The Inflation Enigma
Part A: Price as a Relative Expression of Two Market Values
Part B: The Ratio Theory of the Price Level
Part II of The Enigma Series
Gervaise R.J. Heddle
December 2014
Abstract
• The Inflation Enigma is a two part paper focusing on the theory of
price determination (Part A focuses on microeconomics, Part B on
macroeconomics). In Part A, it is argued that price is a relative
expression of market value and every price is, in fact, a ratio of two
market values. By measuring market value in absolute terms, we can
think of price as being determined by two sets of supply and demand:
supply and demand for the good itself and supply and demand for the
measurement good (typically, money).
• In Part B, the microeconomic theory from Part A is used to develop the
“Ratio Theory of the Price Level”. Ratio Theory states that the price
level is a ratio of the “general value level” and the “market value of
money”. Ratio Theory is then used to develop two tools which will
help to explain the possible causes of inflation: the “Simple Model for
the Market Value of Money” and the “Goods-Money Framework”.
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Gervaise R. J. Heddle, 2014
Index
Section
Slide
• Introduction & Overview
5
• Part A: Microeconomics
• Price Determination: An Introduction
55
• The Measurement of Value
105
• The Ratio of Exchange
• Supply & Demand in “Absolute Terms”
3
132
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Gervaise R. J. Heddle, 2014
Index
Section
Slide
• Part B: Macroeconomics
• Ratio Theory of the Price Level
183
• The Simple Model
• The Goods-Money Framework
234
• The Right Side of the Framework: Money
• The Left Side of the Framework: Goods
4
211
248
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Gervaise R. J. Heddle, 2014
Introduction & Overview
A Brief Overview of The Inflation Enigma
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Gervaise R. J. Heddle, 2014
The Paradox of Price Level
Determination
• “Inflation” is nothing more than the evolution of prices over
time. Microeconomics tells us that the price of a good is
determined by supply and demand for that good. Clearly, this
principle can be easily extrapolated to the price of any number of
goods (the “basket of goods”). So surely, the evolution of the
general price level over time can not be that complicated: it is
simply a matter of changes in supply and demand for a wide
variety of goods? And yet, inflation remains an enigma.
• There is a good reason that macroeconomic models of price
determination (inflation) have limited success: it is because
current microeconomic models of price determination provide a
partial and one-sided view of the price determination process.
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Gervaise R. J. Heddle, 2014
The Price of a Good is a
Ratio of Two Market Values
• The fundamental problem of most microeconomic theories of
price determination is that they fail to distinguish between
“price” and “market value”. The common view in economics is
that the price of a good is its “market value”: but the price of a
good is a relative expression of the market value of a good.
• The price of a good is a ratio of two market values. The price of a
good is determined by two sets of market forces: supply and
demand for the good itself, and supply and demand for the
“measurement good”. Supply and demand for a good can
determine its market value, but, in and of itself, it can’t determine
its price: its price depends upon on the market value of the good
itself and the market value of the other good being exchanged.
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Gervaise R. J. Heddle, 2014
The Measurement of Market Value:
Absolute vs Relative
• Every good has the property of “market value”. The market
value of a good is determined by supply and demand for that
good. We can measure that market value in absolute terms (in
terms of a universal and invariable measure of market value) or
in relative terms (in terms of a variable measure of market value).
• Typically, we measure the market value of a good in relative
terms, that is, in terms of the market value of another good: this
is the “price” of the good. However, the price of the good can
only be determined if we know both the market value of the good
itself and the market value of the “measurement good”. In other
words, supply and demand for a good determines its market
value, but does not, in and of itself, determine its price.
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Gervaise R. J. Heddle, 2014
Price as a Ratio of
Two Quantities Exchanged
• In order to explain this concept, it helps to go back to basics. Let’s
answer the following question: what is the “price” of a good?
• In simple terms, “price” is a ratio of two quantities exchanged: a
quantity of one good as exchanged for a certain quantity of
another good. In mathematical terms, if we let the quantity of
good A be Q(A) and the quantity of good B be Q(B), then the price
of good A in terms of good B, denoted P(AB), is described by:
Q(B)
P(AB ) =
Q(A)
• As a general rule, we express prices in money terms. In the
equation above, good B would normally be “money”.
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Gervaise R. J. Heddle, 2014
Price as a Ratio of
Two Market Values
• How is this ratio of two quantities exchanged determined? Is the
ratio of exchange determined solely by supply and demand for
good A? Or is the ratio of exchange determined solely by supply
and demand for good B? The answer is neither. The price of
good A in B terms is determined by the market value of both
goods. In mathematical terms:
Q(B) V(A)
P(AB ) =
=
Q(A) V (B)
• The market value of good A, which we can measure in absolute
terms as V(A), is determined by supply and demand for good A.
Similarly, the market value of good B, denoted in absolute terms
as V(B), is determined by supply and demand for good B.
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The Principle of Trade Equivalence
• In an efficient market, the ratio of two quantities exchanged (the
price of one good in terms of another) will always be the
reciprocal of the absolute market value of the two goods (the
market value of the goods as measured in absolute terms).
• Let’s assume you want to trade good A for good B. What
quantity of good B do you require in order to give up a certain
quantity of good A? It depends on the relative market value of
the two goods. Why? Because in a free and efficient market,
economic agents will only exchange goods if the total market
value of the two bundles of goods being exchanged are equal:
V(A)×Q(A) = V(B)×Q(B)
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Ratio of Quantities is the Reciprocal
of the Ratio of Market Values
• In simple terms, if good A is twice as valuable as good B (value
in this context is “market value”, ie. the value of the good as
determined by market forces), then for every unit of A you give
up, you would expect twice as many units of B in exchange.
V (A) Q(B)
=
V (B) Q(A)
• We know that the price of good A in terms of good B is, by
definition, equal to the second term in the equation above.
Therefore:
Q(B) V(A)
P(AB ) =
=
Q(A) V (B)
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“Units of Economic Value”: An
Invariable Measure of Market Value
• In order to measure the market value of a good in absolute terms,
we need a universal and invariable measure of market value.
Classical economists spent a lot of time looking for a good that
possessed this quality (the labor theory of value), but there is no
good that possesses the quality of invariable market value.
• However, this doesn’t prevent us from creating a theoretical
measure of market value that is an invariable measure of market
value. For lack of a better term, we will call this invariable
measure “units of economic value”. Just as an “inch” is an
invariable measure of length, so a “unit of economic value” is an
invariable measure of market value. The market value of any
good can be measured in terms of “units of economic value”.
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Gervaise R. J. Heddle, 2014
Absolute vs Relative Market Value
• In our price equation, both the market value of good A, denoted
V(A), and the market value of good B, denoted V(B), are
measured in terms of “units of economic value”. We must
measure the market value of each good in the same terms in
order to be able to compare them.
Q(B) V(A)
P(AB ) =
=
Q(A) V (B)
• In this sense, we can say that V(A) represents the absolute market
value of good A (the market value of good A in terms of an
invariable unit of measure, “units of economic value”). In
contrast, P(AB) represents the relative market value of good A (the
market value of good A in terms of the market value of good B).
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Gervaise R. J. Heddle, 2014
Expressing Supply and Demand in
“Absolute” Market Value Terms
• The market value of a good is determined by supply and demand
for that good. Typically, supply and demand for a good is
expressed in terms of relative market value (price is on the y-axis).
In essence, it is assumed that the market value of the measurement
good (good B) is constant, allowing us illustrate how changes in
supply and demand for the primary good (good A) impact the
relative market value of good A, or P(AB ).
• However, by expressing the market value of both goods (A and B)
in “absolute” terms (in terms of a theoretical and invariable
measure of market value, “units of economic value”), we can
illustrate how changes in supply and demand for either good will
impact not only the absolute market value of each of the respective
goods but also the relative market value of the two goods.
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Gervaise R. J. Heddle, 2014
Supply and Demand in Terms of
Units of Economic Value
Supply and demand for good A determines the equilibrium market value of
good A, which is measured in terms of an invariable measure of market
value (“units of economic value” or “EV”) and denoted as V(A). Similarly,
supply and demand for good B determines the market value of good B, V(B).
Market Value
(EV)
Market Value
(EV)
“GOOD A”
“GOOD B”
S
S
V(B)
V(A)
D
D
Q(A)
Quantity
Q(B)
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Quantity
Gervaise R. J. Heddle, 2014
Using the Model to Determine
the Price of A in B Terms
We can use this simple framework to analyze the impact of changes in
supply and demand for either good upon the price of A in B terms. As
discussed, the price of A in B terms, or “P(AB )”, is equal to the ratio of V(A)
divided by V(B): if V(A) rises, the price rises, if V(B) rises, the price falls.
Market Value
(EV)
Market Value
(EV)
“GOOD A”
“GOOD B”
S
S
V (A)
P(AB ) =
V (B)
V(A)
V(B)
D
D
Q(A)
Quantity
Q(B)
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Quantity
Gervaise R. J. Heddle, 2014
An Increase in Demand for Good A
Let’s analyze two scenarios. In the first scenario, there is an increase in
demand for good A (the demand curve for good A shifts to the right). An
increase in demand for A leads to higher market value for A. V(A) rises while
V(B) is constant and the price of A in B terms rises {P(AB ) = V(A)/V(B)}
Market Value
(EV)
Market Value
(EV)
“GOOD A”
“GOOD B”
S
S
V(A)1
V(B)
V(A)0
D1
D
D0
Q(A)0 Q(A)1 Quantity
Q(B)
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Quantity
Gervaise R. J. Heddle, 2014
An Increase in Demand for Good A
in both EV and Price Terms
Our first scenario is easily demonstrated by traditional supply and demand
analysis. On the left hand side, market value is expressed in EV terms. On
the right hand side, market value is expressed in price terms (the price of A
in terms of good B): this is the “traditional” view.
Market Value
(EV)
Price
(in B terms)
“GOOD A”
“GOOD A”
S
S
V(A)1
P(AB)1
V(A)0
P(AB)0
D1
D0
D1
D0
Q(A)0 Q(A)1 Quantity
Q(A)0 Q(A)1 Quantity
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Gervaise R. J. Heddle, 2014
Why Did Traditional Analysis
Work for First Scenario?
• In this first scenario, traditional supply and demand analysis
provides the right answer. Why? Because traditional supply and
demand analysis assumes that the market value of the
measurement good (good B) is constant. In this scenario, it just
so happens that the market value of good B is constant, therefore
traditional supply and demand analysis gets the right result.
• But what happens when the market value of good B is not
constant? Traditional supply and demand analysis struggles to
explain changes in price due to a change in the market value of
the measurement good because its perspective is so “one-sided”.
However, we can use our alternative version of supply and
demand analysis to illustrate what happens.
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Gervaise R. J. Heddle, 2014
An Increase in Demand for Good B
In our second scenario there is an increase in demand for good B (the
demand curve for good B shifts to the right). The equilibrium market value
of good B rises. The market value of good A is constant. Therefore, the price
of A in B terms, or “P(AB )”, falls: {P(AB ) = V(A)/V(B)}
Market Value
(EV)
Market Value
(EV)
“GOOD A”
“GOOD B”
S
S
V(B)1
V(A)
V(B)0
D
Q(A)
D1
D0
Q(B)0 Q(B)1
Quantity
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Quantity
Gervaise R. J. Heddle, 2014
Why Did the Price Fall?
• Let’s think about what just happened. There was no change in
the supply and demand for good A (as measured in “units of
economic value” terms) and yet the price of good A fell. Why
did the price fall? Because price is a relative expression of two
market values. All else equal, the price of good A as measured in
terms of good B will fall if the market value of good B rises:
V (A)
P(AB ) =
V (B)
• So, how can we represent this scenario in traditional supply and
demand format (with price on the y-axis)? If the market value of
the measurement good (good B) rises, then what happens to the
supply and demand curves for good A in B terms?
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Gervaise R. J. Heddle, 2014
Impact on Good A of an Increase in
Demand for Good B
In our second scenario there is an increase in demand for good B. The
equilibrium market value of good A is constant. However, the price of A in
B terms falls. Why? As the market value of good B rises, the supply and
demand curves for good A (as expressed in B terms) both shift lower.
Market Value
(EV)
Price
(in B terms)
“GOOD A”
“GOOD A”
S0
S
S1
P(AB)0
V(A)
P(AB)1
D0
D
Q(A)
D1
Quantity
Q(A)
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Quantity
Gervaise R. J. Heddle, 2014
Price Determination in a Barter
Economy (No Money)
• The principle that price is a ratio of two market values applies to
every price in the economy. In essence, the prices that we see
around us every day are the physical manifestation (the visible
portion) of a matrix of directly unobservable market values.
• We will use a number of examples to explore this concept. In our
first example, we will consider price determination in a two good
barter economy with no money. If the two goods in our economy
are apples and bananas, then what determines the apple price as
measured in banana terms (remember, there is no “money”)? Is it
supply and demand for apples or supply and demand for
bananas? The answer is both. The price of a good in terms of
another good depends on the market value of both goods.
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Gervaise R. J. Heddle, 2014
Foreign Exchange Rate
Determination
• We will also consider a more modern example: foreign exchange
rate determination. Every foreign exchange rate represents the
price of one currency in terms of another currency. Consider the
USD/EUR rate? Is this “price” determined by supply and
demand for US Dollars or supply and demand for Euros? Again,
the answer is both.
• Supply and demand for US Dollars determines the market value
of the US Dollar V(USD). Similarly, supply and demand for
Euros determines V(EUR). The USD/EUR exchange rate is then
equal to:
Q(USD) V(EUR)
P(EURUSD ) =
=
Q(EUR) V(USD)
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Gervaise R. J. Heddle, 2014
The Money Price of Goods
• Ultimately, the point of these examples is to explain the general
principle that the price of one good in terms of another is
determined by the ratio of their market values. We can then
apply this principle to the determination of “money prices”.
• The money price of a good (the price of a good in terms of
money) is determined by the following ratio:
Q($) V (A)
P(A$ ) =
=
Q(A) V ($)
• Supply and demand for the good determines the market value of
the good V(A). Supply and demand for money determines the
market value of money V($) (not the interest rate!).
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The Price of a Cup of Coffee
• In very simple terms, when you exchange a quantity of dollar
bills for a quantity of a good (say one cup of coffee), the idea is
that you are exchanging two “baskets” of equivalent total market
value.
V(Coffee)×Q(Coffee) = V($)×Q($)
• If the market value of one cup of coffee, as measured in absolute
terms, is three times that of the market value of one dollar bill,
then trade will only occur if you offer three dollar bills for that
cup of coffee. Therefore, the price of coffee, in dollar terms, is
equal to:
Q($) V (Cf )
P(Coffee$ ) =
=
=3
Q(Cf ) V ($)
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Gervaise R. J. Heddle, 2014
Supply and Demand for Money
• It is the view of The Enigma Series that supply and demand for
money, where “money” is defined as the monetary base (see The
Money Enigma), determines the market value of money. The
market value of money is the denominator of every money price
in the economy. Economics has struggled with this concept
because the market value of money is not directly observable (you
can’t observe market values in the absolute). The market value of
money can only be observed in a relative context, as a “price” (a
fact that is true of all market values).
• Supply and demand for money does not determine “the interest
rate”, although the manner in which newly created money is
used (to buy government debt) does influence the interest rate.
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Gervaise R. J. Heddle, 2014
Every Money Price is Determined by
Two Sets of Supply and Demand
We can use our theory to visualize the determination of “money prices”.
Supply & demand for good A determines the market value of good A, V(A).
Supply & demand for money determines the market value of money, V($).
The money price of good A is equal to the ratio of the two market values.
Market Value
(EV)
V(A)
Market Value
(EV)
“GOOD A”
S
V (A)
P(A$ ) =
V ($)
“MONEY”
Supply
V($)
Demand
D
Q(A) Quantity
Q($) Base Money
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Gervaise R. J. Heddle, 2014
Towards a Model of Inflation
• The second part of The Inflation Enigma (Part B) focuses on
extending the microeconomic theory developed in the first part
(Part A) and building macroeconomic tools that can be used to
explain the nature of price level determination.
• While the notion that price is a relative expression of two market
values is a useful tool in a microeconomic context, it is
fundamental in a macroeconomic context. It is the view of this
paper that a comprehensive theory of inflation must build upon
the principle that every money price in the economy is a function
of two market values. More specifically, supply and demand for
money determines the market value of money which, in turn, is
the denominator of every money price in the economy.
