THE MEASUREMENT OF MONEY AND THE DETERMINATION OF EXCHANGE RATES

Author: Owen Venn-Brown

Last Updated August 2001

CONTENTS

Abstract

This paper proposes that units of energy should be used to determine the real value of money, because these units are the true, scientific, measurement of the work done in the production of goods or services. As a unit of energy never changes, its value remains constant regardless of the circumstances, making it a constant in any valuation of monetary units.

The ratio of Net Energy Consumption to Nominal GDP is used to measure the actual value of money. In consequence, a mathematical formula is described which calculates and forecasts the rate of change to the value of money.

A method is described for the calculation of exchange rates. It is claimed that the real value of exchange can be determined by comparing the endogenous ratio, Net Energy Consumption/Nominal GDP, with exogenous ratios of Net Energy Consumption/Nominal GDP.

The growth and prosperity of a nation are said to be indicated by energy consumption .

Consideration is given to how some fundamental monetary activities might affect an economy, which is described in terms of energy rather than money.

The concluding remarks hypothesise how an economy might behave if the principles of this theory were applied.

1.0 Introduction

It was Adam Smith when in 1776 he wrote his Wealth of Nations who first enunciated that "labour" was the source of a nation's wealth. In the era in which he lived, it was indeed true that physical labour provided most of the work to produce the goods that nations consumed. With the coming of industrialisation, machines using other sources of energy provided the work and it has now eventuated that nearly all the work that provides the wealth of a nation comes from the great energy sources that are employed.

Most people understand that money has no intrinsic value yet they perceive it to be the embodiment of wealth. In this paper, money is conceptually different. As an analogy, it can be thought of as a "store for work" but a store that is continually shrinking so that with the passage of time it stores less and less work. Its capacity to store is what is known as its value. In the following treatise this analogy is given mathematical reality. The mathematical development seeks to show that the relationship between work and money can be used for the exact measurement of the economy.

2.0 The Real Value of Money

The determination of the real value of money is fundamental to the working of the principles espoused in this paper. Proper measurements in any scientific endeavour can only be made if there is fixed standard to measure against. The fixed standard in this treatise is the unit of energy.

A unit of energy never changes its value and it remains constant whatever the circumstances. This is an immutable physical fundamental of nature. As energy in transition can also be interpreted as work, it is clear that measuring the energy used in the production of goods or the provision of services is exactly equivalent to measuring the work done in producing those goods and services. Note that energy in this context is not litres of petrol, tonnes of coal, cubic metres of gas or any other source of energy. It is the actual energy, which has been released from its source and has been transformed into another form of energy, thus performing work in the transition. For example a power station converts coal into electricity thus performing work. The electricity is sold and used to produce goods, once again performing work.

Therefore, the Net Energy Consumption (or the total work done) is the real measure of national economic activity. As such it is possible to compare one accounting period with another without resorting to "seasonal adjustment" because Net Energy Consumption is measured in unchanging international standard units. Unlike money the unit value of work does not change

The Net Energy Consumption of many nations is regularly known because various government departments collect the data. For instance, in Australia, the Australian Bureau of Economic Resources compiles this information. In the United States of America the Department of Energy records this information. Further, energy use is measured and recorded accurately by producers or sellers of energy. For these reasons it is possible to have an accurate and continuous measure of energy usage and, consequently, economic activity.

Since the nature of energy and work is intangible it cannot be physically transferred from one person to another. Therefore, money is used to represent the exchange of energy. The exchange of work is acknowledged, recorded and "stored" by using money. Money therefore remains the medium of exchange to be issued and used in commerce in the usual way.

