There is a simple equation that relates the quantity of money to the number of transactions in an economy, and it is a mathematical identity - something that is always true:
MV = TP
Here M is the quantity of money and V is the velocity of circulation. V is the rate of spending - the number of times that M changes hands in a given length of time, say per month or per year. Note that we're not interested in which particular bits of money change hands. Some bits, £1 coins for example, change hands much more frequently than other bits, £50 notes for example, and some bank money is in constant use whereas other such money remains idle. We're only interested in the number of times the total quantity of money in the economy changes hands, however that quantity is made up. It is very probable that some bits won't change hands at all in the time period of interest. T is the number of transactions that occur in the same length of time, and P is the average price per transaction.
What this equation says is that in one unit of time the total quantity of money changing hands (M times V) is the same as the money value of the transactions (P times T). This must be true because every time a transaction occurs money changes hands, and the money value of the transaction is the amount of money that is exchanged.
In our simple three-person economy in chapter 4 the time unit is one week, the quantity of money is 12 bracelets, the number of times that quantity changes hands is once every week, the number of transactions per week is 10 (2 each for basic food, luxury food, clothes, jewellery and wheelbarrows), and the average price per transaction is 1.2 bracelets (12 bracelets for 10 transactions, made up of 8 transactions at 1 bracelet each for all items except wheelbarrows, and 2 transactions at 2 bracelets each for wheelbarrows). So MV = 12 x 1, and TP = 10 x 1.2, giving us 12 = 12, which I hope few will argue with.
The amount of money that changes hands represents the value of wealth that is exchanged. The value of wealth exchanged in each time period is therefore MV, which is also of course TP. This isn't necessarily the same as the quantity of wealth that is created in each time period because stocks of goods awaiting exchange can rise or fall.
Also, with the fixed money supply of 12 gold nuggets and worker A saving money, we saw that B's and C's nugget holdings were progressively reduced. They can postpone the inevitable by increasing V as M drops, in other words by increasing their frequency of trading. Let's say they reach the point when they have 2 nuggets instead of the normal 4. While they continue to trade weekly they can only buy 2 units of wealth each week, and either build up unsold stock or not work for part of the week. However if they trade every half week then at the beginning of the week they can buy 2 units of wealth and after half a week also sell 2 units and be paid for them, then at the beginning of the second half week they spend the two nuggets they have just received on another two units of wealth. Then at the end of the week they sell two more units, receiving again 2 nuggets in exchange ready for the spending at the beginning of the next half week. Here they create and sell 4 units of wealth each week (2 units each half week) and buy 4 units of wealth each week (also 2 units each half week), which is exactly what they bought and sold originally with 4 nuggets, although now they trade with half the nuggets at twice the frequency.
This shows that it is not M in isolation that determines the rate of spend; it is M and V together. What they have done is continue to create wealth at the same rate, but exchange it for money at a rate that allows them to manage with less money overall - their money lies idle for less time. In this case M is halved and V doubled, so MV stays the same. T has also doubled - twice the number of transactions, and P halved - the price per transaction is half what it was because only half the wealth is traded in each transaction. Therefore TP also stays the same. Trading at a higher frequency can only work if others are also willing to trade at the higher frequency. In this simple economy the limit is reached when units of wealth can't be subdivided further, and in the real economy when people spend at the same frequency as that at which they are paid, which many people and especially poor people do all the time.
Note that MV = TP tells us nothing about what happens if one of the factors changes. For example if M doubles, will V and T stay the same and P double? Or will V and P stay the same and T double? Or will both T and P stay the same and V halve? There is a theory known as the quantity theory of money that claims that if M doubles then in the long run P will double, with V and T staying the same. This is generally held to be true by mainstream economists, though they don't define what they mean by the 'long run', but it is strongly challenged by other economists, most notably Keynes, who in a famous quotation declared:
But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean will be flat again. (Keynes 1924 Chapter 3 p80)
Indeed!
Provided that prices are reasonably stable (i.e. the value of money isn't changing - no significant inflation or deflation) and the money supply M isn't changing significantly, then the values of V and T will also stay reasonably constant because people tend not to change their habits without good reason. In fact of these four parameters M is the most independent, being determined by central and commercial bank policies, and also by the business cycle, rather than by changes in V, T or P. As well as being influenced by changes in M, P can change for many reasons such as material shortages, commodity price changes, technological innovation or natural disasters. The behaviour of V and T are almost entirely dependent on the behaviour of M and P.