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Gervaise R. J. Heddle, 2014
The Ratio Theory of the Price Level
• Part B of this paper begins by deriving the “Ratio Theory of the
Price Level”. Ratio Theory states that the general price level p
can be expressed as a ratio of two market values:
Where
VG
p=
VM
p is the general price level of the economy
VG is the “general value level” of the economy
VM is the absolute market value of money
• The general value level VG is a hypothetical measure of overall
market values (as measured in “units of economic value”) for the
set of goods and services that comprise the “basket of goods”.
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Gervaise R. J. Heddle, 2014
Ratio Theory as a Starting Point
for Our Analysis of Inflation
• In essence, Ratio Theory states that a rise in the price level can be
due to either (i) a rise in the overall absolute market value of
goods VG or (ii) a fall in the absolute market value of money VM .
This theory has many implications and can be used to highlight
the overly simplistic nature of the typical “inflation vs deflation”
debate. For example, the common view that a decline in
aggregate demand “must be deflationary” completely ignores the
role of the market value of money.
• It should be noted that Ratio Theory is not a theory of inflation
per se, but rather a starting point for analysis. In order to make
Ratio Theory “useful” we need to understand the principle
factors that drive each of the two key variables (VG and VM ).
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Gervaise R. J. Heddle, 2014
Price Level Determination:
Long Run vs Short Run
• In order to simplify the analysis of price level determination, The
Inflation Enigma separates the analysis into two buckets: price
level determination in the long run and price level determination
in the short run.
• Ultimately, the long run determination of prices is just an
aggregated path of short run processes. It would be preferable not
to distinguish between the long run and short run because the
fundamental price level determination process is the same in both
cases. However, in order to fully understand the short run
process, we need to develop a more comprehensive model of the
price level. This more comprehensive model is constructed in the
last paper in the series, The Velocity Enigma.
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Gervaise R. J. Heddle, 2014
Price Level Determination
in the Long Run
• When measured over very long periods of time, changes in the price
level are strongly correlated to changes in the ratio of base money to
real output. This is the long run application of the quantity theory of
money, an economic phenomenon for which there is strong
empirical support (King, 2001).
• The reason quantity theory works in the long run, but not in the
short run, is because money is a long-duration, special-form equity
instrument. In the short run, the value of a long-duration equity
instrument is highly sensitive to shifts in expectations. However,
when measured from point to point over long periods of time, most
of the change in the value of such an instrument is determined by
the historic change in the output/base money ratio (the
earnings/share ratio), not shifts in future expectations.
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Gervaise R. J. Heddle, 2014
Value of a Long-Duration Asset:
Long Term versus Short Term
• We can highlight this point by think about the pricing of a longduration, proportional claim: common stock. Imagine a stock with
a P/E ratio of 20 and earnings of $1 per share. Over the next two
years, earnings rise to $1.25 per share, but the P/E ratio falls to 16
(lower growth expectations). Over the next eighteen years, earnings
rise to $10 per share while the P/E ratio remains at 16.
• Over the first two years, the stock price performance seems to have
nothing to do with EPS: EPS rises 25% ($1 to $1.25) but the share
price doesn’t change (stays at $20). But measured over the entire
twenty year period, the share price does track earnings per share, at
least roughly: the stock price rises 8x (to $160) while EPS is up 10x.
Over long periods of time, changes in EPS tend to overwhelm
changes in expectations (which are reflected in the P/E multiple).
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Gervaise R. J. Heddle, 2014
A Simplified Analysis of the
Market Value of Money
• In the short term, the value of money may seem to have nothing to
do with the output/money ratio. However, when measured over
long periods of time, the market value of money is driven primarily
by the ratio of real output to base money. Proportional claim
theory states that money represents a variable entitlement to the
output of society. If we can ignore or minimize the impact of
changing expectations (which we can if discussing changes over
very long periods of time), then we should expect that the market
value of a proportional claim to the output of society should rise as
real output rises and falls as the monetary base increases.
• These notions can be further illustrated by merging Ratio Theory
with the quantity theory of money to create the Simple Model for
the Market Value of Money (see next slide).
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Gervaise R. J. Heddle, 2014
The Simple Model for the
Market Value of Money
• Ratio Theory and the Equation of Exchange are used to derive
the “Simple Model for the Market Value of Money”:
VG × q
VM =
M ×v
• The Simple Model states that the absolute market value of
money VM can be expressed as a function of four variables:
1. The general value level VG , a hypothetical measure of overall
absolute market values for the “basket of goods”;
2. Real output q;
3. The monetary base M; and
4. The velocity of base money v.
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Gervaise R. J. Heddle, 2014
Basic Implications of
The Simple Model
• The Simple Model provides further, albeit very limited, insight
into the market value of money. All else equal, the absolute
market value of money is positively related to both the general
value level and real output. As expected, the market value of
money is negatively related to the number of claims issued, the
monetary base: as the number of outstanding claims increases,
the proportional entitlement of each claim falls.
• In the long run, if the velocity of money is relatively stable, then
the market value of money is primarily determined by the ratio
of real output to the money base. Since the value of money is
the denominator in the price level, the price level is primarily
determined by the ratio of money base to real output.
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Gervaise R. J. Heddle, 2014
Price Level Determination
in the Short Run
• One of the primary implications of the Simple Model is that, in
the long run, the general value level VG is irrelevant to the
determination of the price level. Why? Because any rise or fall in
the value of goods VG is reflected in the value of money VM .
(With velocity stable, a rise in VG leads to a rise in VM and there is
no change in the price level which is a ratio of the two). Longterm, only real output and base money matter.
• However, in the short run, changes in the general value level are
not automatically reflected in the market value of money. Money
is a long-duration asset and it will often “look through” what are
perceived to be temporary adjustments in the general value level.
Therefore, we need a model to analyze both variables.
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Gervaise R. J. Heddle, 2014
A Two-Market Model for
Price Level Analysis
• In order to help us analyze short-term movements in the price
level, we will introduce a basic two-market model called “The
Goods-Money Framework”.
• The Goods-Money Framework proposes that (1) the equilibrium
general value level VG is determined by aggregate demand and
aggregate supply in the market for goods/services and (2) the
equilibrium absolute market value of money VM is determined
by supply and demand for the monetary base. The key
implication of the Goods-Money Framework is that the price
level is determined, in a stylized sense, by two sets of supply and
demand, it is not determined solely by aggregate supply and
demand as represented in traditional Keynesian analysis.
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Gervaise R. J. Heddle, 2014
The Goods-Money Framework
Aggregate supply and demand for goods/services determines the
equilibrium general value level VG and real output q. Supply and
demand for money determines the market value of money VM .
“LEFT SIDE: GOODS”
“RIGHT SIDE: MONEY”
General Value Level (EV)
Value of Money (EV)
AS
Supply
VG
p=
VM
VG
VM
Demand
AD
q
Real Output
M
41
Base Money
Gervaise R. J. Heddle, 2014
The Left Side of the Framework
• The Left Side of the
Framework is a short run
model of aggregate demand
and aggregate supply, where
both functions are expressed
in terms of the general value
level and real output.
LEFT SIDE OF
THE FRAMEWORK
General
Value
Level
(EV)
“GOODS/SERVICES”
Aggregate
Supply
VG
q
• The intersection of
aggregate demand and
aggregate supply determines
Aggregate
equilibrium levels of real
Demand
output and the general value
level.
Real Output
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Gervaise R. J. Heddle, 2014
The Right Side of the Framework
• The Right Side of the
Framework is the market for
money. The supply of money
(the monetary base) is fixed.
Demand for money is plotted
in terms of the absolute
market value of money.
THE RIGHT SIDE OF
THE FRAMEWORK
“MONEY”
Value of
Money (EV)
• The intersection of supply
and demand for money
determines, in the first
instance, the equilibrium
absolute market value of
money.
Supply
VM
Demand
fn{VG ,q, v}
M
43
Base Money
Gervaise R. J. Heddle, 2014
Example One: Increase in
Aggregate Demand
• Let’s briefly consider two
basic examples. In this
example, the aggregate
demand curve shifts to the
right. Equilibrium levels of
real output q and the general
value level VG both rise.
LEFT SIDE OF
THE FRAMEWORK
General
Value
Level
(EV)
“GOODS/SERVICES”
Aggregate
Supply
VG,2
VG,1
• All else equal, the rise in VG
will lead to a rise in the price
level:
AD2
AD1
q1 q2
Real Output
44
VG
p=
VM
Gervaise R. J. Heddle, 2014
Example Two: Increase in
Demand For Money
• In this second example, there
is an increase in the demand
for money. The demand
curve for money moves to
the right. The equilibrium
absolute market value of
money VM rises.
THE RIGHT SIDE OF
THE FRAMEWORK
“MONEY”
Value of
Money (EV)
Supply
VM,2
• All else equal, the rise in VM
will lead to a fall in the price
level:
VM,1
VG
p=
VM
D2
D1
M
45
Base Money
Gervaise R. J. Heddle, 2014
Interpreting the Goods-Money
Framework
• Superficially, the implications of the Goods-Money Framework
may seem obvious. A basic reading would suggest that excess
aggregate demand always leads to a rise in the value of goods VG
and the price level, or that an increase in base money always leads
to a fall in the value of money VM and a rise in the price level.
Unfortunately, it is just not that simple.
• The main problem with this simple analysis is twofold. Firstly, a
change in the left side of the framework may (or may not) impact
the value of money VM . If VG and q both rise, then this may or
may not lead to an increase in the value of money depending
upon whether the shift in the value of goods and real output is
perceived to be temporary or permanent.
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Gervaise R. J. Heddle, 2014
Reaction to a Perceived “Temporary”
Increase in Aggregate Demand
Aggregate demand rises, but the rise is perceived to be temporary.
Output and general value level rise. Money is a long-duration asset:
there is no change in long-term expectations and hence negligible
change in VM . The end result is the price level rises (p = VG /VM ).
General Value Level
Value of Money
AS
Supply
VG,1
VM
VG,0
AD0
q0 q1
“No Change”
AD1
Real Output
47
D0 = D1
M
Base Money
Gervaise R. J. Heddle, 2014
What Happens to the Value of
the Financial Instrument?
• In the scenario on the previous page, an increase in aggregate
demand that is perceived to be temporary has no impact on the
value of money. Why? Because money is a long-duration
financial instrument. The value of long-duration equity
instrument is determined primarily by expectations regarding the
distant future. If those expectations are largely constant, then the
value of money doesn’t change.
• The net result in this scenario is that the price level rises and the
velocity of money rises. However, if the increase in both the
general value level and real output was perceived to be more
permanent in nature, then this should lead to a rise in the value
of money, which could offset the rise in the value of goods.
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Gervaise R. J. Heddle, 2014
Reaction to a Perceived “Permanent”
Increase in Aggregate Demand
Aggregate demand rises and the rise is perceived to be more “permanent” in
nature. The value of money rises as it discounts the higher future levels of
output (VG q) that will be claimed by each unit of money. The end result is
little change in the price level: the rise in VG is offset by the rise in VM.
General Value Level
Value of Money
Supply
AS
VG,1
VM,1
VG,0
VM,0
AD0
q0 q1
AD1
Real Output
49
D0
M
D1
Base Money
Gervaise R. J. Heddle, 2014
The Market for Money: Supply and
Demand a “Second Best” Tool
• The second major problem with a superficial interpretation of
the Goods-Money Framework is that it suggests that the value of
money will fall if the money supply curve shifts to the right (the
monetary base increases). Again, it isn’t that simple. Supply and
demand analysis is a “second best” solution for analyzing the
market for money. The better model for analyzing the market
value of money is the discounted future benefits model
developed in The Velocity Enigma.
• Money is a long-duration financial instrument. An increase in
the monetary base may have little or no impact on the value of
money if that increase is perceived to be temporary. What
matters are long-term expectations of the output/money ratio.
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Gervaise R. J. Heddle, 2014
The Right Side of the Framework
• An entire section of this paper is devoted to discussing the Right
Side of the Goods-Money Framework (the market for money). In
particular, we begin to discuss the practical implications of the
notion that money is a long-duration financial instrument.
Namely, that in the short term, the market value of money is
highly sensitive to changing expectations regarding the long-term
path of important economic variables (most notably, real output
and money).
• Unfortunately, we can only scratch the surface of these issues in
this paper. In order to fully understand the determination of the
market value of money, we need the “Discounted Future
Benefits Model” that is developed in The Velocity Enigma.
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Gervaise R. J. Heddle, 2014
“Sticky Wages” Explained by
Rational Expectations
• The last section of the paper discusses the derivation of the Left
Side of the Goods-Money Framework. In particular, it focuses
on the derivation of the aggregate demand and aggregate supply
functions as expressed in terms of the general value level and
contrasts this model with the traditional AD/AS model.
• It is argued that the slope of both functions is largely due to
expectations of cyclicality and mean reversion in the general
value level (a property that is not present in the price level). It
will be argued that these expectations of mean reversion in the
general value level can also be used to explain why wages are (or
at least appear to be) “sticky” in an efficient market with no
nominal rigidities.
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Gervaise R. J. Heddle, 2014
A Preview of
The Velocity Enigma
• The Inflation Enigma should be considered as an introduction to
the issues involved in the determination of the price level. We
will use the tools developed in this paper (Ratio Theory, the
Simple Model and the Goods-Money Framework) in the final
paper in the series, The Velocity Enigma.
• The Velocity Enigma combines the issues discussed in The
Money Enigma (the nature of money) with the issues discussed
in The Inflation Enigma (the basic nature of price level
determination) to develop a much more comprehensive,
expectations-based model of the price level. The Velocity Enigma
concludes by comparing this model with the views of the major
schools of economic thought.
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Gervaise R. J. Heddle, 2014
Part A:
Microeconomic
Price Determination
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Gervaise R. J. Heddle, 2014
Price Determination:
An Introduction
Price as a Ratio of the Market Value of Two Goods
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Gervaise R. J. Heddle, 2014
Microeconomic Price Determination:
An Introduction
• Most people are confident that they understand why the dollar
price of a good goes up or down: “supply and demand”. But
what determines the dollar price of a good isn’t as simple as just
supply and demand for the good itself. That isn’t to say that
supply and demand for that good isn’t important, but it’s only half
the picture. Supply and demand for a good determines its “market
value”, but every price is a ratio of two market values.
• The other half of the picture is the market value of money as
determined by supply and demand for money. The market value
of money is the critical denominator of every “money price” and
is just as important in determining the price of a good as the
supply and demand for that good.
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Gervaise R. J. Heddle, 2014
Price is an Expression of
Relative, not Absolute, Market Value
• Every price is a ratio of two quantities exchanged: a quantity of
one good for a quantity of another. It is the contention of this
paper that this ratio is determined by the relative market value of
the two goods being exchanged.
• Trade, at its simplest level, is nothing but the exchange of two
baskets, one for another. A trade could be one apple for one pear,
or it could be one apple for two dollars. Either way, the ratio of
exchange (pears for apples, dollar for apples) depends on the
market value of both items being exchanged. This “ratio of
exchange” is commonly referred to as the “price” of the
transaction. The ratio of two quantities exchanged (price) can not
be determined by the market value of just one of those goods.
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Gervaise R. J. Heddle, 2014
The Property of Market Value
• In order to understand this concept, we need to think about the
property of “market value”. A good must possess the property of
market value for it to have any value in exchange. The market
value of a good is separate and distinct from its “non-market
value”, more commonly known as its “utility”. The two concepts
are related, but they are fundamentally different.
• The problem with “value”, whether it be “market value” or “nonmarket value” is that it is a very difficult property to measure. In
the case of utility (non-market value), economics has created a
theoretical and invariable unit of non-market value called the
“util”. The “util” is an absolute measure of the non-market value
of a good, just as “inches” are an absolute measure of length.
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Gervaise R. J. Heddle, 2014
Measuring Market Value
• In contrast, economics has not developed an widely accepted
measure of the absolute market value of a good. Instead,
economic theories of price determination rely solely on the
measurement of market value in relative terms.
• Almost universally, market value is measured on a relative basis:
the market value of a good is measured with reference to the
market value of another good. This method of measuring
market value produces a ratio of two quantities exchange, or a
“price”. This practice is so common that most people equate the
“market value” of a good with its “price”. But technically, the
price of a good in terms of another good is only one possible
expression of that good’s market value.
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Gervaise R. J. Heddle, 2014
Height vs Relative Height
• We can simplify our discussion by comparing the concept of
“market value” with a simple physical property with which we
are all familiar: “height”.
