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Fuzziness exemplified

The Quantity Theory of Money (QTM) is variously described in terms of equations. For example the following relationship is a shorthand description of the theory:

M. VT = PT.T

Where: M is the total amount of money in circulation; VT is the velocity of circulation or the average frequency across all transactions where money is spent. PT is the price level associated with transactions in the period under consideration; T is an index of real value of aggregate transactions.

With the development of national accounts this equation was modified to:

M.V = P.Q

Where: M is the total amount of money in circulation; V is the velocity of circulation or the average frequency across all transactions in final expenditures. P is the price level associated with transactions in the period under consideration; Q is an index of the real value of final expenditures.

Several economists2 associated with Cambridge University reasoned that the demand for money was more significant than the supply in that a certain proportion of nominal income (designated as k in the short run) will not be used for transactions but it will be saved or held as cash. So the equation is modified as follows:

M = k . P. Y

Where: P is the price level and Y real income.


M/k = P . Y

The Cambridge economists also considered wealth to have some influence but for simplicity's sake, unfortunately wealth is often omitted from the equation.

Milton Friedman considered the sources of inflation to be related to the growth rate in money supplies and that the demand for money is related to its velocity and is directly related to nominal incomes and interest rates. This was challenged by Nicholas Kaldor and Friedman never produced a convincing argument or evidence to support his position.

The QTM has been promoted as a basis for removing macroeconomic instability by adopting a low growth rate in money supply. However, since the 1970s the growth in financial intermediation and derivatives markets has made the quantification of appropriate money supplies virtually impossible so the interest rate was adopted as a policy instrument.
Real Incomes & the Quantity Theory of Money

Hector McNeill1

As an undergraduate I found the quantity theory of money (QTM) to be slightly odd, I sensed something was missing. Having worked on real incomes analysis for some time and now looking back at QTM it takes on a bizarre surrealist quality, so I still think it is odd. However, I think I now realize why. This essay explains my thoughts on the matter.

If I may exaggerate a little, picture a barrel where the volume of its content represents where money is being exchanged in economic activities. If one pours in more money the height of the money, or prices, will rise. If one ladles out some money, prices will fall. This is one of the basic tenets of the QTM. Some more detail on the QTM is set out in the box on the right. The fuzziness of this whole concept is that if one asks what the mechanisms are that cause prices to rise, the "escape" explanation is "oh, this only happens in the long run." This isn't good enough. In policy making we need to be able to bring about impacts in the short and medium term, using transparent mechanisms, because, after all, as Keynes observed, "in the long term we are all dead".

However, returning to the concept of the barrel within which there are numerous economic transactions exchanging goods, services and money one can see that the QTM does not adequately relate to this "real economy", that is, the real exchange of goods and services determined by investment, productivity, the relative efficiencies of processes, the quality and characteristics of output. Money or financial data occupies a parallel universe devoid of transparent deterministic linkages to this real economy.

As is explained in this essay QTM is not a full explanation of the impact of money on the economy. It does not describe the deterministic relationships between the use of money, interest rates and purchasing power or, one must add, the influence of foreign trade and the value of money reflected in exchange rates. Below I set out some basics on how an economy can increase real incomes and thereby highlight the weakness of the QTM as a basis for guiding policy. The analytical paradigm that has arisen with the development of the Real Incomes approach is to assess the utility of any statement of theory or policy, by identifying the transparent links to impacts on real incomes which are related to the evolutionary process of advances in productivity. So applying this assessment to QTM one has to ask how does QTM permit analysis of improvements in productivity and the state of real incomes? Indeed, how does QTM explain the role of productivity? Tragically, like Keynesianism and Supply Side, QTM has no answer.

Productivity and inflation

Productivity can be measured as the physical output secured in terms of goods and services from measured physical inputs. The output might be an electronic device that requires a recipe of inputs including components, space, energy, labour and information used over production periods. This physical productivity can be converted into economic productivity by multiplying the per unit inputs by their respective prices and comparing this with the likely price the device can be sold at. In financial terms, the financial "productivity" depends upon a range of management issues such as the number of devices in inventory, inventories of inputs and the time. Where production management can link marketed volumes to smaller inventories of both inputs and outputs, the financial outcome in terms of cash in hand can be improved. Inflation or rising prices can be attenuated or even reduced through process design that gain effective control over the Price Performance Ratio (PPR)3 (see "The Price performance ratio"). The ability to manage the PPR to maximize the feasible benefits for a company in terms of the real incomes of owners, shareholders, employees and, indeed, consumers depends upon management applying effective productivity strategies.