Although this premise is perhaps reminiscent of the gold standard there are fundamental differences. Firstly, it should be again emphasised that the reference to energy as the measure, is in fact a reference to actual work done, and not sources of energy. Energy sources such as coal or oil are merely the fuel from which energy is produced and, by themselves, do no work. A tonne of coal has the potential to produce and perform about 24 Giga Joules of work; but a tonne of coal can do no work whatsoever till the energy is released. Similarly gold, as it cannot be induced to release energy, performs no work and hence cannot make goods or produce services. Assuming it takes 10 Mega Joules of energy to make a loaf of bread in Australia, under the same circumstances and conditions it will take 10 Mega Joules to make a loaf of bread anywhere else in the world. However one cannot be sure that a loaf of bread could be purchased with x ounces of gold anywhere in the world - it would depend upon the price and availability of gold. Herein lies of the fallacy of the gold, silver or any other substance, as a money "standard". Gold does not possess a fundamental natural property that allows it to perform work. However its value is described by a ratio, (quantity of gold)/(quantity of money) That ratio, and therefore its value, can be changed by altering either the numerator or the denominator. So consequently it may be possible to offer x ± a ounces of gold for a loaf of bread which still requires 10 Mega Joules of energy to produce it.

2.1 The Relationship of Energy Consumption to Gross Domestic Product

Gross Domestic Product (Y) is defined as the money value of all activities and goods produced by a nation. It is thus the money value of all the work done in that nation. It can be reasoned, a priori, that the Net Energy Consumption (E) is the measure of all work done to produce those goods.

It will be shown that a change in Net Energy Consumption results in a simultaneous and sympathetic change in GDP. This premise leads to the important mathematical relationship expressed in Equation 1:

Equation 1 can be written as:

also if Q = Quantity and P = Price, then

And since E/Q = e or Work per Unit of Product

From Equation 2, it can be deduced that one unit of money is needed to buy m units of energy (or work). Thus, if the unit of money is U and a Joule is the unit of work then:

In other words, m is the actual value of a unit of money, and is the true value of money no matter what circumstances may pertain. Regardless of whether a currency is traded at a price different from its true value, this is of no consequence to the value of money. The value of money is only determined by the size of m. If a trader or a company wishes to purchase (or sell) a currency then the price that is paid for the currency has no influence on the true value; any transaction using money falsely valued will mean that either the buyer or seller has surrendered some worth and must work to recoup the loss.

Only a change in E or Y can bring about a change in m.

Furthermore, E can only change in magnitude. Net Energy Consumption may become greater or lesser depending upon demand or perhaps through changes in population but the unit energy value remains constant. On the other hand, because Y is also equal to QP, where Q is quantity and P is price, Y will change if the price changes or if Q and P change independently of each other.

2.2 The Effect of Improved Efficiency

It may be postulated that innovations and improved efficiency may mean more output from less energy consumption (Q increase independently from E), implying a fall in the value of m. However, the resulting reduced production costs will either cause

a) prices to fall and sales to increase, or

b) profits to increase which will lead to increased Capital investment.

Either of these outcomes will result in increased output once again helping to drive net energy consumption up. For extra production to be sold the price must fall and it must fall by an amount equal to the increase in production, as evidenced in the following mathematical development.

Assuming E does not change, if QP increases then m decreases: in other words the value of money declines. For m to remain constant and thus maintain purchasing power, QP must remain constant. So, when Q increases, P must decrease by the same amount. This is an unlikely outcome since it offers no incentive to the producer.

2.3 The Changing Value of Money

The instantaneous value of m can be represented by the differential equation dy/dt = rt where r is the rate of change. The solution of this differential equation is given by the expression

The value of m at various time intervals can be shown as a graph (see figure 1) with the x-axis representing time and y-axis representing m.

The numerical value of inflation, here called the Natural Inflation Rate is given by the variable r.

Referring for the moment to the analogy described in Section 1 the term inflation might more appropriately be given the antonym contraction. However the traditional and commonly used term is retained.

Note: E in Year 2000 is an Australian Bureau of Economic Resources estimate on 1999

Figure 1 shows how m and consequently the value of money, has declined over the interval. It can be seen that y= 24.478e^0.0651t for this period.

In Figure 2, m has been plotted for the years 1997-98 to 1999-00 and the Natural Inflation Trend line for this period indicates the pattern of the economy has changed in recent years. It can be seen that the inflation trend line indicates changed conditions. The curve has flattened indicating more stability and a slower rate of change. Now y = 6.3248e^-0.0349t and the inflation rate has approximately halved from -0.065 to -0.035.

3.0 The State of the Economy

3.1 Economic Prosperity.

National prosperity, K, is defined as Net Energy Consumption per head of population.