• Most of the physical objects we see around us possess the
property of height. We can measure height in two basic ways. We
can measure the height of an object in absolute terms (in terms of
an invariable unit of height such as feet or inches) or we can
measure the height of an object in relative terms (the tree is three
times taller than the girl). Both are acceptable ways to measure
the property of height. However, in order for us to able to
compare the height of two objects on a relative basis, both objects
must possess the property of height in the absolute sense.
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Gervaise R. J. Heddle, 2014
Any Property Compared on a Relative
Basis, Must Exist in the Absolute
• In economics, common practice is to express the market value of
a good in terms of another good. For example, the market value
of an apple is three dollars. In effect, this is the same as saying
that the height of the tree is three girls.
• However, if it is possible for us to express the market value of a
good in terms of another good, it must be true that both goods
have market value and that we can, at theoretically, measure the
market value of each good in terms of an invariable unit of
market value. Just as we can measure the height of a tree in
terms of feet and/or inches, so we can measure the market value
of the apple in terms of a universal and invariable measure of
market value. All we need to do is create one.
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Gervaise R. J. Heddle, 2014
“Units of Economic Value”
An Invariable Measure of Market Value
• Classical economists such as Adam Smith and David Ricardo
spent a lot of time looking for a good that could, in effect, act as
an invariable measure of market value. (The labor theory of
value suggested labor is that invariable measure).
• In reality, no good has the property of invariable market value.
However, this does not prevent us from creating a theoretical
measure of market value that is universal and invariable. So, let’s
create a universal measure of market value and let’s call it a
“unit of economic value” or “EV”. Units of economic value are
an invariable measure of the market value of a good. Just as
height can be measured in feet and/or inches, the market value
of any good can be measured in terms of units of economic
value.
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Gervaise R. J. Heddle, 2014
Price as a Ratio of
Quantities Exchanged
• Once we have created an invariable measure of the market value
(“units of economic value”), the task of understanding price
determination becomes much easier.
• Let’s start with the general case. Assume we have two goods:
apples (good “A”) and bananas (good “B”). We want to
determine the price of apples in banana terms. We know that
price is a ratio of two quantities exchanged: a quantity of B,
denoted Q(B), for a given quantity of A, Q(A). Mathematically,
the price of A in B terms, denoted P(AB ), can be stated as:
Q(B)
P(AB ) =
Q(A)
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Gervaise R. J. Heddle, 2014
The Principle of Trade Equivalence
• So, how is this ratio of quantities exchanged determined? We
need to start with one basic principle that we shall call “the
principle of trade equivalence”.
• The principle of trade equivalence is the simple notion that, in an
efficient market, two parties will never exchange baskets of goods
unless those baskets are of equivalent total market value. If we
denote the market value of apples in EV terms (“units of
economic value”) as V(A) and the market value of bananas in EV
terms as V(B), then the principle of trade equivalence states that
trade will only occur if:
V(A)×Q(A) = V(B)×Q(B)
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Gervaise R. J. Heddle, 2014
The Reciprocal Relation Between
Quantities and Market Value
• Let’s rearrange the formula on the previous slide and discuss
what in means in practical terms:
Q(B) V (A)
=
Q(A) V (B)
• What determines the ratio of exchange in our example? How
many many bananas must you receive in order to give up one of
your apples? In essence, the principle of trade equivalence states
that it depends on both the market value of apples V(A) and the
market value of bananas V(B). If an apple is three times more
valuable than a banana {V(A) = 3V(B)}, then someone must offer
you three bananas for you to give up one apple.
65
Gervaise R. J. Heddle, 2014
Price is a Ratio of
Two Absolute Market Values
• As stated earlier, the price of good A in good B terms, denoted
P(AB ), is equal to the ratio of two quantities exchanged. The
principle of trade equivalence implies that this ratio of two
quantities exchanged is equal to the reciprocal of the ratio of the
absolute market value of the two goods. Therefore, the price of
good A in terms of good B is equal to:
Q(B) V(A)
P(AB ) =
=
Q(A) V (B)
• The price of one good in terms of another is determined by a
ratio of two market values (the absolute market value of the
primary good, good A, divided by the absolute market value of
the measurement good, good B).
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Gervaise R. J. Heddle, 2014
The Money Price of Goods
• So far, we have discussed the principle of price determination in
general terms: the price of one good in terms of another is
determined by the ratio of their absolute market values. Now, we
can apply this principle to the determination of “money prices”.
• The money price of a good (the price of a good in terms of
money) is simply the ratio of the number of units of money
(dollars) that must be exchanged in return for one unit of a good
(good A). Therefore, the price of good A in dollar terms is equal
to the quantity of dollars exchanged, Q($), for a certain quantity
of good A, Q(A).
Q($)
P(A$ ) =
Q(A)
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Gervaise R. J. Heddle, 2014
The Market Value of Money
• Why is it possible to exchange good A for money? Because both
good A and money possess the property of “market value”. As
discussed in The Money Enigma, money can only act as a
medium of exchange because it has value (derived from its status
as a financial instrument). More specifically, money possesses
the property of market value and we can, at least theoretically,
measure this market value in terms of a universal and invariable
unit of market value (“units of economic value”).
• It is the relative relation between the market value of money and
the market value of a good that determines the price of a good in
money terms. We can see this by applying the principle of trade
equivalence to a money-based transaction.
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Gervaise R. J. Heddle, 2014
Principle of Trade Equivalence Applied
to a Money-Based Transaction
• Money is accepted in exchange for goods because money has the
property of market value. We can measure the market value of
money in terms of units of economic value: this is the absolute
market value of money, denoted V($).
• In an efficient market, a money-based transaction will only occur
when the total market value of the basket of good A exchanged
is equal to the total market value of the basket of money
exchanged:
V(A)×Q(A) = V($)×Q($)
• In simple terms, in an efficient market, trade only occurs when
two parties swap baskets of equal market value. In most
transactions, one of those baskets contains a quantity of money.
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Gervaise R. J. Heddle, 2014
The Price in Dollar Terms is a
Ratio of Two Market Values
• Rearranging the previous equation, the ratio of the quantity of
dollars exchanged and the quantity of good A exchanged is
determined by the relative market value of the two goods:
Q($) V (A)
=
Q(A) V ($)
• As we know, the price of good A in dollar terms is equal to this
ratio of quantities exchanged. Therefore, the price of good A in
dollar terms is a ratio of two market values:
Q($) V (A)
P(A$ ) =
=
Q(A) V ($)
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Gervaise R. J. Heddle, 2014
What Determines Market Value?
Supply and Demand
• If price is determined by a ratio of two market values, then what
determines market value? Economics already has a well established
paradigm for answering this question: supply and demand. Supply
and demand determines market value: we can measure market value
in absolute terms or, as is common practice, in relative terms.
• If supply and demand determines the market value of a good where
that market value is measured in relative terms (in terms of another
good), then supply and demand must also determine the market
value of that good where the market value is measured in absolute
terms (in terms of an invariable unit of measure). Put another way, if
supply and demand does not determine market value as measured in
absolute terms, then it doesn’t determine market value as measured
in relative terms (in terms of “price”).
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Gervaise R. J. Heddle, 2014
The Market for Apples in
“Units of Economic Value” Terms
• Supply and demand for apples
determines the market value of
apples. In this case, the market
value of apples is measured in
absolute terms V(A).
Supply
THE MARKET FOR APPLES
Market value in
“EV” terms
V(A)
Q(A)
• The supply and demand curves
for apples are both expressed in
terms of units of economic value,
an invariable measure of market
value. The intersection of supply
Demand
and demand determines the
equilibrium market value of
Quantity
apples V(A).
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Gervaise R. J. Heddle, 2014
Two Ways to Illustrate Exactly
The Same Thing
The two diagrams below are identical in every aspect except one: the unit of
measurement. In the first, supply and demand are represented in terms of an
invariable unit of market value. In the second, the schedules are represented
in terms of a good (dollars), the market value of which is assumed constant.
Market Value
(Units of EV)
“APPLES”
Market Value
(Dollars)
“APPLES”
S
S
V(A)
P(A$ )
D
D
Q(A)
Quantity
Q(A)
73
Quantity
Gervaise R. J. Heddle, 2014
Every Price is Determined by
Two Sets of Supply and Demand
• If the price of a good is determined by the relative market value of
two goods and the market value of a good is determined by
“supply and demand”, then it follows that the price of a good is
determined by two sets of supply and demand.
• The traditional representation of supply and demand for a good
in price terms provides a rather simplified and somewhat
misleading view of the price determination process. If there is
little or no movement in the unit of measurement (the currency),
then changes in the price of the good will primarily reflect
changes in supply and demand for that good. However, if the
market value of the unit of measurement (money) is not
constant, then we have a problem.
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Gervaise R. J. Heddle, 2014
The Problem with Traditional
Demand & Supply Analysis
• The issue can be illustrated by considering the determination of
prices in a barter economy with no money. Imagine an economy
with two goods (apples and bananas) and no currency. What is
the price of apples and how is that price determined?
• There is only one meaningful way to express the price of apples
in our two good economy: in terms of bananas. For example, an
apple might cost two bananas. If there is more demand for
apples, then the price of apples might rise to three bananas. If the
demand for apples falls, then the price might fall to one banana.
The traditional demand/supply framework works fine so far. But
what happens to the price of apples (in banana terms) if there is
an increase in the demand for bananas?
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Gervaise R. J. Heddle, 2014
The Price of Apples
• If there is an increase in the demand for bananas, then (all else
equal) the price of apples in banana terms will fall. But how is
that possible with “no change” in supply and demand for apples?
• Consider this question: What determines the price of apples as
expressed in banana terms? Is it supply and demand for apples?
Or is it supply and demand for bananas?
• The answer is simple: both. The price of apples, in banana terms,
depends on both the supply and demand for apples and the
supply and demand for bananas. If there is a sudden increase in
demand for bananas, the value of an banana rises and, all else
equal, the number of bananas required to purchase an apple falls.
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Gervaise R. J. Heddle, 2014
The Blind Spot: The Market Value
of the Measurement Good
DEMAND & SUPPLY
FOR APPLES
Price of apples in
“banana terms”
P(AB)
Q(A)
• This traditional supply and
demand diagram for apples
focuses on changes in supply and
demand for apples and the
impact on the price of apples.
Supply
• But what happens if there is a
change in the supply and demand
for bananas? The problem is that
this representation of the
“market for apples” assumes that
Demand
there is no change in the market
value of bananas (the
Quantity
“measurement good”).
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Gervaise R. J. Heddle, 2014
Is There a Solution?
• How can we illustrate the impact of a change in supply and
demand for bananas on the price of apples. [Remember, there is
no money in our economy: we can’t just express the price of both
goods in money terms and then calculate the price of apples in
banana terms by dividing the two money prices.] What we need
is a way to illustrate how the price of apples (in banana terms)
changes in response to changes in both the supply and demand
for apples and the supply and demand for bananas.
• The solution is quite simple (although a little abstract): we use
our independent unit of measurement of market value, “units of
economic value”, to express supply and demand for each good in
terms of absolute measure of market value.
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Gervaise R. J. Heddle, 2014
Two Markets: Apples & Bananas
The price of apples (in banana terms) is determined by both supply and
demand for apples and supply and demand for bananas. We can represent
this by expressing both sets of supply and demand schedules in terms of an
invariable measure of market value, “units of economic value”.
Market Value
(Units of EV)
“APPLES”
Market Value
(Units of EV)
“BANANAS”
S
S
V (A)
P(AB ) =
V (B)
V(A)
V(B)
D
D
Q(A)
Quantity
Q(B)
79
Quantity
Gervaise R. J. Heddle, 2014
Calculating the Price of Apples
in Banana Terms
• It is the contention of this paper that supply and demand for
apples determines, in the first instance, the market value of
apples, not the “price” of apples. Similarly, supply and demand
for bananas determines, in the first instance, the market value of
bananas. In both cases, we can measure market value in
“absolute terms”: in terms of an invariable unit of market value.
• As discussed, the price of apples, in banana terms, is then a ratio
of these two absolute market values. More specifically, the price
of apples in banana terms P(AB ) can be calculated as:
V (A)
P(AB ) =
V (B)
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Gervaise R. J. Heddle, 2014
An Increase in Demand for
Bananas….
We can now use our model to illustrate the impact of an increase in the
demand for bananas on the “apple price”. The demand curve for bananas
shifts from D0 to D1. The absolute market value of bananas increases from
V(B)0 to V(B)1. There is no change in the absolute market value of apples.
Market Value
(EV)
“APPLES”
S
Market Value
(EV)
“BANANAS”
S
V(B)1
V(A)
V(B)0
D1
D
Q(A)
D0
Q(B)0 Q(B)1
Quantity
81
Quantity
Gervaise R. J. Heddle, 2014
…Causes the Price of Apples (in
Banana Terms) to Fall
Although there is no change in the “absolute” market value of apples, the
“relative” market value of apples, the price of apples in banana terms,
must fall as the market value of bananas rises (apples become cheaper in
banana terms). Both supply and demand curves for apples shift down.
Market Value
(EV)
“APPLES”
Apple price
(in bananas)
“APPLES”
S0
S
S1
P(A)0
V(A)
D0
P(A)1
D
Q(A)
D1
Quantity
Q(A)
82
Quantity
Gervaise R. J. Heddle, 2014
A Counterintuitive Result?
• The graphical result may seem counterintuitive: an increase in
demand for bananas shifts both the supply and demand curve for
apples. Indeed, the supply and demand curves for apples (as
expressed in banana terms) both move in the exact same direction
(downward) and by the same proportion. How is this possible?
Because both of the original supply and demand schedules (as
expressed in banana terms) assume a certain market value for the
unit of measurement (bananas).
• Consider the supply curve as measured in banana terms. If the
market value of bananas rises (bananas are more valuable), then,
all else equal, someone should be willing to supply more apples
for a given number of bananas (supply curve shifts to the right).
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Gervaise R. J. Heddle, 2014
Bananas as Currency
• Now, suppose that over time our barter economy evolves to
produce more goods. As this process evolves over time, more and
more goods are priced in “banana terms”. For examples, one
apple costs two bananas, one potato costs three bananas, one cup
of rice costs half a banana etc. Increasingly, bananas are used as
the relative measure of value (one can speak of the value of all
things in “banana terms”).
• In effect, bananas become the “currency” in our barter economy.
However, the market value of bananas will continue to fluctuate
with the result that the “general price level, in banana terms” will
generally fall when bananas are more valuable (eg. when the
banana crop fails) and rise when bananas are less valuable.
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Gervaise R. J. Heddle, 2014
The Currency May Change, but the
Principle Remains the Same
• In our modern economy, we don’t use bananas as “currency” (for
many good reasons we won’t discuss here). Over time, the money
in our economy has evolved from one “good” to another. Firstly,
it evolved from the ancient equivalent of bananas to gold. Then,
governments began issuing paper claims to gold (a “asset backed
financial instrument” became money). More recently, the claim
to gold was dropped and money became a proportional claim on
output (the nature of the financial instrument changed).
• While the nature of the “good” used as money has changed, the
fundamental principle of price determination has not. The money
price of a good is determined by the relative relation between the
market value of the good and the market value of money.
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Gervaise R. J. Heddle, 2014
Supply and Demand
The Traditional Narrative
• Let’s think about price
determination in “dollar terms”.
The traditional narrative is that
supply and demand for a good
determines the equilibrium price
of that good as measured in
dollar terms.
• But what happens to the price of
the good if demand increases for
the unit of measurement (the
dollar)? Now we have a problem.
Why? Because the diagram
opposite assumes a constant
market value for money.
86
THE MARKET FOR GOOD A
IN DOLLAR TERMS
Price ($)
Supply
P(A)
Demand
Q(A)
Quantity
Gervaise R. J. Heddle, 2014
Marshall’s Assumption that
“Money Retains a Uniform Value”
• Alfred Marshall, developer of “scissors analysis” (the standard
representation of supply and demand that we use today), was
well aware of the problem and the assumption of constant
money value. In relation to the demand schedule, he states:
“So far we have taken no account of the difficulties of getting
exact lists of demand prices… A list of demand prices represents
the changes in the price at which a commodity can be sold
consequent on changes in the amount offered for sale, other things
being equal; yet other things seldom are equal… To begin with, the
purchasing power of money is continually changing, and
rendering necessary a correction of the results obtained on our
assumption that money retains a uniform value.” Marshall,
(1890), Chapter III.IV.17-19 (bold emphasis added).
