-efficient) houses and issuing money (real cash money) backed by these new assets. At the same time, we should be improving the existing stock, again using publicly issued cash, rather than borrowing.

      This would be much better than simply tipping money out of a helicopter, since that is liable to cause inflation without growth. The creation of new assets would give the new fiat money a form of collateralisation which would have the effect of stimulating real economic activity. As the money supply stabilises or even rises again, the new capital assets will add to the productive capacity of the economy.

      So, actually the diagram in the article is still an oversimplification. It is not only the money supply which changes from T to T+1, but the productive capacity of the economy also changes in response to capital formation or erosion. This complicates the picture further. In fact, it may be the reason why we haven’t seen any price deflation in the current crisis, despite monetary contraction (QE has been insufficient to offset the private sector deleveraging). What we are seeing is capital erosion sending our economy into a death spiral. It is exacerbated by global factors, the most important being ‘peak oil’ (more precisely ‘peak net energy’).

    • Andrew Kirkham


      Where I live a modest home starts at around £100k 4 times an average family income (and more like 6 times most families income).

      House prices are already way, way too high and would need to come down significantly to reverse the trend towards renting (which is more trouble than it is worth, but people are trapped).

      What you’re talking about is artificially maintaining the value of debts built up during a huge housing bubble. A long term plan for misery, misery and more misery for those not already on the ladder.

  • DaveCr

    Pleas fix heading

    “So what has this all has to do with economics?”

  • Voice of Treason

    Hello Michael. It has irked me for years that economists are truly rubbish at maths. Maybe it’s because we have a very similar academic background, as I also have a PhD in neural networks, machine learning etc, with degrees in maths and physics. In addition, I also studied psychology and economists are rubbish at that, too, which leads them to make further errors.

    • Andrew Kirkham

      Economists (generally) look like second rate scientists even when compared to the worst social scientist. Certainly there “assumptions” would be funny if the implications were not so serious

      You’re right about their maths skills, truly useless and the economy is easily complicated enough to justify study by some really good epidemiologists.

      Of course we should remember that most of modern economic theory had two aims; to trash Marx (still a better economist that Hayek, Keynes and that intellectual sell out Milton Freedmen) and to “prove” that capitalism was morally right and purely “natural”. It fails by these measures as well.

  • Bill

    Great article. I recently read Keynes’ General Theory in which he makes exactly the mistake you describe. (It’s at the end of chapter 6 of the General Theory, where he states “income = value of output = consumption + investment”). It seemed to me obviously wrong, precisely because he hadn’t factored in time and debt, but thought I must be missing something because surely he couldn’t make such an obvious error? Now I know I’m not going mad and it’s as wrong as it look. Thanks!

  • Jolyon Lovell

    Sadly I don’t believe this is any kind of ‘Oversight’ on the part of the establishment. If we are having some kind of financial problem (which certainly doesn’t seem to be true for the very wealthy) it is because the powers that be want it this way.

  • Steve Keen

    Very nice illustration Michael. I have been arguing for years now that aggregate demand equals income plus the change in debt, and have struck the same resistance I’m sure you have encountered even from progressive economists. It’s good to see another analogy that helps people get past the conceptual block of seeing the accounting (recorded income = recorded expenditure) and therefore not grasping the causal process that new money creation adds to demand from income alone.

    • Mick Reiss

      Thanks Steve. It all follows from the diagram I made here this earlier article includes a discussion of how changes in the proportion of money used in the real economy vs the proportion used in the, erm, financial economy, make things more complicated.

  • Björn

    So you alter the original equation so that you can proclaim your altered equation is wrong? Seems to me that for example a loan has no bearing on the aggregate expenditure = aggregate income equation at all, because the lenders loss is the loaners gain (say the loan is x, then the loaner has earned x and the lender has lost x, so the equation is ae+x-x = ai+x-x which boils down to the same thing).

    • Andrew Kirkham

      Yes, that works if you assume a fixed amount of money and the bank actually lent you someone else’s money. They don’t they lend you money they have just issued for the purpose, increasing the money supply. So lender the lender has X and lends you X and then you have X and so does the lender.

      Seems pretty incredible and when you full realise the implications it’s apparent that the tax payer allows the banks to cream the vast majority of wealth created by the nation without ever knowing it.

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  • Bill

    Reading this again, you could be accused of straw-manism, in suggesting that the model comes from assuming that all the income earned is then spent. The way Y = E was explained to me by an economist is that all expenditure represents income for someone else, and all income comes from someone else’s expenditure. So the starting point is that total expenditure in a given time period will equal total revenue. Income for a firm will be their revenue minus their expenditure, but that expenditure becomes revenue for someone else, and hence the argument is that ultimately the total expenditure in a given time period will equal the total income.

    This straight away ignores foreign trade, but it also ignores the time issue, that some profit will be earned on goods the costs of production for which occurred before the specified time period began; and similarly some expenditure on production will be on goods not sold till after the time period ended – your diagram is a very good way to illustrate this.

    In addition, some expenditure will be on re-payment of loans. While the payment of interest represents profit for someone else, the re-payment of the principle represents destruction of the money supply, as you describe.

    So if we explain the theory that Y = E on the basis that all expenditure in a time period becomes income for someone else (rather than, as you do, that all income earned is subsequently spent) all of your arguments till apply – but if this is not explicit an economist may use this as an excuse to dismiss your arguments.

  • Steve Roth

    Michael, Steve, et. al.:

    While I’m greatly supportive of the conclusions drawn here, I really, really don’t understand this:

    “aggregate expenditure (at end of interval T)”

    “At the end” means “at a particular moment,” right?

    You can’t measure a flow (expenditure) at a particular moment — only over a period.

    Unless it’s some instantaneous-flow statistical construct, constructed out of flows preceding, succeeding, or encompassing that moment.

    Love to hear this explained. I’m confused.



    • Neil Thorburn

      Surely aggregate means total expenditure over the period T as opposed to the measurement of an isolated instance of expenditure. Aggregate is the sum of all instances (expenditures) over the period T considered.

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