Productivity strategies

Productivity strategies can be divided conveniently into:
  • physical processes
  • economic processes
    • people - human processes
  • access processes
  • consumption processes
  • financial processes
Physical processes

Corporate survival depends upon appropriate responses to market opportunities that all relate to increases in productivity. As has been mentioned a fundamental basis for productivity is physical productivity. Physical productivity is a fairly complex topic involving changes in technology, refinement in human techniques4, and careful selection of inputs all with the objective to achieving the output desired in terms of product or service quality specifications.

Communication and most work undertaken by people designing products, services, production and delivery processes is based on explicit knowledge ...
There exists copious examples of ways to manage the physical processes so as to make them more efficient and effective. An example would be the "process approach" 5 of the International Organization for Standardization (ISO).


Explicit knowledge

People involved in economic activities both detract from, as well as contribute to, physical, economic and financial productivity. One or two characteristics of people are of immense significance in planning productivity strategies. Through usually simple instructions, people can pick up and begin to carry out tasks. Naturally some basic levels of education are useful so that what is communicated is understood. In more complex processes some prior formal training in the relevant field can help improve communication as well as knowledge of what needs to be accomplished. All of this information flow which is also used to design products, design production processes and analyse markets is what is referred to as "explicit knowledge". This if made up of information that can be fairly easily communicated and understood by people.

George Boole, the English logician, published a book in 1854 entitled, "The Laws of Thought", in which he described how humans deduce and make decisions on the basis of explicit knowledge. He produced a mathematical logic to model deductive processes. Today this is known as Boolean logic the basis for all computer programs and hardware design.... observation and deduction is the essence of innovation ...

Tacit knowledge

People have a remarkable productivity-related characteristic associated with learning. People with more experience in carrying out some production procedure usually perform better than those with less experience. The rise in productivity associated with experience and learning is often refereed to as the "learning curve". The gains in performance in the carrying out of repetitive procedures can be measured. The relationship between production efficiency and experience in carrying out a procedure is well-established6 and can be used to predict rates of improvement in productivity. The capabilities resulting from such experience are known as tacit knowledge. Tacit knowledge of various kinds is accumulated by all individuals both during the life and within the work environment.

One of the characteristics of tacit knowledge is that it is embedded in each individual and, unlike explicit knowledge, it is difficult to communicate to others. Another person can observe someone doing something in a more productive fashion, however, to acquire tacit knowledge, that is the capabilities of the experienced person, it is necessary to descend the learning curve. The well-known phrase, "practice makes perfect" applies here, as it does, indeed, in most human situations (See: Tacit & explicit knowledge).

Economic processes

Economic processes are essentially the conversion of physical production input and output relationships into economic input and output assessments by multiplying the unit prices of inputs to measure costs and to subtract these from the income generated by unit of output multiplied by their unit prices. This aspect of productivity strategies is important because it summaries, in economic terms, the result of the allocation of a company's resources in the form of company people applying their explicit and tacit knowledge operating plant and equipment using purchased inputs. However, good managers take the trouble to understand the contribution of each of these resources to corporate productivity. If managers do not understand the qualitative contribution of each of these inputs to physical and economic productivity, they are not in a good position to advance their production and marketing strategies so as to optimism their generation of real incomes. As will become apparent in the next three sections.

Access processes

The Real Incomes Approach to economics does not make use of the Aggregate Demand Model (ADM) applied by KMS theory and policies, but applies a Production Accessibility Consumption Model (PACM) (see "The PACM Model of the economy"). Companies can invest their efforts in innovation, be this in new plant or equipment, in a new product or process design undertaken through the application of explicit knowledge, or to facilitate the constant stream of rising productivity driven by the human's innate innovative characteristics accumulated in tacit knowledge. The result will a something that has never need "marketed" before. There is therefore no existing demand, how can there be, the product is not in the market and isn't being consumed. Therefore the producing company needs to invest in access processes, of which there are three:

What goes into the design and building of aeroplanes is an optimized mix and application of explicit and tacit knowledge. The logistics of aviation using separated flight paths using radar and other systems are also built and run on the basis of explicit knowledge. The dissemination of explicit knowledge maintains the spread of best practice. The companies who have invested in and who make effective use of tacit knowledge usually gain an edge in performance in the design, building and running of aircraft.
  • providing potential users of a product or service access to appropriate information
  • ensuring that the potential users' location has conditions to permit local access to the product or service
  • ensuring that the purchasing power of the potential consumers allows them to gain access to the products and services
All of these processes are important, but once the first two are in place the process of accessing consumer purchasing power, assessing competing products and what can be done to penetrate the market the trade-off ends up as a unit pricing versus quality trade-off. Outside fixed dimension national markets, the elasticity of potential demand for a product or service in the international market is extremely high and it increases the lower unit prices can be set. Thus the strategy related to accessibility is to minimize unit prices to ensure adequate market penetration through substitution of existing products and services or by facilitating first time users' acquisition. This process is the investment that supports the process of innovation by gaining the payback for innovative effort. But to optimism this process and maximize the gains from the process attention has to have been given to the optimization of the contributions of technological change and refinements in technique arising from learning in the form of accumulated explicit and tacit knowledge.


The take up of offered products and services results from individuals, families and companies deciding to make use of products and services on offer, including new products and services appearing in the "market". The point to note is that consumption patterns are constantly driven by innovation so that "growth" is reflected in the fact that the make up of yesterdays's consumption is not the same as today's consumption make up and tomorrow's will also be different. But we need to ask a question. What drives successful growth and how can we ensure all can benefit from such growth in economic activities? The answer is that production and service provision needs to maximize the provision quality while minimizing feasible unit prices. In this way the benefits of growth can reach a larger proportion of the world's population.

The difference between the Real Incomes Production Access Consumption Model (PACM) and the KMS Aggregate Demand Model (ADM) is that the PACM recognizes that a considerable amount of economic activity that has no relation to current final demand but relates to activities whose output is not yet marketed but which represents the main source of evolving growth in economic activity. The ADM doesn't make this distinction. The PACM also sees growth a real contribution of products and services whereas the ADM sees growth as an increase in nominal output measured in currency units.

Each person is unique with different genetic make-up and perspective on life arising from nurture, education, social context and experience with different activities and techniques. As a result, each person's capabilities in using explicit knowledge and their accumulation and application of tacit knowledge results in different contributions of company performance.

The Real Incomes Approach acknowledges this reality and provides a policy framework that provides a more equitable compensation for contributions to economic performance.

As consumption rises and volumes of output increase there are several important impacts on productivity:
  • The utilization of plant and equipment capability rises to high levels helping reduce overhead
  • The accumulation of explicit and tacit knowledge accelerates leading to:
    • significant cost reductions in output of human inputs
    • significant rises in product output quality
    • rises in production yields5 rise
  • The ability to negotiate lower unit input prices rises with throughput
  • The ability to negotiate favourable terms in logistics services improves
Financial processes

The distinction between economic and financial processes is that the time dimension is an important factor in financial processes. Therefore one can have what appears to be a very high profit economic process but the management of the activities over time can result in a good financial return or even losses.

The procedures applied to optimization of resources allocation and assessment of investment options involve a considerable amount of financial analysis and calculations to generate projected cash flows of options. Market projections are used to assess risk and usually calculations used to determine production relate existing market prices to marginal costs resource allocation. In this sense existing price ranges are used as the competitive reference benchmarks. Usually the aim is to maximize unit profits for prices close to those in the market. Inventory control and similar forms of cost control dominate management decisions.

Under the Real Incomes approach there is an over-riding policy concern with the maximization of the spread of benefits of innovation in the form of enhanced real incomes of:

  • company owners including shareholders
  • employees
  • the self-employed
  • the population in general as consumers

The profit paradox, or why conventional policies fail

To make sense of this list we need to identify why conventional policies cannot achieve this. Company owners and shareholders gain their returns largely as a function of the size of the net of tax margins existing between revenue and total costs. Company owners and shareholders are then taxed on what is paid as income. Because of government revenue-seeking, largely through corporate and personal taxation,
Training - investing in people

Targeted and appropriate training is a vital input to ensure that people's capabilities in the handling of explicit knowledge and subsequent accumulation of tacit knowledge can result in expressive impacts on corporate productivity and employee income levels.