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The Fixed Value of Money
• Benjamin Anderson (1917) highlights the problem with
traditional supply & demand analysis as follows:
“One point is to be added, making explicit what is implicit in the
modern theory of supply and demand. Supply and demand
doctrine assumes money, and a fixed value of money. That there
should be a given schedule of money-prices for varying quantities
of a good, is possible only if there be a given value of the moneyunit.”
• So, how do we illustrate price determination if the market value
of money is not constant (if the market value of money is not
“fixed”)? We need to illustrate supply and demand for both the
good and money separately by using an invariable unit of market
value, or “units of economic value”.
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Every Money Price is Determined by
Two Sets of Supply and Demand
Supply and demand for good A determines the market value of good A,
V(A). Supply and demand for money determines the market value of money,
V($). The “money price” of good A is equal to the ratio of the two market
values.
“GOOD A”
Market Value
(EV)
“MONEY”
Market Value
(EV)
S
V (A)
P(A$ ) =
V ($)
V(A)
Supply
V($)
Demand
D
Q(A)
Quantity
Q($)
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Quantity
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What Factors Might Cause the
Dollar Price of Good A to Rise?
• Let’s step back and think about this in simple terms. What are
the factors that might cause the price of good A, as measured in
dollar terms, to rise?
• All else equal, a rise in the market value of good A will cause the
price of good A, in dollar terms, to rise. A rise in the market
value of good A could be due to an increase in demand for good
A or a decrease in supply of good A. Either way, if V(A) rises
and V($) is constant, then the price of good A, P(A$ ) will rise.
• Alternatively, a fall in the market value of the dollar will cause
the price of good A, in dollar terms, to rise. One scenario is
illustrated on the next slide: a fall in the demand for money.
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A Fall in the Market Value of the Dollar
Causes the Price of Good A to Rise
The demand curve for money shifts to the left and the market value of
money, V($), falls. Both supply and demand schedules for good A, as
expressed in money terms, rise. The absolute market value of good A, V(A),
is unchanged, but the price of good A, in dollar terms, rises.
Market Value
Of Good (A) Stable
÷
EV
EV
=
Market Value
Of Dollar Falls
Dollar Price of
Good (A) Rises
S1
Price
S
S
V($)0
P(A$)1
S0
P(A$)0
D1
D0
V(A)
V($)1
D1
D
V(A)
÷
V($)
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D0
=
Price(A$)
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Why is the Market Value of Money not
“Front of Mind” in Negotiations?
• If the market value of money is so important, then why doesn’t it
seem to come up in many of our day-to-day negotiations? In the
case of a barter economy and an exchange of two goods (bananas
for apples) it is clear that the market value of both goods is
relevant to the ratio of exchange (the price of the trade) because
the market value of both goods tends to be quite volatile.
• But in a modern monetary economy, the market value of money
seems to be irrelevant when negotiating the dollar price of a good.
Why? Probably because it doesn’t change much: one dollar today
buys almost exactly the same as what one dollar bought yesterday
and what one dollar will buy tomorrow. In effect, the market
value of money is treated as a constant benchmark.
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Market Value of Money is
Negotiated in Every Trade
• It you watch negotiations between buyers and sellers of fish in
the market, then it may seem that the only thing that is being
negotiated is the market value of the fish. The market value of a
fish can fluctuate wildly based on the day’s catch.
• But ultimately, buyers and sellers are negotiating the market value
of two items: the value of the fish and the value of the money
that is being used to purchase them. A trade is successfully
concluded when the parties agree that the value of the fish is
equal to the value of the money being exchanged for the fish.
However, the negotiation over the value of money, in and of
itself, generally only becomes a real point of contention when the
value of money is fluctuating nearly as wildly as the value of fish.
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Foreign Exchange Markets &
The Market Value of Money
• While the “absolute market value of money” may seem to be a
somewhat abstract and obscure concept, there is one place where its
role is more easily understood: foreign exchange markets. A foreign
exchange rate is the price of one currency in terms of another. A
foreign exchange rate, like any price, is a ratio of two quantities
exchange: a certain number of units of one currency for a certain
number of another.
• How is this particular ratio of exchange determined? Once again, we
can invoke the rule that for an exchange to be successfully
conducted, the total market value of one basket exchanged must be
equal to the total market value of the other. Therefore, the ratio of
quantities exchange is the reciprocal of the ratio of the absolute
market value of the two currencies.
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Foreign Exchange Rate
Determination
• The principle of trade equivalence states that, in an efficient
market, the two baskets of goods being exchanged must be equal
in total market value. Therefore, if one currency (the Euro) is
exchanged for another (the US Dollar), then:
V(EUR)×Q(EUR) = V(USD)×Q(USD)
• Supply and demand for US Dollars determines the market value
of the US Dollar V(USD). Similarly, supply and demand for
Euros determines V(EUR). The USD/EUR exchange rate is then
equal to:
Q(USD) V(EUR)
P(EURUSD ) =
=
Q(EUR) V(USD)
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Determination of USD/EUR
Exchange Rate
The USD/EUR exchange rate (Dollars per Euro, or P(EURUSD) is
determined by the ratio {V(EUR)/V(USD)}. The market value of the each
currency is determined by supply and demand for that particular currency.
“EUROS”
“US DOLLARS”
EV per Euro
EV per USD
S
V (EUR)
P(EURUSD ) =
V(USD)
V(EUR)
S
V(USD)
D
D
Q(EUR) Money (Base)
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Q(USD)
Money
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A Fall in the Value of the USD…
Demand for US Dollars falls and the absolute market value of the USD,
V(USD), falls. There is no change in the absolute market value of the EUR.
What happens to the USD/EUR (Dollars per Euro) exchange rate?
“EUROS”
“US DOLLARS”
EV per Euro
EV per USD
S
S
V(USD)0
V(EUR)
V(USD)1
D
D1
D0
Quantity
Quantity
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…Leads to a Rise in the
Price of EURs (in USD Terms)
There is no change in the absolute market value of the EUR, but the relative
market value of EUR (the price of EUR in USD) rises as the value of the
USD falls and demand and supply for Euros, in USD terms, are rebased.
“EUROS (EV Terms)”
“EUROS (USD terms)”
EV per Euro
USD per Euro
S
S0 = S1
P(EUR)1
V(EUR)
P(EUR)0
D
D0
Q(EUR) Quantity
Q(EUR)
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D1
Quantity
Gervaise R. J. Heddle, 2014
The Matrix of Market Values
• In our example, we focus on the determination of one price,
P(EURUSD). The market value of the USD falls and the price of
Euros, in USD terms, rises. In practice, a fall in the absolute
market value of the USD will, all else equal, raise the price of all
currencies in terms of USD. This phenomenon can be observed
by watching a display of foreign exchange cross rates.
• In essence, the foreign exchange cross rates that we see are the
physical manifestation of a matrix of unobservable absolute
market values. Every currency has a market value: we can’t
observe the absolute market value of each currency (as measured
in units of economic value) but we an observe the relative market
value of each currency in terms of the others (the “cross rates”).
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Prices are the Observable Portion of
a Matrix of Market Values
This general principle extends to all prices: every price we see, whether it be
the barter price of a good, the money price of a good or a foreign exchange
rate, is the relative relation of two directly unobservable absolute market
values. Consider the simple example below with two goods and two
currencies. Absolute market values are in the dark shade. Prices, in the light
shade, are calculated as (EV top row)/(EV first column).
Good (EV)
Apple (5)
Banana (10)
USD (2.5)
EUR (5)
Apple (5)
1
2
0.5
1
Banana (10)
0.5
1
0.25
0.5
USD (2.5)
2
4
1
2
EUR (5)
1
2
0.5
1
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Explaining the Matrix
• On the previous slide, there is a matrix of market values.
Absolute market values (in the darker shade) are across the top
row and first column: these can not be directly observed. Relative
market values (in the lighter shade) can be directly observed as
“prices”.
• For example, the price of apples in USD terms is equal to $2 per
apple (5/2.5 = 2). The price of USD in banana terms (notice I
have flipped the unit of measurement) is equal to 0.25 bananas
per USD. The price of EUR in USD terms is 2 USD per Euro.
• Now, let’s change one input. If the absolute market value of USD
falls from 2.5 to 2, then what happens to the prices in the matrix?
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The Impact of a Fall in the Absolute
Market Value of US Dollars
If the market value of the USD falls (from 2.5EV to 2EV), then the
price of all goods in USD terms rises, as indicated by the row of green
numbers. For example, the price of apples in USD terms rises from $2
per apple to $2.5 per apple. Conversely, the price of USD in terms of all
other goods falls, as indicated by the column of red numbers.
Good (EV)
Apple (5)
Banana (10)
USD (2)
EUR (5)
Apple (5)
1
2
0.4
1
Banana (10)
0.5
1
0.2
0.5
USD (2)
2.5
5
1
2.5
EUR (5)
1
2
0.4
1
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The Relative Volatility of
Different Types of Prices
• In practice, price determination is not quite as simple as the matrix
on the previous slide suggests. For example, foreign exchange rates
are highly volatile on an intra-day and intra-month basis, whereas
the money price of of a good (for example, the dollar price of
bananas) is very stable on an intra-day basis and relatively stable on
an intra-month basis.
• This phenomenon suggests that there is some inertia built into
goods prices: for example, “menu costs” may discourage vendors
from regularly changing display prices. Nevertheless, just because
some prices (forex rates) exhibit more volatility than others (money
prices of goods), does not mean that they are not determined by the
same fundamental process. Ultimately, every price is a relative
expression of two market values.
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Review and Path Forward
• We have covered a lot of ground in a short space of time with
very little acknowledgement of the academic literature in this
area. The remainder of Part A of this paper is focused on
exploring some of the key concepts discussed in more detail and
providing a brief overview of some of the selected literature in
this area. In particular, we explore the concept of value, the
concept of price (the ratio of two quantities exchange) and a little
of the philosophy behind supply and demand analysis and how it
can be illustrated in absolute market value terms.
• If you are not interested in this level of detail, then you can skip
to Part B of this paper which begins to apply this theory to a
macroeconomic context.
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The Measurement of Value
Relative vs Absolute Market Value and a Review of the Attempts
by Ricardo and Anderson to Define and Explain the Concepts
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The Concept of Value &
The Measurement of Value
• The concept of “value” has a long history in economics. Today,
there two primary ways that economists think about the value of
a good: utility (or, in its relative form, preference relations) and
price. Utility is a measure of the non-market value of a good. In
contrast, price is a measure of the market value of a good.
• It is generally believed that price is the measure of market value:
in other words, “price” and “market value” are synonymous. But
this paradigm has a flaw: price is a relative expression of two
market values. Market value is a property possessed by a good.
We can measure that property on an absolute basis (in terms of
an invariable measure of market value) or on a relative basis (in
terms of the variable market value of another good).
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Market vs Non-Market Value
• Every economic good has two forms of value associated with it:
“market value”, a value determined by the interaction of buyers and
sellers of a good (market forces), and “non-market value”, a value
which depends entirely upon an individual’s “appetites”.
• For example, one person may love oysters (receives significant utility
from their consumption) while another person may hate oysters
(receives disutility from their consumption). The non-market value
of oysters differs greatly between those two individuals. In contrast,
the market value of oysters is determined by the sum of individual
demands for oysters coupled with the market supply of oysters.
There is a positive market value for oysters even though many
people don’t like them (their non-market value is zero or negative to
some people).
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Absolute vs Relative
Non-Market Value
• It is the contention of this paper that both of these forms of value
(non-market value and market value) can be thought of in both
absolute and relative terms.
• The first of these, non-market value, is already understood and
analyzed in both absolute and relative terms. Utility is a measure of
the absolute non-market value of a good. Over the years, the
concept of utility has become less fashionable in economics and
has been overtaken by “preference relations”. In modern economic
theory, utility is generally used as a way to summarize (or
represent) a consumer’s preferences between goods (Jehle, Reny,
2011). In essence, these “preference relations” are functions for
expressing the relative non-market value of goods (the relative
utility of goods).
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Absolute vs Relative
Market Value
• In contrast, market value is generally understood only in the
relative sense, as a “price”. This somewhat blinkered perspective is
understandable: price, the relative expression of two market
values, is the way we “experience” market value in day to day life.
But any property that can be compared on a relative basis must be
a property that both objects in question possess and must be
measurable, at least theoretically, on an absolute basis (in terms of
an invariable measure of that property).
• In this sense, every price can be considered to be a relative
expression of two absolute market values and every good can be
considered to possess the property of absolute market value
(market value measured in the absolute).
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Relative Expressions Imply
Absolute Properties
• In order to express a relative difference between two objects, both
of those objects must possess the property being compared. For
example, it makes no sense to ask “is the girl happier than the
tree?” Trees do not posses the property of “happiness” so it is not
possible to make the comparison. However, it is reasonable to ask
“is the girl taller than the tree?” Why? Because both the tree and
the girl possess the property of “tallness”.
• Moreover, we need an “invariable” or “constant” unit of
measurement (feet & inches) to determine the “tallness” of both
the girl and the tree (especially if the comparison is being made
across time or space). In this sense, both have an “absolute
tallness” that can be compared on a relative basis.
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Price Implies Goods Have the
Property of Absolute Market Value
• The determination of price is, by definition, the determination of
the ratio of two quantities exchanged (x dollars for y oranges). In
order to determine the ratio of two quantities exchanged, we must
answer the question “Is one unit of this good more valuable than
one unit of that good?”
• One good can only be more valuable than another if both goods
possess the property of market value. The relative market value of
the goods (the price) can not be determined unless both goods
possess the property of market value, a property that, at least
theoretically, can be measured in the absolute sense. Similarly, the
relative height of a girl and a tree can not be determined unless
both possess the property of tallness, a property that can be
measured in a absolute sense (in terms of feet and inches).
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Absolute Market Value
• In order to determine the relative market value of two goods (the
“price” of one good in terms of another), both goods must have
the property of “market value”. Furthermore, there must exist a
theoretical unit of measurement that is invariable and constant
that can be used to measure the absolute market value of each
good (“units of economic value”).
• In practice, it may be impossible to directly measure the market
value of a good in “units of economic value” terms but that
does not mean that from a theoretical perspective we can or
should ignore it. Why? Because understanding the
determination of absolute market value is the key to
understanding determination of relative market values.
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Challenges of Measuring
Value in the Absolute
• Measuring value is easy in a relative sense, but very difficult in an
absolute sense. It is impossible to measure the absolute level of nonmarket value (utility) that someone receives from the consumption
of a good, but it is relatively easy to measure a person’s preferences
between goods (an expression of the relative non-market value they
enjoy). While utility is difficult to measure, this does not mean it
doesn’t have an important role to play in economic theory.
• Similarly, it is easy to measure the relative market value of a good
(it’s price). The measurement of absolute market value of a good is
problematic, but that fact alone does not mean that the concept
should be ignored in any theoretical attempt to develop models of
price determination.
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A Brief History of
Absolute Market Value
• The notion that the relative value of a good (its “exchangeable
value” or “price”) can and should be distinguished from its
absolute value has a history that dates back to the beginning of
modern economics. The remainder of this section will focus on
two writers who have made concerted and articulate attempts to
highlight the difference between the two concepts: David
Ricardo (1823) and Benjamin Anderson (1917).
• While both writers provide an excellent exposition regarding the
relationship between relative and absolute market value, both
ultimately fail to develop plausible models for how absolute
market values are determined: Ricardo focuses on a labor theory
of value and Anderson on his own “social value theory”.
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Ricardo and Anderson on
Price and Absolute Value
• As will be discussed, both Ricardo and Anderson provide
excellent illustrations of how price (the ratio of exchange) is
determined by two values. Unfortunately, neither went the extra
step which was to state that each of these two values must be
determined by their own respective market forces (although
Anderson gets frustratingly close to this). It is the contention of
this paper that price is determined by two market values. The
market value of a good is determined by supply and demand for
that good. Therefore, every price is a function of the joint
equilibrium of two sets of supply and demand.
• Let’s begin our review of their work by going back to the
beginning of modern economics, Smith’s “Wealth of Nations”.
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Adam Smith &
The Definition of “Value”
• Possibly the most famous quote regarding the concept of value
comes from Adam Smith’s “Wealth of Nations” (1776), Chapter
IV, Of the Origin and Use of Money”.
“What are the rules which men naturally observe, in exchanging
[goods] for money, or for one another, I shall now proceed to
examine. These rules determine what may be called the relative or
exchangeable value of goods. The word VALUE, it is to be
observed, has two different meanings, and sometimes expresses
the utility of some particular object, and sometimes the power of
purchasing other goods which the possession of that object
conveys. The one may be called ‘value in use’: the other, ‘value in
exchange’.” (Smith, 1776), bold emphasis added.