From the analysis in chapter 15 it can be seen that if M drops sufficiently then deflation occurs, with an increase in spare capacity and reduced spending, in turn causing V to fall as people cut back and delay spending, T to fall as fewer transactions are carried out, and P to fall as there are fewer buyers. If M increases when spare capacity exists then spending picks up, prices recover, and spare capacity reduces, so V, T and P all rise. If M increases when there is full employment then as explained in chapter 17 P also rises as more buyers compete for limited products, causing inflation. In these circumstances initially V and T stay more or less the same because people don't change their habits quickly, but if M keeps increasing causing substantial inflation then V also starts to rise as people try to turn their money into wealth as quickly as possible before it loses value. They do this by bidding up prices further - holders of money are in a hurry to be rid of it because delay buys them less for their money, and holders of wealth are in no hurry to part with it because delay brings more money for their wealth. When this happens an inflationary spiral is almost inevitable (provided that M keeps increasing), driven by changes in V as well as M. If this danger materialises there is hyperinflation - as happened in the Weimar Republic in 1922 and Zimbabwe in 2008.
When inflation becomes significant it can spiral out of control because people spend their money ever faster to be rid of it before it drops in value. The result can be hyperinflation.
The equation also tells us nothing about what the money is spent on, which can be newly produced wealth for consumption or investment; existing assets for consumption or investment; or not spent at all - lying idle as cash or in bank accounts.[94] Of these only spending on new wealth promotes wealth creation; the others represent transfer of ownership of things that are not new, or idle money. We can therefore split M into three parts: money that is used in the purchase of new wealth, which we shall abbreviate to MNW; money that is used in the purchase of existing assets, which we shall abbreviate to MEA; and money that is not used in transactions, which we shall abbreviate to MNU. Financial contracts can also be split in the same way, so money spent on contracts can also be allocated to one of these three according to the type of contract.
MEA is money that doesn't affect wealth creation, though it can and does affect asset prices, and MNU affects the economy negatively by removing money from circulation - it's like the nuggets that A removed from circulation in order to save. The economic impact of this split is considered further in the next chapter.
The earlier equation can now be rebuilt from these separate components, noting that MNW and MEA have their own corresponding velocity, transaction type, and average price, and MNU, because it isn't used, doesn't have any corresponding velocity, transaction type or average price.
Therefore we have:
MNW x VNW = TNW x PNW
and
MEA x VEA = TEA x PEA
where VNW, TNW and PNW are velocity, transactions and average price for new wealth, and similarly for existing assets. Also, since every transaction either creates new wealth or transfers an existing asset:
MV = (MNW x VNW) + (MEA x VEA)
MNU isn't relevant in this equation because its velocity is zero. Additionally, from the earlier equations:
MV = (TNW x PNW) + ( TEA x PEA)
which also equals TP as before.
Here the value of new wealth exchanged in each time period is TNW x PNW, which is also of course MNW x VNW, and for the domestic economy this is referred to as the Gross Domestic Product (GDP) - at least this is what GDP is intended to be, though the way it is calculated falls well short of the intent - see chapter 27. Existing wealth that is exchanged in each time period is TEA x PEA, which is also MEA x VEA. GDP refers to the domestic output in terms of wealth, focusing on transactions and prices, but it is also equal to Gross Domestic Income (GDI), which focuses on the money earned from the sale of wealth.
You are probably wondering by now where all this is leading. But please bear with me. It leads to a conclusion that isn't widely appreciated and results in misplaced economic policy.
The split in the money supply M into MNW, MEA and MNU is of great importance to the functioning of the economy but is ignored by many economic texts which assume that spending on existing asset transfers is negligible, as is the amount of money that remains idle, but that is a very misleading assumption to make and leads to erroneous conclusions being drawn. For example when credit creation is expanding fast but being spent on existing assets - usually investments or housing, the increase in the TEA x PEAcomponent causes MV to rise and financial or property prices to inflate, i.e. bubbles are created, but the TNW x PNW component does not change. If it is thought, as is often the case, that MV = TNW x PNWwithout any TEA x PEAcomponent, then since it is known that new wealth prices haven't risen and the frequency of new wealth transactions remains steady, the rise in M is assumed to coincide with a fall in V, so as to keep MV constant. M is known to have risen because it can be measured, but V can only be deduced, so the wrong assumption is made, and the apparent fall in V is a mystery. This can lead to governments and central banks continuing their attempts to grow the economy by encouraging the public to take on more debts and the banks to create yet more money, without realising that the new money is merely creating bubbles and future inevitable crashes, rather than stimulating wealth creation. All this is very well explained by Richard Werner with particular reference to Japan's economy (Werner 2005 Chapters 13, 14 and 20 and Werner 2012). Werner refers to the separated version of the equation as the quantity theory of credit. See also Ryan-Collins et al. 2012 Box 12 pp109-110.