Equation 6, which is the energy consumption per head of population, gives a measure of national prosperity. It is obviously the average amount of energy consumed by each individual and therefore a useful Indicator of Living Standards. For instance it is an easy matter to convert a household wage to an energy value by multiplying the money value of the wage by m and compare the result with K.

It will be noted that K can be increased either by increasing E or by decreasing N. It is an important observation that an increasing population is not necessary for increased economic prosperity. A source of energy and an appropriate technology could provide increasing prosperity, even with a declining or static population.

3.2 Economic Growth .

Economic growth is the percentage change in net energy consumption per capita.

This measure is independent of the value of money because it represents the actual change in the amount of goods and services produced.

4.0 Applying the Theory

The three parameters, Net Energy Consumption, Nominal GDP and Population are all that are required to

a) Measure the value of money and predict its future value

b) Measure the rate of inflation

c) Determine exchange rates.

d) Provide a measure of prosperity

e) Measure economic growth.

Energy is the prime parameter and it is the use of energy that activates the economy and is the real "currency".

The data, Energy and GDP can be collected as frequently as is necessary. In line with usual practice, quarterly would seem the appropriate interval. The Net Energy Consumption is the energy used for the production of goods and services as well that used for mining, agriculture, transport and domestic consumption. It should be possible to collect accurate energy statistics from the energy producers and suppliers.

Equation 2 calculates m, the actual value of a currency. If E is expressed in Exa Joules, (Joules x10¹⁸) and Y is the Nominal GDP expressed in billions of currency units (U x 10¹²) then m Mega Joules is the amount of energy that can be bought with one unit of money.

Equation 4 is derived by regression analysis of historical values of m although in practice commonly available computer programs like Microsoft Excel can provide the result with a few keystrokes. The historical period of analysis need not extend over years and quarterly data for a few preceding quarters should be adequate.

4.1 Foreign Exchange Rates

By definition one unit of money, U, is equivalent to m units of energy. If energy is measured in Mega Joules (MJ) then U = m MJ. Therefore, if U_A = m_A is the value of the money for country A and U_B = m_B is the value of the money of country B, then the exchange rate of A in terms of B can be represented by the following formula:

One unit of money, U_A, is equivalent to m_A/m_B units of money U_B. This method defines the True Exchange Rate.

Calculating exchange rates in this way, in effect establishes the Terms of Trade. Consider a country where the exchange rate used in trade is greater than the calculated true rate by a factor 'b'. This means that the apparent value of its currency is bm

Clearly the ratio E/Q cannot change because this, the unit energy e, is also in effect the quality that would be demanded by the purchaser.

Therefore the export price, P_x = P/b. In other words the export price is too low by the factor 1/ b.

An overvalued currency is equivalent to an export subsidy. This subsidy however is applied to all exported products and since it also means that imports are more expensive an overvalued currency could have serious consequences.

4.2 Inflation

The Natural Inflation Trend, y = Ce_-rt defines the expected value of money at time t and may be defined as the average value of m.

The inflation rate is defined as the value of r in the equation y= Ce_-rt

By comparing m and y it is possible to make the following observations.

a. At any time, the difference between m, the actual money value and y, the calculated trend value, indicates the way the economy is changing.

b. If m-y is negative the inflation rate is increasing.

c. If m-y is zero the inflation rate is constant.

d. If m-y is positive then the inflation rate is decreasing

These relationships can be used to anticipate changes to inflation and the future behaviour of the economy.

4.3 Price Adjustment

It is often necessary to adjust prices, allowances, wages or pensions to compensate for the effects of inflation.

If it is assumed, at some initial period, that the price of goods was P₀ and the value of m was m₀, then it can also be assumed that at some later period the value of m changes to m₁. To calculate the new price the following formula can be applied:

4.4 Comparative Prosperity

The Energy Consumption per Capita (Equation 6) is an indicator of the prosperity of a nation. This of course may not reflect lifestyles or any other judgment of national or individual contentment. It does however provide a means of showing where a nation stands with respect to its degree of industrialization and its importance as a trading nation.

An index of Energy per Capita can be assigned to any nation as direct way of comparing one with another. By assuming 400 GJ as a base figure for K it is now possible to give a Prosperity Index (I) where I = K/400. This information can now be tabulated to show comparative prosperity of a range of countries.