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Smith’s Search for a “Real” or
“Universal” Measure of Value
• Smith’s “value in use” and “value in exchange” are generally
considered the forerunners to our modern day conceptions of
“utility” and “price” respectively. What is clear from the preceding
passage is that Smith explicitly recognizes that value in exchange is
a relative concept of value.
• Smith doesn’t explicitly discuss value in an absolute sense, but he
does ask the question “What is the real measure of this
exchangeable value?” and answers it “Labour therefore, is the real
measure of the exchangeable value of all commodities.” Smith was
trying to find an absolute measure of value (for both market and
non-market value), a measure that tied the value of commodities to
what many regarded at that time as the only “universal” (nonvariable) measure of value: the value of labor.
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Ricardo’s “Absolute Value”
• In the last few weeks of his life, David Ricardo (1823) completed a
rough draft of a paper called “Note on ‘Absolute Value and
Exchangeable Value’ which was a clear and concerted attempt to
define the notion of “absolute value” as something separate and
distinct from “value in exchange”. After Ricardo’s death, the paper
was sent to James Mill (one of Ricardo’s intellectual sparing
partners), but Mill, for reasons unknown, decided it was unsuitable
for publication (it wasn’t published until 1951).
• What makes Ricardo’s paper unique is his keen awareness that
value in exchange is a function of the absolute value of two goods.
His keen awareness of this fact is matched only by the fruitlessness
of his search for a commodity that can act as the standard of
absolute value.
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“Absolute” vs “Exchange” Value
• Ricardo (1823) attempted not only to make a clear distinction
between exchangeable value and absolute value but to explain
the relationship between them.
• First, here is Ricardo regarding exchangeable value:
“By exchangeable value is meant the power which a commodity has
of commanding any given quantity of another commodity, without
any reference whatever to its absolute value… Any commodity
having value will measure exchangeable value, for exchangeable
value and proportional value mean the same thing”. He continues:
“We should say that an ounce of gold had increased in exchangeable
value in relation to cloth if from usually commanding two yards of
cloth in the market, it could freely command or exchange for
three…”
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A “Perfect” Measure of Value
• Ricardo contrasts this with absolute value, or “a ‘perfect’ measure
of value”, which he described as follows:
“The only qualities necessary to make a measure of value a perfect
one are, that it should itself have value, and that value should itself
invariable, in the same manner as in a perfect measure of length
the measure should have length and that length should be neither
liable to be increased or diminished…”
“…if we had a perfect measure of value, itself being neither liable
to increase or diminish in value, we should by its means be able to
ascertain the real as well as the proportional variation in other
things and should never refer to the variations in the commodity
measured to the commodity itself by which it was measured”.
(Ricardo, 1823)
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Ricardo’s Examples of
Absolute vs Exchangeable Value
• Although Ricardo’s definitions of absolute and exchangeable
value are imprecise, it is clear from reading his countless
examples that he had a clear grasp of the distinction in practice.
• The following passage (an earlier draft published as a note to the
main text) provides the most succinct example:
“But although in the case just supposed we should know the
relative value of these commodities we should have no means
of knowing their absolute value. If an ounce of gold from
commanding 2 yards of cloth came to command 3 yards of
cloth it would alter in relative or exchangeable value to cloth
but we should be ignorant whether gold had risen in absolute
value or cloth had fallen in absolute value.” (Ricardo, 1823)
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The “Money Price” of a Good
Depends on the Value of Money
• Why are these observations regarding the price of cloth in gold
terms so interesting? Well, it must be remembered that gold, in
1823, was as close to “money” as any of the US Dollar bills that we
exchange today (Britain officially adopted the gold standard in 1816,
seven years prior to these writings).
• In essence, Ricardo is explicitly recognizing that the price of a good,
as expressed in money terms (at that time gold was synonymous
with money), could change due to either a change in the market
value of the good (as measured in absolute terms), or the market
value of money (as measured in absolute terms). Both cloth and
money possessed the property of “value” which could be measured
in absolute terms and changes in the absolute value of either
impacted the exchangeable value of cloth in money terms.
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Ricardo’s “Price is a Relative
Expression of Two Values” Theory
• In 1823, shortly before he died, Ricardo succinctly summarized
the theory that price (“exchangeable value”) is a relative
expression of the two values (two “absolute” values).
Furthermore, he applied this model to prices expressed in
money terms such that the money price of a good depends on
the absolute value of the good and the absolute value of money.
• Ricardo did not have the benefit of “marginalism” to link utility
to these concepts of market value and did not explicitly propose
that supply & demand determine the absolute market value (and
consequently relative market value) of goods and currencies. But
it is clear that he believed that absolute value plays a critical role
in determining relative value, or what we call “price”.
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The Fruitless Search for the
Embodiment of Absolute Value
• Ricardo, in common with many of his classical contemporaries, felt
compelled to try and link “absolute value” to the value of labor.
Rather than postulate that there exists only a theoretical measure of
absolute market value (an invariable unit of measure) and leave it
that, Ricardo (and others) believed that they might be able to find
this invariable unit of measure embodied in the nature of some
good (generally labor).
• Ultimately, the search for a particular commodity (whether it be a
good, a currency or a unit of labor) that can act as a perfect or
absolute measure of market value was a fruitless endeavor and so
the search was called off. But that should not have resulted in the
abandonment of the concept of “absoluteness” as a useful tool in
understanding price determination.
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“Absolute Value” Pushed Aside
• The Marginalist Revolution and the publication of Alfred Marshall’s
“Principles of Economics” (1890), in particular Marshall’s “scissor
analysis” (the now standard representation of supply and demand in
money terms), largely pushed the concept of “absolute value” into
the footnotes of economics.
• Despite the fact that Marshall explicitly recognized that his supply
and demand analysis was based on an “assumption that money
retains a uniform value”, the notion that price is a function of two
“absolute” market values was largely ignored. In particular, the
notion that money itself has the property of market value, as
determined by the supply and demand for money, almost completely
faded from view, due in no small part to Keynes’ liquidity preference
theory.
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Anderson’s “Economic Value”
• By the 20th century, even prominent monetarists had abandoned the
term “the value of money”, preferring instead “the purchasing
power of money”. Irving Fisher (1911), in his paper “The
Purchasing Power of Money”, seems to almost purposefully avoid
the term “value of money”. It was one of the contemporary critics
of Fisher’s “mechanical quantity theory of money”, Benjamin
Anderson, who, in his aptly titled “The Value of Money” (1917),
first used the label “Economic Value” in the context of the
“absolute value” of economic goods.
• Anderson defines “Economic Value” as the common quality of
“wealth” (broadly defined): a property that is both a quality and a
quantity. Just as “length” is a quality and a quantity, so value is a
quality and a measure of that quality.
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Anderson’s “Price as a Ratio of
Two Absolute Values”
• Anderson’s description of the relationship between the absolute
value of a good and the exchangeable value of a good (its price)
is similar, but arguably more precise, than that of Ricardo.
• Anderson (1917) describes the relationship between the ratio of
exchange (price) and value as follows: “The ratio of exchange
presupposes two values… The ratio of exchange is a relation, a
reciprocal relation. It works both ways. But behind this relativity,
this scheme of relation between values, there lie two values
which are absolute… Values lie behind ratios of exchange, and
causally determine them… A price is merely one particular kind
of ratio of exchange, namely, a ratio of exchange in which one of
the terms is the value of the money unit.” (pp. 6-7)
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Anderson Falls at the Last Hurdle
• While Ricardo (1823) wrote his note before the popularization
of “supply and demand”, Anderson (1917) had the benefit of
coming after Marshall’s “scissor analysis” which allowed
Anderson to make the observation that “supply and demand
doctrine assumes money, and a fixed value of money”.
• Unfortunately, Anderson developed his own heterodox solution
for the determination of absolute value: “social value theory”.
Somewhat frustratingly, Anderson recognizes that value rests
“not in the minds of individuals thought separately” (pp. 41),
but then doesn’t take the “simple” step of recognizing that
absolute market value is determined by “market forces”, or the
interaction of individuals as expressed by supply and demand.
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Section Review
• In summary, a handful of economists have recognized a clear
relationship between the relative and absolute value of a good.
Unfortunately, those writers have not explicitly recognized the
notion of “absolute market value”: the market value of a good (a
value determined by supply and demand) as expressed in terms
of an invariable unit of measurement.
• Price is an expression of the relative market value of two goods.
In order for such a relative expression to occur, both goods must
have market value and, at least theoretically, the market value of
each good can be measured in “absolute terms”, that is to say, in
terms of an invariable or constant unit of market value which this
paper has denoted as “units of economic value”.
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“Real Price” of a Good is Not an
“Absolute” Measure of Market Value
• Before we conclude this section of the paper, we need to discuss
one more important point which becomes more relevant as we
move into the macroeconomic discussion of price level
determination. There seems to be an underlying sense amongst
many economists that somehow the “real price” of a good is an
“absolute” measure of the market value of that good. This is
simply not the case.
• The “real price” of a good is, by definition, a relative price (the
price of a good relative to the price of the basket of goods) and is,
itself, a price (the price of a good in basket of good terms).
Therefore, the “real price” of a good is a price and, consequently,
a relative expression of two market values.
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The Market Value of the
“Basket of Goods” is Variable
• The easiest way to think about this somewhat abstract point is to
remember that the market value of the “basket of goods” is itself
variable. The “real price” of a good measures the market value of
the good in terms of the market value of the “basket of goods”.
If the market value of the “basket of goods” was invariable, then
the “real price” could indeed be considered to be an “absolute”
measure of the market value of a good. But this is not the case.
• Part B of this paper will discuss this issue in more detail. In
particular, we will discuss the math behind the concept of “real
prices” and it will argued that the “real price” of a good is the
same as the “real market value” of a good (the market value of a
good in terms of the market value of the basket).
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The Ratio of Exchange
Price Determination: The Ratio of Two Quantities Exchanged is the
Reciprocal of the Ratio of Two Market Values
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Price as a Ratio of Exchange
• The study of price determination could be more accurately called
“The Study of the Determination of the Ratio of Exchange”.
Clearly, the second title is more awkward, but arguably it conveys
an important point: price is a ratio. The label “price
determination” suggests a study in the determination of the
market value of just one good: but price determination is a study
in the relative market value of two goods.
• By convention, price is expressed as a ratio of two quantities: the
quantity of one item exchanged for the quantity of another item.
It will be argued that this ratio is the reciprocal of the ratio of the
absolute market value of the two items. It is this ratio of absolute
market values that determines the ratio of quantities exchanged.
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The Concept of “Price”
• Most of us feel that we are so familiar with the concept of
“price” that we don’t need to define it. Most introductory
microeconomics textbooks don’t’ define “price” and, perhaps
quite reasonably, don’t discuss the concept of price in terms other
than those with which we are most familiar: “money prices” or
the dollar price of a good.
• A common definition of “price” might be “the amount of money
expected, required, or given in payment for something”. But this
is a very narrow interpretation of the concept. Wikipedia
provides a comment on price in more general terms: “Economists
sometimes define price more generally as the ratio of the
quantities of goods that are exchanged for each other.”
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Price as the Ratio of
Two Quantities Exchanged
• Irving Fisher (1911) describes “price” as follows: “When a certain
quantity of one kind of wealth is exchanged for a certain quantity
of another, we may divide one of the two quantities by the other,
and obtain the price of the latter”.
• In mathematical terms, the price of good A, expressed in terms of
good B, or P(AB ), is equal to the quantity of good B exchanged,
Q(B), divided by the quantity of good A exchanged, Q(A).
Q(B)
P(AB ) =
Q(A)
• As Fisher states, we divide the quantity of one good, Q(B), by the
quantity of another, Q(A), to obtain the price of the latter, the price
of A in B terms or P(AB ).
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The Dollar Price of a Good as a
Ratio of Two Quantities Exchanged
• In a barter economy, price is a ratio of two quantities exchanged. If
two apples are exchanged for one banana, then the price of bananas
in apple terms equals the quantity of apples exchanged divided by
the quantity of bananas exchanged (the price of bananas is “2
apples”).
• In a modern economy, prices are typically expressed in dollar terms.
The “dollar price” of a good describes the number of dollars that are
required to purchase a definite quantity of a good. The price of a
good A in dollar terms, P(A$ ), is the ratio of the quantity of dollars
exchanged, Q($), for a quantity of good A exchanged, Q(A).
Q($)
P(A$ ) =
Q(A)
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The Nature of Trade
• In order to understand price determination, we need to think about
the fundamental nature of trade. Jevons (1875) states:
“In every act of exchange, a definite quantity of one substance is
exchanged for a definite quantity of another. Every act of exchange
thus presents itself to us in the form of a ratio between two numbers.”
• This statement really tells us little more than we have already
discussed. Every trade involves an exchange of two definite
quantities and the price of the trade is the ratio of these two
quantities. The real question that needs to be answered is how are
those relative quantities determined. While mainstream economics
might jump straight to “supply and demand” analysis at this point,
there is another more fundamental aspect of trade that needs to be
discussed: trade is an exchange of equivalents.
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Henry Thornton: the Nature of
Trade and the Role of Money
• One of the earlier observations regarding the nature of trade and
money’s role in that process comes to us from Henry Thornton:
“Society, in its rudest state, carries on its trade by the means only
of barter. When most advanced, it still conducts it commerce on
the same principle; for gold and silver coin, banker’s notes, and
bills of exchange, may be considered merely as instruments
employed for the purpose of facilitating barter. The object is to
exchange such a quantity of one sort of goods for such a quantity
of another as may be deemed, under the circumstances, a suitable
equivalent.” (Thornton, 1802, Chapter II).
• Thornton’s observation captures two key ideas that we will discuss
in more detail. Firstly, trade is based on the exchange of “suitable
equivalents”. Secondly, money merely acts as an instrument to
facilitate this exchange of suitable equivalents.
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Trade and the Exchange of
“Suitable Equivalents”
• Thornton states that the object of commerce is to exchange such
a quantity of one sort of goods for such a quantity of another as
may be deemed, under the circumstances, a “suitable
equivalent”. It is this notion of “equivalence” that holds the key
to a simple, but fundamental, principle of trade.
• In a free and efficient market and in the context of a commercial
transaction (not a gift), an exchange of goods between two parties
will occur when the total market value of each of the parcels or
baskets of goods being exchanged are equivalent. If this is not the
case, then one party is “losing out” and, in an efficient market
with zero transaction costs, an arbitrage opportunity exists which
will soon be exploited and closed.
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The Principle of Trade Equivalence
Expressed in Money Terms
• Thornton states that his principle describes commerce in both a
barter and an advanced (money-based) economy. In the case of a
money-based economy, it is easy to describe and understand the
principle of trade equivalence. In the ordinary course of trade in
an efficient market (and assuming no money changes hands),
parties will only exchange baskets of goods on the basis that
those baskets have an equivalent total dollar value.
• If one party is selling a quantity of good A, Q(A), with a price
P(A) and another party is selling a quantity of good B, Q(B), with
a price P(B), then an exchange of those goods will only occur, in
an efficient market when:
P(A)×Q(A) = P(B)×Q(B)
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Removing Money From
Both Sides of the Equation
• Although the equation on the previous slide is stated in money
terms, we can argue that money itself is irrelevant to the
principle. Why? Because both sides of the equation are expressed
in money terms. Money is being used on both sides of the
equation as merely a measure of “something else”: that
something else is “market value”. More specifically, money is
being used to measure the market value of good A and the
market value of good B. Rather than measuring market value of
each good in dollar terms, we can measure the market value of
each good in terms of a universal and invariable unit of market
value. In effect, we can eliminate money from both side of the
equation:
V(A)×Q(A) = V(B)×Q(B)
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Principle of Trade Equivalence
Applied to a Barter Economy
• This idea is easier to understand in the context of a barter
economy. Let’s examine how the principle of trade equivalence
applies in a barter economy (an economy where there is no
money to act as “unit of account”).
• Assume you live in a barter economy with many producers of
apples and bananas. You are a banana producer. If the current
ratio of exchange of apples for banana is two apples for one
banana, then would you, as a seller of bananas, accept only one
apple for one banana? No. You would demand two apples. But
why? Perhaps you may say: “Selling a banana for only one apple
is selling it for less than it is worth. The market value of an
banana is twice that of an apple.”