If the existing asset component of spending is ignored then when credit for existing-asset investment is expanding bubbles are created with little change in the real economy. Governments and central banks respond by encouraging yet more lending in the hope of promoting economic growth, but all that grow are asset bubbles.
These relationships can also shed more light on the income multiplier encountered in chapters 16 and 17 where chapter 17 showed that under certain conditions adding a one-off quantity of money to an economy generates several times its value in economic growth. The conditions required are that the money added must be spent on wealth that provides an income for others, i.e. on consumption or wealth-creating investment rather than saved or spent on existing assets, and that there must be spare capacity in the economy. It must therefore add to MNW and not to MNU or MEA.
Using the formula
MNW x VNW = TNW x PNW
we assume an initial steady state with all values at 100% and choose for ease of calculation a time period of one round of spending (VNW = 1). Now, if prior to the first round MNW increases by say £100 million (as before), say by the government stimulating the economy by extra spending, then MNW x VNW also increases by £100 million, and during the first round TNW will increase in the same proportion as the £100 million is as a proportion of the money supply because the spending of the extra money represents additional new wealth transactions. VNW won't change because all that has happened is that there is more money available as MNW and it is all spent in each round. PNW won't change because there is spare capacity and therefore no excess of demand for wealth over supply of wealth.
During the first round therefore £100 million worth of more wealth than before is created and exchanged - recall that wealth creation is given by MNW x VNW. When the money is received by the workers who have produced the wealth that has been bought, they too are able to spend it in the second round of spending, so prior to the second round there is still £100 million of additional money available, but it is very unlikely that the whole £100 million will be spent on new wealth creation, as some will be saved, some invested in existing assets, and some spent on imported goods - see below, hence some of the second round MNW leaks away into MEA and MNU. Let's say (as earlier) that 30% leaks away leaving £70 million available as MNW. This is spent on new wealth in the second round creating another £70 million worth of additional wealth. The same happens in the third and subsequent rounds, the additional money diminishing by 30% each time until it has all gone. At that time the entire £100 million has leaked out so that £100 million represents 30% of the new wealth that has been created, so the total wealth created is £100 million/30%, which is £333 million, i.e. a multiplier of 3.33 more wealth than additional money - as before. Beyond this of course is the additional effect of animal spirits that kick in provided that the initial injection is enough to stimulate renewed confidence in the business community - see chapter 17.
A word should be added about spending on imported goods, which for the domestic economy is just like money leaking out as MEA in that it isn't available as income to domestic workers so it can't be spent again to create more wealth. It does stimulate foreign production however so for the world as a whole it is still MNW. Part of the above 30% that leaks out from MNW will be spent on imported goods. Domestic exports have the opposite effect in that money is earned from abroad for the sale of wealth which stimulates domestic production, without it having to be added by government or taken from anywhere else in the domestic economy. These aspects will be discussed in Part 3.
A further word should also be added about average prices - PNW and PEA. On the face of it these seem quite obscure because we can never know what their values are, being made up of very many vastly different prices for all the many transactions that occur for both new wealth and existing assets. In fact their usefulness lies not in what their values are, but in how they change over time, which is known at least in broad terms from the various inflation figures. Therefore a specific year is chosen as a reference and the average price for that year taken as 100%. Then the price values for subsequent years can be given in terms of relevant inflated or deflated values.
Although MNW and MEA are discussed as representing physical amounts of money it should be noted that they don't have any practical meaning other than when combined with their respective velocities, where MNW x VNW is the rate of spend on new wealth, and MEA x VEA the rate of spend on existing assets. These rates of spend do have practical meaning and are important in that they have significant effects on the economy. Having recognised these limitations it is convenient during discussion to talk about money being MNW or MEA so the terms will continue to be used. MNU in contrast does have practical meaning as it is the amount of money that remains idle.