Velocity and the Dangers of Mathematical Economics

A wonderful exposition of Austrian Economics by Frank Shostak and the dangers of seemingly innocuous mathematical economics in this article: I’ll re-hash so that I solidify this critical concept in my own head… This is unlikely to be valuable to those who haven’t studied formal economics.

Mathematical economists manipulate;

(1) Velocity (V) = Value of Transactions / Money (M) to,

(2) V = Quantity of Transactions (T) * Average Price (P) / M to,

(3)  M*V=T*P and thereafter

(4) M*V = Gross Domestic Product (GDP).

The final equation suggests that increasing money & velocity can result in higher GDP, and that higher velocity increases the value of money. These are incorrect & dangerous conclusions.

Velocity is not the value of money. Money’s value is determined by its purchasing power in terms of goods and services. Money is a MEDIUM of exchange, not the MEANS of exchange. The actual means of exchange is the previous good or service that was exchanged to get hold of money. Hence why money’s value always relates back to the purchasing power of goods & services.

Prices are the outcome of purposeful action, demand and supply. Velocity and the number of transactions has nothing to do with how prices are determined. Who cares who many times this $ has been used?! The purchasing power of money is dependent on inflation, not its velocity.

High velocity merely states that the value of transactions is higher relative to money and low velocity that the value of transactions is low relative to money. Neither is necessarily a good or a bad thing. There will reasons for each outcome, depending on proclivity to saving and inflation, amongst other factors. But its these other factors that deserve attention, not velocity.

If economics where are simple as M*V=GDP, then global poverty would easily be eradicated by Mugabe-economics. Authorities can create lots of money & make it circulate, quickly, to produce GDP. That sounds familiar… Of yes, that’s is what we’re doing at the moment! Logically, historically and theoretically, we know that money creation doesn’t work, but an innocuous mathematically trick has mislead many into arguing for these dangerous economic policies that destroy society.

2 thoughts on “Velocity and the Dangers of Mathematical Economics

  1. Thanks for your feedback Mak.

    Honing in on your last paragraph… Think about a high-inflation scenario – the velocity of money will likely be elevated as consumers won’t want to hold onto money. But this doesn’t imply that the money has much value. On the contrary, it money has very little value in a high inflation scenario. This is why I agree with the argument that velocity doesn’t denote the value of money. The value of money is determined by its purchasing power.

    Moreover, I think its dangerous to focus on velocity as though it’s a variable worth targeting, which is what policymakers are currently biased towards. They hope “if we can just get velocity higher” GDP will increase, but this is a misdiagnosis of the problem. Sure, it may assist growth if people conducted more transactions, but you cannot just compel people to conduct more transactions and think that this is healthy. Perhaps people are saving for very good reasons, maybe they need to save, maybe the mechanism in the market doesn’t favour transactions… There are all sorts of complexities that are ignored below the surface if we merely think “it would be better if velocity were higher”

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    From: Makhosonke Madi
    Sent: Wednesday, 20 May 2020 15:07
    To: pricelesseconomics ; Rob Price
    Subject: RE: [New post] Velocity and the Dangers of Mathematical Economics

    Thanks for expanding on a very technical concept. What I understand you saying is that whilst there is a place for maths in the field of economics, we ought to be discerning in its use as it can sometimes be used to recklessly and thus deprive us practical solutions and potentially lead us to dangerous places from a public policy perspective. This point is well made and the admonishment is fitting – we can’t worship mathematics in our pursuit to better understand the field of economics.

    I think that on one hand economics can be very philosophical because it also speaks to us about how we ought to conduct ourselves in order for the economy to expand and give others with an avenue through which they might attain prosperity. There is obviously some rigor and sound logical reasoning that leads various economists to their conclusions. However, philosophy can itself be dangerous in that this field can also be very subjective and biased in trying to understand what makes economic agents “tick”. And I say this as someone who believes that philosophers make our world. Both maths and philosophical reasoning are critical in helping us get a better grip of how the economy works or indeed how it ought to work. Of course, for one to achieve this ideal, it is not just maths and philosophy alone that we would need to grapple with, we need to think about, our psychology as human beings, our history, our human anthropology and many other items. And we need to use these as carefully and as carefully and as parsimoniously as we can (if this is even possible).

    The article you’ve written has forced me to think more carefully and to sharpen an idea in my head. You state that “velocity is not the value of money”. However, if one thinks about velocity of money as the rate at which money changes hands, we can say that the higher the velocity of money, the more valuable the money since it signifies that money is in higher demand. This is because it is moving more rapidly across economic agents. What I take the final equation to mean is that money is a veil. Which is to say, that the GDP part should not be separated. As in: GDP = P*Q. This to me means that new money into the system pushes GDP up through the increase in prices – and not the creation of economic value. Therefore we should focus more on the velocity of money as the velocity of money also signals the prevailing demand in the underlying economy. If there are people promulgating for M only to increase in order for the economy to grow without thinking about the V, we are in deep trouble.


  2. I agree that velocity of money is difficult to control/predict. However, I think there is an opportunity to look empirically, to times in history when the velocity of money has been high and think to about the underlying policy measures and/or economic conditions that we in play during these times. We might then be able to critically study whether these conditions are good enough to explain the cause of a higher velocity of money. I’m sure there is much room to be creative around this. There’s a PhD topic for you if you’re keen Robster. 😉

    You’ve made it clear that it is your conviction that it is impossible for savings to be too high in an economy. You obviously caveat that by stating that the economy in question must be driven by a free market. I think it is possible simply because we have high savings now in certain areas/sectors of the global economy. Companies are doing buybacks and don’t have clue where to invest. Maybe then we do not operate in a free market and perhaps you are protesting the low interest rates as a grave policy error that has led to high savings – and extremely high debt on the government side. Or maybe the chain starts with high debt, leading to low interest rates as a way to control this debt. This then crowds out the private sector from taking on investment risk. I’ll have to dig deeper for both explanations.

    You have spoken to me about market-determined interest rate. In the past I quite like the idea actually, but thinking about it from a practical standpoint, I worry that it is almost impossible to sell since it would signify the end of Central Banks. And central banks will tell you that they are going nowhere. Have there been instances in the past where rates were determined wholesomely by market forces?


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