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If One is “Twice as Valuable” as Another,
Then Both Items Must Have Value
• There are two things to note about the statement on the previous
slide. Firstly, the claim that a banana is worth twice that of an
apple is based on “objective” market evidence (the current ratio
of exchange in the market). The market value of a banana, by
any objective measure, is twice that of an apple at that time.
• Secondly, the very language itself suggests a concept of an
absolute market value, possessed to varying degrees by each of the
goods, that can be compared on a relative basis. For one good to
be twice as valuable as another, then both goods must have a
certain quantity of value associated with them in the first place.
By way of analogy, you can’t say one thing is “twice as long” as
another thing without both items having the property of length.
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Total Market Value of Baskets
Exchanged Must Be Equal
• As a rational economic agent and producer of bananas, you want
to ensure that the total market value of the basket of apples you
receive, the market value of each apple V(A) multiplied by the
number of apples in the basket Q(A), is equal to (or greater than)
the total market value of the basket of bananas that you sell. In
mathematical terms, we can say:
V(A)×Q(A) = V(B)×Q(B)
• In the case of a barter economy, there is no money to measure
the market value of each good. However, we can still measure
the market value of each good in terms of a theoretical and
invariable measure of market value (“units of economic value”).
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Ratio of Quantities is the Reciprocal
of the Ratio of Market Values
• We can rearrange the equation of the previous slide to state:
V (A) Q(B)
=
V (B) Q(A)
• In simple terms, all this equation implies is that if bananas are
twice as valuable as apples, then for every banana you give up,
you would expect twice as many apples in exchange.
Furthermore, we know that the price of good A in terms of good
B is, by definition, equal to the second term in the equation
above. Therefore, the price of apples in banana terms is given by:
Q(B) V(A)
P(AB ) =
=
Q(A) V (B)
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Extending the Principle to a
Money-Based Economy
• The second key point to note regarding Thornton’s statement is
that the basic principle of trade does not change in an advanced
society. “When most advanced, it still conducts commerce on
the same principle” (Thornton, 1802). Money is merely an
instrument employed for the purposes of facilitating barter. In a
money-based economy, the same economic principles apply but
now there is a currency inserted in the middle of the trade.
• The equivalence of total market value exchanged does not
change because the exchange is conducted using money. The use
of money to conduct the transaction does not change the
fundamental mathematics of the trade. Money simply acts as a
medium of exchange in the back and forth of commerce.
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Money as Intermediary in the
Barter Exchange
• If money is an intermediary that facilitates barter, then money
itself must conform to the principle of trade equivalence. Let’s
take our previous barter trade and break it into two steps: money
for a basket of good A and then money for a basket of good B.
V(A)×Q(A) = V($)×Q($) = V(B)×Q(B)
• If money is capable of being an instrument for facilitating the
barter exchange of good A for good B, then it must be true that (i)
money itself has market value, and (ii) the total market value of
the basket of money exchanged “{V($)Q($)}” is equal to the total
market value of basket A which is also equal to the total market
value of basket B.
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Anderson’s “Quid Pro Quo”
• Benjamin Anderson neatly summarizes the general principle of
trade equivalence and uses this to illustrate why money must
have (market) value in order to act as the medium of exchange.
“There can be no exchange, in the economic sense… without a
quid pro quo, without value balancing value, at least roughly, in the
process. Now when it is remembered that the intervention of the
medium of exchange, taking the place of barter, really breaks up a
single exchange under the barter system into two or more
independent exchanges, and that the medium of exchange is
actually received in exchange for valuable commodities, it follows
clearly that the medium of exchange must either have value itself,
or else represent that which has value.” (Anderson, p.133)
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The Money Price of a Good as
A Ratio of Two Market Values
• Let’s return to our example. Using money, we can break up our
barter trade into two transactions. The first transaction is a money
for apples trade. The second transaction is a money for bananas
trade. In each case, we can calculate the ratio of quantities
exchanged, the price of the trade, using the principle of equivalence.
• In the first trade (apples for money), the total market value of the
basket of apples and the basket of money must be equal. Therefore:
V(A)×Q(A) = V($)×Q($)
• This can be rearranged to calculate the price of apples in money
terms:
Q($) V (A)
P(A$ ) =
Q(A)
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V ($)
Gervaise R. J. Heddle, 2014
Price of Bananas as a Ratio of
Two Absolute Market Values
• Similarly, the ratio of quantities exchanged in the second trade can
be determined by:
V(B)×Q(B) = V($)×Q($)
• Therefore, the price of bananas in terms of money is equal to:
Q($) V(B)
P(B$ ) =
=
Q(B) V($)
• In both cases, the price of the good in money terms is determined
by the relative relation between the market value of the good and
the market value of money. Why? Because, in an efficient market,
people will only buy/sell a basket of goods for money if they
give/receive a basket of money with equivalent total market value.
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Price is a Relative Expression
of Two (Absolute) Market Values
• In summary, every trade can be reduced to the exchange of two
items, one item for another. Both of these tradable items possess
“market value”, in the ordinary sense of that term, or there
would be no reason to trade the items.
• In order for an exchange to occur, both parties to the trade must
agree on the relative market value of the goods. Implicitly, both
items must have some type of absolute market value for it to be
compared on a relative basis. This relative market value
determines the ratio of quantities to be exchanged, or “the price”
of the trade. This principle holds true if one of those goods is
money. The dollar price of a good is determined by the market
value of the good relative to the market value of money.
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How is (Absolute) Market Value
Determined?
• The key question that remains to be answered is how is the
market value of a good determined? In particular, how is the
absolute market value of a good, the market value of a good as
measured in terms of an invariable measure of market value,
determined? Fortunately, there is a well established paradigm that
can answer this question: “supply and demand”.
• While most student of economics are only familiar with supply
and demand as a framework that is expressed in dollar price
terms, the role of money in constructing models of supply and
demand is merely as a “unit of account”. This role as “unit of
account” can be performed by any good with market value,
including a theoretical good with invariable market value.
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Caveat Regarding Next Section
• Before we begin the final section of Part A, I want to make one
important observation. The macroeconomic theory of price level
determination that is developed in Part B of this paper and the
final paper in the series, The Velocity Enigma, does not actually
require the analysis contained in the next section. In particular,
all that matters to our macroeconomic theory is that all goods
(including money) have market value, that this market value can
be measured on an absolute basis and that every price is a ratio of
two (absolute) market values.
• Nevertheless, while the illustration of supply and demand for an
individual good in absolute terms may be of little relevance to the
theory of inflation, it is an important concept in and of itself.
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Supply and Demand:
An Alternative Representation
Using the Theoretical and Invariable Measure of Market Value
(Units of Economic Value) as the y-axis Measure of Market Value
in Supply and Demand Analysis
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Traditional Supply & Demand
Analysis: A One-Sided View
• The traditional representation of supply and demand presents a very
one-sided, but nevertheless useful view of the price determination
process. In essence, it allows us to analyze how a change in supply
and demand for a good (which we can call the “primary good”)
impacts the price of that primary good as expressed in terms of a
second good (the “measurement good”).
• This traditional representation is useful for many microeconomic
applications, but it has one fundamental drawback: price is a ratio
of two market values. In order for traditional supply and demand
analysis to be meaningful, it must assume that the market value of
the measurement good is constant. While this may be fine for most
applications, it will always be a “second best” model for illustrating
price determination.
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The Traditional View
• The diagram opposite provides a
useful framework to discuss how the
price of good A will respond to
changes in either demand and/or
Supply
supply for good A.
MARKET FOR GOOD A
Price ($)
P(A)
Q(A)
• The problem with this view is that
both supply and demand schedules
implicitly assume the market value
of money is constant. For example,
imagine the market value of the
Demand
dollar collapses. Will firms still
supply the same amount of the
Quantity
good at the same dollar price? No.
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An Alternative Representation of
Supply & Demand
The better way to represent the determination of the price of good A is to
break the analysis into its two components. Supply & demand for good A
determines the market value of good A. Supply & demand for money
determines the market value of money. The price is a ratio of the two.
Market Value
(EV)
“GOOD A”
Market Value
(EV)
S
V (A)
P(A$ ) =
V ($)
V(A)
“MONEY”
Supply
V($)
Demand
D
Q(A)
Quantity
Q($)
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Quantity
Gervaise R. J. Heddle, 2014
Supply & Demand Diagrams and
the Representation of Market Value
• We are so accustomed to the illustration of supply and demand
schedules for a good in terms of “dollar prices” that we forget
that this is only one of many possible representations of the
supply and demand schedules for a good.
• By convention, the y-axis in a supply and demand diagram
measures the “market value” of a good in terms of money.
However, we can express the market value of the good in terms
of any other good. For example, we could express the market
value of a banana in terms of dollars, apples, toasters, diamonds
or any other good. All of these items have one thing in common
which make them interchangeable in the analysis: they are items
that possess the property of market value.
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The Philosophy of
Supply & Demand
• In order to understand this point, it helps to think about the
philosophy behind “supply and demand”. At its heart, the concept
of supply and demand is not about the exchange of green paper
notes (dollars) for goods. Supply and demand, and all trade in
general, is about the exchange of a quantity of one thing of value
for a quantity of another thing of value.
• It is important to note that this must be the case, otherwise supply
and demand could not be used to analyze the determination of
prices in a barter economy with no money. If the “unit of account”
must be money, then the principle of supply and demand can not
apply to a barter economy. Clearly, this is wrong. The unit of
account used on the y-axis can be any good we choose, provided it
has the property of market value.
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The Demand Schedule
• Let’s consider the demand schedule. The demand schedule
represents a simple trade off. Economic agents have limited
resources, but unlimited wants. How much of any particular
good we will purchase will depend on the total market value of
other items that we have to give up to get it. If we have to give up
a large quantity of an item of value (be it dollars, oranges or
other) to purchase one apple, then the total quantity of apples
that we will demand will be less than if we have to give up a
much smaller quantity of that same item.
• The point is that we can plot the demand schedule for a good in
terms of any other good, provided that the other good (the
measurement good) has the property of market value.
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The Supply Schedule
• Similarly, we can apply the same general principle to the supply
function. It is a less intuitive proposition in this case because most of
us think of a firm’s supply curve as being derived from a series of
input costs all expressed in dollar terms. But again, the supply
function represents a relationship between one thing of value and
another thing of value.
• In particular, the supply function represents the willingness of a
producer to supply one thing of value in exchange for varying
amounts of another thing of value. If the purchaser offers a greater
quantity of this other thing of value per unit of good the producer
supplies, the producer will be prepared to supply more of it. The
producer can then trade this other thing of value for a range of other
goods which he/she will consume.
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Supply & Demand Maps Responses
to the Change in Market Value
• In summary, supply and demand schedules try to capture the
way economic agents will react when the market value of one of
the goods being exchanged, the primary good, changes. As a
general rule, as the market value of the primary good rises, the
quantity demanded falls and the quantity supplied rises. An
equilibrium occurs when the market value reaches a level where
the quantity demanded and the quantity supplied are equal.
• The challenge in constructing this supply and demand analysis is
that the market value of the primary good needs to be measured.
It is the choice of this “benchmark”, the measure of the market
value of the primary good, that is the main concern of this
paper.
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Choosing the Benchmark of
Market Value
• In choosing a benchmark for the measurement of the market value
of the primary good, the only criteria that must be met is that the
benchmark itself has the property of market value. If the benchmark
does not have the property of market value, then it can not measure
the market value of the primary good.
• Inevitably, economics has selected a “real life” good to act as the
benchmark of value. In particular, it has selected the rather
enigmatic good that we know as “money” to act as the benchmark.
However, not only could we choose any good to act as the
benchmark, we can also choose a “theoretical good” to act as the
benchmark. This is an attractive proposition because we can assign
that theoretical good with a unique property that other “real life”
goods do not possess: invariable market value.
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The Problem with Using “Real Life”
Goods as the Measurement Good
• The problem with using any “real life” good as the measurement
good on the y-axis of supply and demand analysis is that the
market value of all “real life” goods is variable. We can use the
analogy of length: would the concept of “feet and inches” be of
any use if the length defined by “feet” and/or “inches” was itself
variable? If this was the case, then you might be 5ft6 one week
and 8ft3 the next!
• In practice, this problem is “assumed away”. In order to make
supply and demand analysis as presented in “price terms”
meaningful, it is (at least implicitly) assumed that the market
value of the measurement good is constant (at least for the period
under analysis) for each supply/demand schedule represented.
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Market Value of the Measurement
Good is Assumed to be Constant
• It is the view of this paper that every supply and demand
schedule which describes a relationship between “price” on the
y-axis and “quantity” on the x-axis assumes, at least implicitly,
that the market value of the measurement good is constant. In
other words, any change in the market value of the measurement
good will shift both the supply and demand schedules as
expressed in “price/quantity” terms.
• The best way to illustrate this is to consider a three good barter
economy with no money. Imagine you are a supplier of bananas.
As payment for bananas, you will accept either apples (a low
value good) or mangoes (a high value good). Let’s start by
describing your supply curve for bananas in apple terms.
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The Supply Curve for Bananas
as Expressed in Apple Terms
SUPPLY CURVE
FOR BANANAS
Price
(in apples)
8
6
4
10
20
• The diagram opposite represent
your individual supply curve for
bananas (you grow bananas) in
apple terms. At a price of 4 apples
Supply
per banana you will supply 10
bananas. At a price of 6 apples, you
will supply 20 bananas. Etc.
• Now, if mangoes (a more exotic and
rare fruit) are twice as valuable as
apples (their “market value” is twice
that of apples), then what would
your supply curve look like
30 Quantity
expressed in mango terms?
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The Supply Curve for Bananas
as Expressed in Mango Terms
SUPPLY CURVE
FOR BANANAS
Price
(in mangoes)
4
3
2
10
20
• If mangos are twice as valuable as
apples, then how does your banana
supply schedule change if we plot it
in mango terms? Will you only
Supply
supply 10 bananas if the price of
bananas is 4 mangoes? No. Why?
Because 4 mangoes is equivalent to
8 apples. At a price of 8 apples (4
mangoes) you will supply 30
bananas.
• Your supply schedule is “rebased”
to reflect the higher value of the
30 Quantity
measurement good (mangoes).
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Combining the Two Supply
Curves on the Same Diagram
SUPPLY CURVE
FOR BANANAS
Price
(in fruit terms)
8
6
4
2
10
20
• We can combine the two supply
curves on the same diagram by
expressing the y-axis as a “quantity
Supply
of fruit per banana”. What is the
(in apples)
difference between these two supply
schedules? Nothing really: the only
difference is the unit of
Supply
(in mangoes) measurement.
• What happens if the market value
of apples doubles? (A shortage of
apples occurs). Apples are now as
valuable as mangoes and the banana
30 Quantity
supply curves should be identical.
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Supply Curve Rebases as Market Value of
Measurement Good Doubles
SUPPLY CURVE
FOR BANANAS
Price
(in apples)
Supply0
8
6
• If the market value of apples
doubles (apples become as valuable
as mangoes), then, all else equal,
your supply schedule for bananas as
expressed in apple terms will shift to
the right (shift down).
• The only difference between the two
supply curves opposite is that they
assume a different market value for
the measurement unit (apples). As
apples become more valuable, your
are prepared to supply more
30 Quantity
bananas at each price point.
Supply1
4
2
10
20
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Supply & Demand Schedules in
Dollar Terms
• The same principle applies to a supply and/or demand schedule
which is plotted with “dollar price” on the y-axis. The principle is
slightly less intuitive because, in our day to day life, many of us
treat a dollar as if it is an invariable measure of market value.
The fact is that it is not. The market value of a dollar may be less
volatile than the market value of most other goods, but its market
value does change significantly over extended periods of time.
• As the market value of a dollar falls, then, all else equal, the
supply curve for any good, as expressed in dollar terms, will shift
to the left (shift up) and the demand curve for that good will shift
to the right (shift up). In effect, both supply and demand curves
are rebased as the market value of the dollar falls.
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Supply and Demand: Response to a
Fall in Market Value of Dollar
• As the market value of the unit
of measurement falls (the value
of money falls), both supply and
demand schedules (as expressed
in money terms) are rebased.
• In very simple terms, as dollars
become less valuable (the market
value of the dollar falls), people
are more willing to part with
them and less willing to accept
them in exchange for some other
good of given market value.