Energy Consumption per Capita is a mathematical not a subjective measure of prosperity. People's perception of quality of life and their aspirations do vary. However it is usual for people's wants not to be satisfied and so there is an ever-increasing demand for Energy. Energy usage may vary for a variety of reasons including lifestyles, living conditions and climate. When measuring the economy it is net energy usage that is important, not what the energy is used for. How energy is used is for the consumer to choose.

A good example is to compare Canada with Australia (from Table 2). A comparison of the Energy Consumption per Capita of the two countries shows that Canada's energy consumption per capita is much higher than Australia's (where for Australia K = 242.2 and for Canada K = 412.5). One reason for this phenomenon may be that Canada expends considerably more energy for winter heating. It is sometimes supposed that Australia and Canada enjoy similar levels of prosperity but closer examination may reveal otherwise. It could be argued from the Australian point of view that a large expenditure on home heating is not essential for high living standards. The fact remains that a Canadian has more energy available than an Australian does.

5.0 Regulating the Economy

In Section 2 it was illustrated how an economy can be measured. The accuracy is only dependent upon the precision of the statistics. Only the application of the theory over several quarters or perhaps a year or more can confirm the validity of the following arguments.

It can be reasoned that economic systems are largely self-regulating. Under normal circumstances the economy is stable, energy consumption is growing as are prices and incomes. From a mathematical perspective E is increasing and consequently so is Y=QP and the value of money changes over time as predicted by Equation 5. It is only when the value of m falls above or below the Trend Line (y) that the Inflation Rate (r) changes.

5.1 The Need for Regulation

When m deviates markedly above or below the Trend Line the Government or Central Bank may decide that intervention might be necessary.

In Section 1 it was shown that the exchange rates of trading nations is determined by comparing the respective values of money for each nation.

Changes to the exchange rate may be endogenous or exogenous and a Central Bank or Government may decide that some appropriate fiscal or monetary action is necessary.

However, the value and volume of imports and exports tend to move in unison with the exchange rate. When the exchange rate increases, imports rise and exports fall. If imports replace local production this causes a drop in energy consumption, tending to return m to a lower value, moderating the flow of imports..

If m-y is positive the rate of growth of E is exceeding the rate of growth of Y. This might indicate a shortage of labour. Longer hours worked by means of overtime may mean more energy consumed without a commensurate increase in production. It could also mean over production and a build-up of stocks causing prices to fall.

Conversely, if m-y is negative, the growth rate of Y is exceeding the growth rate of E and inflation is increasing.

5.2 The Effect of Money Supply

The way in which an increase in Money Supply is distributed or how it is used will effect the way m changes. The part of any increase in Money Supply that is used for infrastructure or capital growth will cause Energy Consumption E to increase. Subsequently, if E increases more rapidly than Y, then m will grow and the inflation rate will slow. On the other hand, that part which goes to increased spending and speculative investment will cause Y to grow and if Y increases more rapidly than E then m decreases and the inflation rate will increase.

5.3 Interest Rates

Interest rates have only an indirect influence on m through their effect upon deposits and consequently Money Supply. The effects of changes to Money Supply have been postulated previously in Section 4.2.

5.4 Fiscal Policy

Fiscal policies, if and when they are used, can be aimed at restoring m to the Trend Line, y.

6.0 Summary

It has been shown that it is possible to accurately measure the value of any currency at any time and simultaneously measure the value of any other currency. The important significance of this is that by knowing the contemporaneous value of any two currencies measured on an identical standard it is possible to determine the exact relative exchange rates of the two currencies.

The International Monetary Fund stresses the importance of stability of exchange rates in Article 1, section (iii) of the Articles of Agreement .

Currently, countries that are members of the IMF may chose to arrange the setting of exchange rates by one of several ways. This lack of constancy means that there can be no common measurement. Often however, rather than Governments or Central Banks or a country's internal macroeconomic performance, the values of currencies are determined by external subjective decisions made within the Currency Markets, the value of one currency being compared with the value of another. However there is no mathematical logic in measuring one independent variable against another variable and such a system is prone to instability.

The well-being of nations largely depends upon economic stability and vigorous trade. Hopefully the procedures described in this paper will go some way to achieving better economic outcomes for nations.