On the job training or hands-on training tend to be more effective in the corporate setting rather than "chalk and talk", also trainees need to be encouraged to question what is provided during the course of training sessions because often employees can identify problems that are specific to their work circumstances. Such feedback can often provide the basis for significant improvements in performance and training content.
there is a significant legally based accountancy framework that sets "profits" as the target of taxation while it is corporate practice to use profits as the measure of success expressed as the return on investment or dividends paid on a given share price. This creates a serious conflict in what need to be rational management decisions on how to minimize taxation while maximizing profits. Accountancy norms classify employee wages as an input and therefore a cost. The objective of maximizing profit is therefore in contention with any requirements to raise wages. As a result the incentives that exist to maximize profits have resulted in a medium to long term decline in wages in proportion to profits as a share of national income. This means that the majority of the social constituency are subject to a relative decline in real incomes in comparison with corporate owners and shareholders. An additional factor is that the profit paradox and government revenue-seeking has led to a worldwide epidemic in tax evasion and avoidance. This complex of cause and effect relationships is a perverse result of the profit motive and is known as the profit paradox (see "The profit paradox")

The hidden conflict between the asset & productive economies

This state of affairs is further exacerbated by the Bank of England's long term policy of setting an inflation rate of 2% as being equivalent to "price stability". This results in a 20% depreciation in the purchasing power of wages each decade. The 2% price stability target is applied to prevent there being any "deflation" of assets. This is because assets are used to provide collateral guarantees for finance. Companies can purchase assets to increase the overall worth of the company and the beneficiary ownership of potential income from future use or sales of these assets will accrue to the company owners and shareholders rather than to wage earners. On the other hand wage earners and indeed production systems have a preference for falling prices or deflation.

A significant transfer of benefits from wage earners to corporate ownership lies in the poor levels of recognition of the real significance of the contributions to productivity of wage earners associated with their individual acquisition of explicit and tacit knowledge. Thus the medium to long term returns on an investment can be increase as a direct result of the evolution in individual and team capabilities of employees. However, these benefits are more likely to accrue to corporate owners than find expression in pay packets of employees. As a result of this significant oversight and the current conventional KMS policies there is a built in systemic tendency to sustain pressures to create significant differentials in the relative impacts of policies across the social and economic constituencies. This has been apparent for many years with the outcome of KMS policies being the creation of winners, losers and those who remain in a policy neutral impact state.

The Real Incomes Approach eliminates this systemic flaw created by KMS policies by giving particular emphasis to the stabilization of prices, not through the setting of money volumes, interest rates, government taxation, public expenditure and debt but through the provision of incentives for productivity.

QTM, the Cambridge economists, Knut Wicksell and Mises

An important consideration introduced by the Cambridge economists (see box top right) was the fact that money is held, not only as cash for immediate use in transactions but it can also be held onto as a store of value. Today, unless investment is made in some income generating process monetary policy proactively devalues the pound. It isn't a sound store of value. However, the Cambridge economists also thought "wealth" has a role to play in the analysis of th QTM. This it true, in the sense that assets which make up components of wealth are more strongly supported by monetary policies at the expense of the productive economy. Put another way, the preference given to avoiding asset depreciation, that is, avoiding deflation, by maintaining a 2% inflation, creates a negative impact on real incomes of employees and raises input costs.

Knut Wicksell7 was one of the few economists to set the QTM in the context of the real economy. He identified the fact that whereas money supply can lead to rises in prices, the original increase is endogenous, that is, it is the behaviour of firms that generates inflation. This agrees with the analysis of the Real Incomes Approach. This is why the Price Performance Ratio (PPR) is a key instrument used by firms operating under Price Performance Policy. Wicksell correctly stated that there are two interest rates. One is set by central banks and commercial banks and constitutes no more than a "financial construct". The other lower interest rate is directly related to productivity and referred to as the natural rate or the return to capital and the marginal return on investment.

It is therefore evident that the requirement for money is endogenous and comes from companies deciding to innovate to produce products and services that are currently not marketed. They are going to be added to final consumption eventually and some will fail and not feature in consumption. Therefore the "demand" does not come from overall economic activity.

Ludwig Von Mises8 also criticised QTM for its lack of explanation for the demand for money and its failure to explain the value of money. Although a change in the quantity of money may eventually affect all prices, he did not agree that it can affect all prices in the same manner, to the same degree or at the same time. So the all-encompassing concept of QTM is a very weak axiom with serious consequences for the economic and social constituencies when used to justify policies. The Real Incomes Approach analysis bears out and supports Wicksell's and Mises' views.