171
THE MARKET FOR GOOD A
IN DOLLAR TERMS
Price ($)
S1
P1
S0
P0
D1
D0
Q(A)
Quantity
Gervaise R. J. Heddle, 2014
The Achilles Heel of Traditional
Supply and Demand Analysis
• As discussed, we can express the market value of any good in terms
of any other good (provided both goods have the property of
“market value”). The problem with expressing market value in this
way (relative market value) is that if the unit of measurement (itself
a good) fluctuates in market value, then we need to keep rebasing the
supply and demand schedules.
• There is an alternative: express supply and demand for a good and
the equilibrium market value of that good in terms of a constant unit
of measurement, units of economic value. We can use this invariable
unit of measurement to isolate whether changes that occur in the
price of a good are a result of a change in market dynamics for the
good itself or a change in the market dynamics for the unit of
measurement.
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Transforming Supply & Demand into
“Units of Economic Value” Terms
• Transforming a supply and demand chart from “dollar terms” into
“units of economic value” terms is a simple process. None of the
important information that is contained in the original supply and
demand schedules is lost in the process.
• More importantly, none of the fundamental tenets of
microeconomics are breached. It would almost be impossible for
this to occur because we are simply replacing one unit of account
(dollars) for another unit of account (units of economic value).
Removing “money” should have no impact on the analysis as
standard microeconomic models assume economic agents do not
suffer from “money illusion”. In the words of Jehle and Reny, “the
only role that money has played in constructing our model is as a
unit of account” (Jehle, Reny, 2011, p. 49).
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The Standard Supply & Demand
Diagram
PRICE OF GOOD (A)
Price ($)
P(A)
Q(A)
• Let’s start with a traditional
supply and demand diagram with
price, in dollar terms, on the yaxis.
Supply
• The supply and demand
functions both assume a constant
absolute market value for the
dollar. (If they didn’t, then that
would imply that people suffer
Demand
from “money illusion”). The first
step in the transformation is to
Quantity
re-label the y-axis (see next slide).
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Transforming Supply & Demand:
Re-label the Y-axis
• From our earlier discussion, we
know that:
PRICE OF GOOD (A)
Q($) V (A)
P(A$ ) =
=
Q(A) V ($)
Ratio of Market Values
Supply
V(A)/
V($)
Q(A)
• Therefore, we can re-label the yaxis as a ratio of absolute market
values. Furthermore, since it is
assumed that V($) is constant,
the relationships that are being
Demand
plotted are really between V(A)
and Q(A). Hence, we can remove
Quantity
V($) from the analysis.
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Supply & Demand:
The General-Form Representation
• Supply and demand schedules
MARKET VALUE OF GOOD (A)
describe a relationship between two
variables, V(A) and Q(A). The
Market Value (EV)
market value of money, V($), is
Supply
incidental to the analysis: we
remove the constant V($) by
multiplying all y-axis values on the
previous slide by V($).
V(A)
Q(A)
• What we are left with is the
“general-form” representation of
supply and demand analysis. Both
Demand
schedules are expressed in terms of
an invariable measure of market
Quantity
value (units of economic value).
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Modification to Assumptions
• The general-form representation of supply and demand captures
all the basic principles of traditional supply and demand analysis,
except that in this case market value is measured in terms of a
theoretical and invariable measure of market value.
• The general-form model allows us to “loosen up” one of the
assumptions made by traditional supply and demand analysis. In
particular, we don’t need to assume the market value of money is
constant. The implication of this is that we don’t need to assume
constant money income or constant money prices of related
goods & input goods. However, the general-form model does
assume constant market value of income (income in EV terms)
and constant market value of related/input goods (in EV terms).
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The Benefit of the General-Form
Representation of Supply & Demand
The general-form representation of supply and demand allows us to isolate
and illustrate changes in the price of a good that are due to a change in the
market value of the good itself as compared with changes in price that are
due to a change in the market value of the measurement good.
Market Value
(EV)
Market Value
(EV)
“GOOD A”
“GOOD B”
S
S
V (A)
P(AB ) =
V (B)
V(A)
V(B)
D
D
Q(A)
Quantity
Q(B)
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Gervaise R. J. Heddle, 2014
Supply & Demand:
The Special-Form Representation
PRICE OF GOOD (A)
IN TERMS OF GOOD (B)
Price (in B terms)
Supply
V(A)/
V(B)
• We can transform the general-form
representation of supply and
demand (supply & demand in EV
terms) back into any “specialform” representation of supply
and demand where market value is
measured in relative terms (say
relative to the market value of
good B).
• We do this by assuming a constant
market value for the measurement
good (good B) and dividing all yQuantity
axis values by V(B).
Demand
Q(A)
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Supply & Demand
in Dollar Terms
PRICE OF GOOD (A)
IN TERMS OF GOOD ($)
• The most common special-form
representation of supply and
demand is the market value of a
good measured in terms of the
Supply
market value of money.
Price (in $ terms)
V(A)/
V($)
Q(A)
• We transform the general-form by
assuming a constant market value
for the dollar, V($). Then, all y-axis
values in the general-form schedules
are divided by this constant value.
Demand
As a result, the y-axis is expressed in
terms of V(A)/V($), or the “dollar
Quantity
price of good A”.
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Section Review
• In summary, trade is an exchange of two goods (one for another)
and every price is a relative expression of two market values. There
is nothing wrong with analyzing how changes in supply and
demand for only one of the goods will impact the price of the
transaction, nor with expressing this analysis in terms of relative
market value by assuming that the market value of the second good
constant.
• However, a comprehensive model of price determination should
recognize that the price of the trade (the ratio of quantities
exchanged) depends on supply and demand for both of the goods
being exchanged. In order to analyze these market forces
individually, we need to use a theoretical, universal and invariable
measure of market value (“units of economic value”).
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Part B:
Macroeconomic
Price Determination
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Ratio Theory of the Price Level
The Price Level as a Ratio of Two Market Values: the General
Value Level and the Market Value of Money
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Microeconomic Theory is
Not a Theory of Inflation
• At the outset, it is important to note that the microeconomic
theory of price determination from Part A is not a theory of
inflation. While the theory does represent the core
microeconomic foundation for the macroeconomic models
developed in The Enigma Series, it requires significant adaptation
and thought to translate any simple microeconomic theory of
price determination into a macroeconomic theory of inflation.
• The first step in that process is to extend the microeconomic
relationship described by the theory into a useful macroeconomic
relationship. In particular, we will attempt to demonstrate that
the price level is a function of two absolute market values: the
general value level and the market value of money.
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Extending Microeconomic Theory
to the Price Level
• In Part A of this paper, we established that the dollar price of an
individual good, P(A$ ), is a function of two market values:
V (A)
P(A$ ) =
V ($)
• In Part B, we will extend this principle to the general price level. In
particular, it will be argued that the general price level can be
expressed as:
Where
VG
p=
VM
p is the general price level of the economy
VG is the “general value level” of the economy
VM is the absolute market value of money
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The Ratio Theory of the Price Level
• The Ratio Theory of the Price Level states that the general price
level p can be expressed as a ratio of two market values:
VG
p=
VM
where
p is the general price level of the economy
VG is the “general value level” of the economy
VM is the absolute market value of money
• The general value level VG is a hypothetical measure of overall
market values (as measured in “units of economic value”) for the
set of goods and services that comprise the “basket of goods”.
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Cheat’s Method:
Price Level as an Index
• Conceptually, the easiest way to understand the relationship
between the three variables (p, VG and VM ) is to think of each of the
variables as an index. In particular, readers can consider the price
level p to be an output weighted average of the individual prices
(relative market values) of a basket of goods. In a similar vein, the
general value level VG can be considered to be an output weighted
average of the individual absolute market values of a basket of
goods.
• The output weighting scheme for both the price level and the
general value level are identical at all times. Therefore, if every
individual price in the economy shares a common denominator,
(the value of money), then the price index p* can be decomposed
into a general value index VG* and a money value index VM*.
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Expressing Relationship in
Index Terms
• We can demonstrate that the relationship holds when each of those
three variables are expressed in index form (p*, VG*, VM*) such that:
*
V
p* = G*
VM
• In order to do this, we need to consider how a price level index,
such as the consumer price index, is constructed. A price level
index is constructed in a two step process. The first step is to create
an individual price index for each good and service in the basket
using the base year as reference point. For example, if the price of
apples in the base year is $2 and the price in current year is $3, then
the price index for apples is 150 in the current year (assuming a 100
base year value for the apples index).
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Construction of Indices
• We can denote an individual good price index as p*i . The next step
is to weight these individual price indices for each good/service
according to their share of total consumer expenditure wi to create
an index of the price level p*.
p = å p × wi
*
*
i
• Similarly, we can create an index for the general value level VG*.
Again, we need to create an individual absolute market value index
for each good V*i and then weight these individual market value
indices for each good/service according to their share of total
consumer expenditure wi such that:
V = åVi × wi
*
G
*
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Calculation of
Individual Price Index
• The price index for an individual good at time t (with base 100) can
be calculated as:
pi,t* = ( pi,t pi,B ) ×100
where pi,t is the current price of the good
pi,B is the price of the good in the base year
• The microeconomic theory in Part A states the price for an
individual good at time t can be determined by:
pi,t = Vi,t VM,t
where Vi,t is the absolute market value of good i at time t
VM,t is the absolute market value of money at time t
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Applying the Microeconomic
Theory of Price Determination
• Therefore, applying our microeconomic theory, the price index
for an individual good at time t can calculated as:
p = éë(Vi,t VM,t ) (Vi,B VM,B )ùû ×100
*
i,t
where Vi,t is the abs. market value of the good at time t
VM,t is the abs. market value of money at time t
Vi,B is the abs. market value of the good in base year
VM,B is the abs. market value of money in base year
• This can be restated as:
pi,t* = éë(Vi,t Vi,B ) × (VM,B VM,t )ùû ×100
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Analyzing the Two Terms
In Previous Equation
• Let’s consider the final term in the last equation on the previous
slide:
(VM,B
VM,t )
• This term is the reciprocal of an index for the absolute market
value of money (with base 1):
V
*
M,t
= VM,t VM,B
• Furthermore, the first term in the last equation of the previous
slide is nothing more than an absolute market value index for an
individual good:
V = Vi,t Vi,B
*
i,t
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Calculating the Price Level
Index
• Therefore, the price index for an individual good at time t can be
expressed as:
*
* ù
é
p = ëVi,t VM,t û ×100
*
i,t
• We can now calculate the index for the overall price level p* at
time t as follows:
*
*
é
p = å p × wi,t = åë(Vi,t VM,t ) ×100ùû × wi,t
*
t
*
i,t
• The term V*M,t is identical for all goods in the index, therefore
the price level can be restated as:
æ
ö
1
pt* = çç * ÷÷ åVi,t* × wi,t ×100
è VM ,t ø
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Price Level Index is a Function of
Two Absolute Market Value Indices
• Finally, if you refer back to the initial part of this discussion, you
can see that the general value index VG* at time t (with base 100)
can be calculated as:
*
VG,t
= åVi,t* × wi,t ×100
• Therefore, the price level index p* at time t can be expressed as:
V
p =
V
*
t
*
G,t
*
M ,t
• The price level index (base 100) is equal to the general value
index (base 100) divided by the market value of money index
(base 1).
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Price Level is Not an Index
• While the preceding analysis highlights that the posited
relationship between the three variables p, VG and VM holds when
each variable is expressed in index form, the problem with this
analysis is that, technically, it does not prove the point we are
trying to make. Why? Because the price level is not an index.
Nor, for that matter, is the general value level, nor the absolute
market value of money.
• The “price level” is a conceptual notion, not an index.
Technically, the price level is a hypothetical measure of overall
prices for some set of goods/services, not an index per se. In
order to prove the relationship between p, VG and VM we need to
follow a similar, but more abstract, line of thought.
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The Price Level is a
Conceptual Notion
• Firstly, we need to review the concept of the price level. There is
no such physical thing as a “price level”: rather, it is a conceptual
notion spun off from a larger idea, namely, the classical
dichotomy: “The classical dichotomy is the name given to a
theory that says that real things – allocations and relative prices –
are determined separately from nominal things – the quantity of
money, nominal prices…” (Wallace, 2008)
• In essence, the price level is born from the idea that the price of
an individual good can be described by two components: (1) the
change in the market value of the good relative to that of other
goods (a real component), and (2) the overall change in the price
of all goods (a nominal component).
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Theoretical Foundations of
The Price Level
• The theoretical foundation for the price level can be described by
the following identity. The price of good a, denoted as pa,t , can
be expressed as follows:
é pa,t ù
pa,t = [ pt ] × ê ú
ë pt û
Nominal
Component
Real
Component
• In simple terms, the price of good a can be decomposed into two
elements: (1) an “average” of all prices in the economy pt (the
nominal component) and (2) the price of good a relative to that
average (the real component). The price level is the common
component in the price of every good in the economy.
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The Price Level and the
Money Value of Transactions
• The role of the price level in the determination of nominal
economic activity can be described as follows. Given a set A of
goods and services, the total money value of transactions in A at
time t is:
å (p
a,t
aÎA
× qa,t ) = å éë( pt × p¢a,t ) × qa,t ùû = pt å ( p¢a,t × qa,t )
aÎA
aÎA
where qa,t is the quantity of a at time t
pa,t is the price of a at time t
p’a,t is the “real” price of a at time t
pt is the price level at time t
• The price level pt is the “common element” of each price in the
economy while each good in the economy (each good in the set of
A) has its own unique “real price”, p’a,t .
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The General Value Level
• The next step is to define the “general value level”. The general
value level is a concept that is almost identical the price level: the
key point of difference is that while the price level is a hypothetical
measure of overall market values for some set of goods as measured
in relative terms, the general value level is a hypothetical measure of
overall market values for that same set of goods as measured in
absolute terms (in terms of an invariable measure of market value).
• To the degree that the absolute market value of a good changes over
time, that change can be decomposed into two components: (1) the
change in the absolute market value of the good relative to that of
other goods, and (2) the overall change in the absolute market value
of all goods. The general value level is the conceptual measure of
this second component.
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Theoretical Foundations of
The General Value Level
• The theoretical foundation for the general value level can be
described by the following identity. The absolute market value of
good a, denoted as Va,t , can be expressed as follows:
é Va,t ù
Va,t = [Vt ] × ê ú
ë Vt û
General Value
Level
Real Market
Value
• In simple terms, the absolute market value of good a can be
decomposed into two elements: (1) an “average” of all absolute
market values in the economy Vt (the general value level) and (2)
the price of good a relative to that average (the real absolute
market value of the good).
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The General Value Level and the
Absolute Market Value of Transactions
• Given a set A of goods and services, the total absolute market value
of transactions in A (the market value of transactions in A as
measured in “units of economic value” terms, at time t is:
å (V
a,t
aÎA
× qa,t ) = å éë(VG,t × Va,t¢ ) × qa,t ùû = VG,t å (Va,t¢ × qa,t )
aÎA
aÎA
where qa,t is the quantity of a at time t
Va,t is the absolute market value of a at time t
V’a,t is the “real” market value of a at time t
VG,t is the general value level at time t
• The absolute market value of each good can be decomposed into a
shared component (the general value level VG,t ) and a unique
component (the “real” market value of the good V’a,t ).
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The “Real Price” is a
Ratio of Prices
• The next step of the proof requires an understanding of the nature
of real prices. As discussed, the concept of the “real price” is
derived from the following identity, where pa,t is the price of good a
at time t and pt is the price level at time t:
pa,t
pa,t = pt ×
pt
• The “real price” is nothing more than a relative expression of two
prices (pa,t/pt). Traditionally, it is an expression of the price of a
good relative to the output weighted average price of a basket of
goods (the price level). Furthermore, the “real price” is itself a
price: namely, the price of a good in terms of the basket of goods.
(Note: the real price is, by definition, a non-money price).
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“Real Price” Equals
“Real Market Value”
• We can demonstrate that the “real price” of a good is the same
as the “real market value” of a good such that:
p¢a,t = Va,t¢
• The general principle is as follows: the relative market value of a
good relative to the relative market value of the basket of goods
is the same as the absolute market value of a good relative to the
absolute market value of the basket of goods. In other words, the
absolute market value relation between two goods is the same as
the price relation between those two goods.
• While this may sound complicated, it is actually very simple to
demonstrate mathematically.
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Ratio of Prices Equals
Ratio of Absolute Market Values
• Let’s suppose there are only two goods in the economy, a and b.