The conversion of innovative activities into products and services that impact the economy in terms of real economic growth depend upon moderation of prices, a constant drive to increase productivity and the more equitable compensation of employees so that the overall final consumption capacity rises in real terms. Although banks can satisfy this money requirement by creating money by recording credits in the relevant accounts, this has an inflationary impact on costs. The Real Incomes Approach, through the Price Performance Levy, helps companies generate higher cash flows leading to a reduction in the reliance on financial intermediation and therefore the payment of financial interest rates. The transfer of equity from cash flow into investment can bring interest rates down to the internal rate of return or to the natural return identified by Wicksall. The process can result in a competition between financial rates and natural rates leading to a new form of "investment bank" where considerable effort will have been invested in explicit knowledge on specific sectors so as to end up with more realistic assessments of general risk rather than relying exclusively on assets as guarantees. In addition such organizations would have better methodologies and techniques upon which to base risk assessment of any investment proposition that comes their way. This also means such organization would devote more time to understanding the deployment of technology, explicit and tacit knowledge within any proposition. As a result the provision of loans should result in lower demands for asset guarantees as well as interest rates nearer to the natural rate of each investment project. This would make interest rates subject to competition within a free market. What is evident is that this is incompatible with central bank policies concerning money volumes and interest rate-setting. If policy is geared towards enhancing real incomes on the basis of productivity and pricing the role of conventional policies and central banks the constructed support for assets becomes unnecessary. This does not mean assets would see price declines except for those that are currently over-priced. The general rise in real incomes would continue to provide sufficient liquidity in asset markets for transactions at that "end" of the markets. However, the ability of policy to support a better distribution of income and generate real growth would improve.

Back to the drawing board

As it stands QTM is not a full explanation of the impact of money on the economy since it does not provide any of the deterministic relationships between the use of money, interest rates and purchasing power and, one must add, it does not provide any explanation on the influence of foreign trade and the value of money reflected in exchange rates. The Real Incomes Approach has attempted to identify determinants that have utility in policy-making with some modest success and, in particular, providing transparent propositions for a proactive microeconomic basis for controlling inflation and increasing the purchasing power of the currency based on increases in productivity and achieving traction in the growth of real incomes.

The QTM is unsatisfactory as a working model and it needs a lot more work.

1 Hector McNeill is direcor of SEEL - Systems Engineering Economics Lab.
2 Marshall, Pigou & Keynes.
3 PPR-Price Performance Ratio: This is the ratio of changes in unit output prices to changes in aggregate unit input costs; it is a measure of the degree to which companies pass on rises or declines in input costs to their customers.
4 Technique is the way in which people apply a given technology. Companies using the same basic technology can have significantly different levels of productivity due to the expertise of those applying technique. Expertise rises with tacit knowledge gained in applying techniques on a repetitive basis.
5 The process approach is a way to establish activities that are more efficient and effective. However, it is important to also ensure that the process is a learning process that helps refine explicit and tacit knowledge so that the activities remain responsive to change, such as customer requirements. It is possible to allow quality standards to remain a reference benchmark and end up with a "frozen" unresponsive system whose standards relate to past requirements resulting in competitors becoming more productive resulting in a loss of market share.
6 Learning curve predictability. The learning curve has a well-established evidence-based relationship between experience in production and gains in productivity. The general relationship is that for every historic doubling of output of a specific product or service, those carrying out the production activities improve their productivity by a fixed amount (known as the learning coefficient). Because of the historic doubling conditions this means gains are of diminishing marginal significance with each step. However, they can be significant. More labour-intensive technologies are associated with higher productivity gains from learning while semi-automated technologies have lower gains from learning.
7 Johan Gustaf Knut Wicksell (18511926) was a leading Swedish economist of the Stockholm School whose work influenced the thinking and work of a large number of economists.
8 Ludwig Heinrich Edler von Mises (1881-1973) was a German philosopher, economist and sociologist who was associated with the Austrian School of economic thought. He was particularly concerned with the study of human choice and action. He emigrated to the United States in 1940.

Update 16th September, 2014; Clarity issues. 22nd September, 2014, Typos.
Updated 10th June, 2015; Introduction of links to PAC Model and reference to profit paradox, Typos (yet again) ;-)
Updated 24th August, 2015; Corrected foot note error.

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