Part A microeconomic theory states that we can describe the price
of each good as follows:
pa,t = Va,t VM,t
pb,t = Vb,t VM,t
• The relative market value of good a relative to the relative market
value of b (the price of a relative to the price of b) is equal to:
pa,t æ Va,t ö æ VM,t ö Va,t
= çç
= p(ab )
÷÷ × çç
÷÷ =
pb,t è VM,t ø è Vb,t ø Vb.t
• The ratio pa/pb is the same as the ratio Va/Vb : the price of a relative
to the price of b is the same as the price of a in b terms.
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Real Absolute Market Value Relations
Same as Real Price Relations
• If this ratio relation applies between good a and good b, then, by
extension, it also applies between good a and every other good in
the economy, including an average of those goods. Therefore, we
can say that the “real price” of good a is the same as the “real
market value” of good a (the absolute market value of a relative to
the general value level):
pa,t Va,t
p¢a,t =
=
= Va,t¢
pt VG,t
• There is another way to think of this. The price of a relative to the
average price of the basket of goods is the same as the price of a in
basket of goods terms. The price of a in basket of goods terms is
equal to the absolute market value of good a divided by the average
absolute market value of the basket of goods.
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Expressing Price Level in
Absolute Market Value Terms
• Returning the beginning of this discussion, the total money value
of transactions at time t can be described by:
å (p
a,t
aÎA
× qa,t ) = å éë( pt × p¢a,t ) × qa,t ùû = pt å ( p¢a,t × qa,t )
aÎA
aÎA
• The last step in the process is to express the total money value of
transactions at time t in terms of absolute market values:
éæ V ö
ù
éæ V × V ¢ ö
ù
a,t
G,t
a,t
ê
ú
ê
(p
×
q
)
=
×
q
=
ç
÷
ç
å a,t a,t å êç V ÷ a,t ú å êç V ÷÷ × qa,t úú
û aÎA ëè M,t ø
û
aÎA
aÎA ëè M ,t ø
• As discussed, “real price” equals “real market value”:
p¢a,t = Va,t¢
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Final Step
• Therefore, substituting in p’a,t for V’a,t in our total money value
of transactions formula:
éæ V × p¢ ö
ù
pt å ( p¢a,t × qa,t ) = å êçç G,t a,t ÷÷ × qa,t ú
úû
ëè VM ,t ø
aÎA
aÎA ê
• Rearranging:
æV ö
pt å ( p¢a,t × qa,t ) = çç G,t ÷÷ å ( p¢a,t × qa,t )
è VM ,t ø aÎA
aÎA
• Therefore:
VG,t
pt =
VM ,t
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The Ratio Theory of the Price Level
• The “Ratio Theory of the Price Level”, or “Ratio Theory”, states
that the price level p is a function of two absolute market values: the
general value level VG , a hypothetical measure of overall absolute
market values for goods in the economy, and the absolute market
value of money VM .
VG
p=
VM
• In terms of the “nominal/real” paradigm, the theory states that a
change in the nominal component of any price (a change in the
price level, or the overall relative market value of goods versus
money), is itself divided into two further components: (1) the
change in the overall absolute market value of goods, and (2) the
change in the absolute market value of money.
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A Small First Step
• Ratio Theory represents a small, but critical, first step in the
direction of developing a model of inflation that includes an
explicit role for the absolute market value of money, or, in
layman’s terms, “the value of money”.
• Both Keynesianism and monetarism are largely silent on “the
value of money” and its role in inflation because they don’t
acknowledge the existence of such a notion. Both schools of
thought ascribe to the Keynesian notion that supply and demand
for money determines the interest rate. While monetarism
recognizes that “money” (albeit, poorly defined) has a critical
role to play in price level determination, it does not recognize the
critical role that the “value of money” has in this process.
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Building the Basic Toolset
• The remainder of this paper and the final paper in the series (The
Velocity Enigma) are devoted to developing tools that might help
to explain how both key variables, the general value level and the
absolute market value of money, are determined and, just as
importantly, the interaction between those two variables.
• In the next section, we are going to introduce a model, called the
“Simple Model for the Market Value of Money”, that will help
us to think about the determination of the price level in the longterm. Once that task is completed, we will begin the difficult
process of analyzing price level determination in the short term.
To assist us in this task, we will introduce a framework called the
“Goods-Money Framework”.
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The Simple Model for the
Market Value of Money
The Application of Ratio Theory to the Quantity Theory of Money
and a Discussion of Price Level Determination in the Long Run
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Long Run Determination of
the Price Level
• Before we begin this section, I would like to make a couple of
important points. Firstly, this section of the paper is solely
concerned with the determination of the absolute market value
of money and the price level as measured, from point to point,
over very long periods of time (many years, not months).
• Secondly, the analysis of long run price level determination that
will be presented in this section of the paper has been highly
simplified in order to provide readers with an introduction to the
general concepts involved. Ultimately, a more comprehensive
analysis of the long-term evolution of the price level requires an
understanding of the short-term evolution of the price level,
something that we shall embark on in the next section.
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The Enigma Series Theory of
the Demand for Money
• Let’s start with a theory of the demand for money and then we
can simplify it. The view of the Enigma Series is that money is a
long-duration financial instrument. More specifically, it is a
proportional claim on the output of society (money is a specialform equity instrument issued by government as trust and trustee
on behalf of society).
• Demand for any financial instrument is a function of the
expected discounted future benefits of that instrument. Demand
for money is not an exception to this rule. Demand for money is
determined by the discounted future benefits that someone in the
immediate possession of money expects to receive from its
ultimate use as a claim on the output of society.
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A Simplified Theory of the
Demand for Money
• In essence, Enigma Series theory states that demand for money
is highly dependent upon long-term expectations of the future
levels of important economic variables such as the monetary
base and real output. Furthermore, changes in these long-term
expectations are the primary driver of the market value of
money in the short term.
• However, over very long periods of time, we can simplify the
analysis by “ignoring” the role of expectations. Another way of
saying this is that over the very long-term, we can simplify the
analysis by holding expectations constant. In order to explain
this we can use a simple analogy: let’s consider the drivers of a
share price in the short run and in the long run.
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Short-Run vs Long-Run
Drivers of a Share Price
• Common stock is a long-duration asset: it is a financial
instrument that entitles its holder to an extended series of future
cash flows. In the short term, stock prices are highly sensitive to
any change in expectations regarding the long-term future of that
series of cash flows.
• However, when stock price performance is measured over the
long term, shifts in expectations tend to be less critical. Over the
long term, the key driver of share price performance is the
historical growth in earnings per share. If, over a long period of
time, earnings per share have increased tenfold, then it is likely
that the price of each share has increased by a similar amount,
(offset only slightly by changes in EPS growth expectations).
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Example: Determination of Stock
Price in Long-Run vs Short-Run
• Let’s examine this point by using some hard numbers. Imagine a
stock with a P/E ratio of 20 and earnings of $1 per share. Over the
next two years, earnings rise to $1.25 per share, but the P/E ratio
falls to 16 (lower growth expectations). Over the next eighteen
years, earnings rise to $10 per share while the P/E ratio remains at
16.
• Over the first two years, the stock price performance seems to have
nothing to do with EPS: EPS rises 25% ($1 to $1.25) but the share
price doesn’t change (stays at $20). But measured over the entire
twenty year period, the share price does track earnings per share, at
least roughly: the stock price rises 8x (to $160) while EPS is up 10x.
Over long periods of time, changes in EPS tend to overwhelm
changes in expectations (which are reflected in the P/E multiple).
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Absolute Market Value of Money:
Short-Run vs Long-Run
• As discussed in The Money Enigma, money is a special-form of
equity instrument and a long-duration asset. (See The Velocity
Enigma for a more detailed discussion of this point). Prima
facie, in the short-run, the absolute market value of money
should be highly sensitive to changes in long-term expectations.
• However, when the absolute market value of money is analyzed
over a long period of time, changes in expectations are far less
relevant. Over the long-run, the main driver of the value of
money is the historical growth in real output per unit of base
money. If, over a long period of time, real output per unit of base
money has fallen by 90%, then we should expect that money has
lost roughly 90% of its absolute market value over that period.
217
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The Simple Model
An Introduction
• We can illustrate this long run relationship by taking the quantity
theory of money and combining it with Ratio Theory in order to
develop a long run model for the market value of money called
“The Simple Model of the Market Value of Money”.
• The “Simple Model” is a simple introductory model that we can
use to think about what factors might influence the absolute
market value of money over long periods of time. The simplicity
of the model is both its strength and its weakness. For reasons
that will become obvious, the model suffers from the same
strengths and weaknesses as the quantity theory of money: the
model is useful in analyzing the long-run evolution of the value
of money, but it has little practical use in the short-run.
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Derivation of The Simple Model
• The derivation of the Simple Model begins with the Equation of
Exchange:
p× q = M × v
where p is the general price level
q is real output (final expenditures)
M is the monetary base
v is the velocity of base money
• We can apply Ratio Theory by substituting for the price level p
in the Equation of Exchange:
VG
×q = M ×v
VM
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The Simple Model for the
Market Value of Money
• The previous formula can be rearranged to form the “Simple
Model for the Market Value of Money”:
VG × q
VM =
M ×v
• The Simple Model states that the absolute market value of
money VM is a function of four variables:
1. The general value level VG a hypothetical measure of overall
absolute market values for the “basket of goods”;
2. Real output q;
3. The monetary base M; and
4. The velocity of base money v.
220
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Basic Implications of
The Simple Model
• In the Money Enigma, it was argued that money is a financial
instrument and, hence, an asset and a liability. Money has value
as an asset because it is an equity instrument of society, issued
on its behalf by government as trust and trustee. In particular,
money is a proportional claim on the output of society.
• The Simple Model provides further, albeit very limited, insight
into the nature of the value of money. All else equal, the
absolute market value of money is positively related to both the
general value level and real output. As expected, the market
value of money is negatively related to the number of claims
issued, the monetary base: as the number of outstanding claims
increases, the proportional entitlement of each claim falls.
221
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Simple Model as a Long-Run
Model for the Value of Money
• The Simple Model provides a useful perspective on the evolution
of the value of money over long periods of time. Ultimately,
money is nothing more than a proportional claim on output.
While shifting expectations may lead to variations in the value of
money in the short-run, over long periods of time the absolute
market value of money should reflect changes in the absolute
market value of output relative to the growth of money.
• Simply put, if over a period of several decades, the rate of
money growth has outstripped the rate of growth in output, then
we should reasonably expect that the market value of a financial
instrument that represents a proportional claim on the output of
society (money) has declined significantly.
222
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In Long Run, General Value Level
Doesn’t Matter to Price Level
• The Simple Model provides another important insight. Over the
long term, the path of the general value level VG is irrelevant to
the path of the price level. Remember the two models:
VG
p=
VM
VG × q
VM =
M ×v
• If velocity is held constant, then any percentage change in VG is
automatically reflected as an identical percentage change in VM .
Think about this for a moment. Over the long-term, the absolute
market value of goods has nothing to do with inflation: the only
thing that matters to inflation is the absolute market value of
money. In this sense, Friedman was right: long-term, inflation is
purely a monetary phenomenon.
223
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Quick Review
• Let’s pause for a moment and review. Money is a financial
instrument: in particular, it is a proportional claim on the output
of society. In very simple terms, we can say that over long periods
of time the value of the proportional claim (the value of money)
will increase as the value of output each unit of money can claim
increases. Therefore, the value of money is positively related to
the absolute market value of output (VG & q) and negatively
related to the number of claims outstanding (the money base, M).
• Ratio Theory states that as the value of money declines, the price
level rises. In the long-term, changes in the overall value of goods
are irrelevant because they are reflected in the value of money.
All of this reconciles neatly with “long-term” quantity theory.
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Derivation of
Demand Curve for Money
• We can use the Simple Model to derive a simple supply and
demand model for money. We can rearrange the Simple Model to
express it in the following terms:
æ VG × q ö 1
M =ç
÷×
è v ø VM
• We know that in equilibrium, money supply (MS) must equal
money demand (MD). Therefore:
æ VG × q ö 1
MD = ç
÷×
è v ø VM
• We can use this relationship to plot the demand for money in terms
of VM and M.
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Supply & Demand for Money
• The Simple Model can be
SUPPLY & DEMAND
represented with a basic supply
FOR MONEY
and demand diagram. The
supply of money is fixed
Market Value
(supply curve is vertical).
(EV)
Supply
• All else equal, the quantity of
money demanded is inversely
related to the value of money
VM
(demand curve slopes down).
Demand
The demand curve shifts to the
fn{VG ,q ,v}
right if the absolute market
value of output (VG q) rises or if
the velocity of money v falls.
M Base Money
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Money Supply is
the Monetary Base
• As discussed in The Money Enigma, it is the view of The
Enigma Series that “money”, properly defined, is solely
comprised of the monetary base. The monetary base is the
“equity finance” of society, a series of direct claims on the output
of society that have been created by society in order to fund
public activities & projects (such as purchasing government
securities, or in extreme cases, directly financing budget deficits).
All other forms of “money” (banking deposits etc.) are really just
claims to money (claims on a claim).
• The monetary base is determined exogenously by “political
process” (typically, central bank decisions). Therefore, the supply
of money is fixed and the money supply curve is vertical.
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Long-Term Impact of an
Increase in the Monetary Base
• Over long periods of time, an
increase in the monetary base
will push the supply curve to
the right and the equilibrium
absolute market value of
money will fall.
LONG-TERM IMPACT OF
AN INCREASE IN
MONETARY BASE
Market Value
(EV)
• The analysis opposite assumes
VM,0
that the absolute market value
of output (VM .q) has remained
VM,1
constant and that velocity v has
remained constant (the demand
curve has not shifted).
228
S0
S1
Demand
M0
M1
Monetary
Base
Gervaise R. J. Heddle, 2014
Long-Term Impact of an
Increase in Real Output
• Over long periods of time, an
increase in real output (or the
general value level) will push
the demand curve to the right
and the equilibrium market
value of money will rise.
LONG-TERM IMPACT OF
AN INCREASE IN
REAL OUTPUT
Market Value
(EV)
Supply
VM,1
• The analysis opposite assumes
that the monetary base M has
remained constant over this
period and the velocity of
money has remained relatively
constant.
VM,0
D1
D0
M
229
Monetary
Base
Gervaise R. J. Heddle, 2014
Explaining Why Quantity
Theory Works in the Long-Run
• If we go back to the discussion at the start of this section, we can
begin to understand why the quantity theory of money works in
the long-term, but not in the short-term. In very simple terms,
the velocity of money is the “long-term expectations term” in the
formula for the absolute market value of money.
• If we hold those long-term expectations relatively constant, then
the velocity of money is relatively stable: the Simple Model
works as a model for the market value of money and quantity
theory works as a model of the price level. For the purposes of
long-term analysis, holding expectations constant is a reasonable
simplification (remember the share price example). However, in
the short-term, we can not make these types of assumptions.
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Velocity of Money:
A Preview
• The notion that the velocity of money is really just an
expectations term in a valuation model for money is explained in
more detail in The Velocity Enigma. However, here is a quick
preview of the model for velocity:
é n-1 (1+ g)t+1 (1+ i)t+1 ù
vt = (n × vk ) êå
t+1
t+1 ú
ë t=0 (1+ m) (1+ d) û
• Without going into all the details, the formula above states that
the velocity of money is a function of long-term expectations
regarding the growth rate of real output g and the growth rate of
the monetary base m. This formula for velocity is derived from a
discounted future benefits model for money (see next page).
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The Value of Money: Collapsing
Down to The Simple Model
• The formula for velocity is derived from the following constant
growth version of the Discounted Future Benefits Model for
Money.
VM ,t
1 (VG,t × qt ) é n-1 (1+ g)t+1 (1+ i)t+1 ù
=
êå
t+1
t+1 ú
n × vk M t ë t=0 (1+ m) (1+ d) û
• If we hold the “expectations term” constant (the term in square
brackets above), then what we have left is, in essence, the long run
application of the Simple Model. [Note: both n and vk are
constants]. The Simple Model and quantity theory both work in the
long-term because, in most circumstances, the impact of a change in
the expectations term is minimal when changes in VM are measured
over very long periods of time. 232
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Key Limitations of
The Simple Model
• Unfortunately, we are getting ahead of ourselves, so let’s return
to the Simple Model and discuss its limitations. The key
limitations of the Simple Model are (1) its reliance on the
“enigmatic” velocity of money and (2) it is a model that, by its
nature, downplays the role of expectations in the determination
of the value of money.
• Intuitively, it makes no sense of the value of money to be solely
determined by current economic conditions. Money is a longduration asset and long-duration assets are highly sensitive to
long-term expectations. The upcoming section “The Market for
Money” will examine the relationship between the short-term
demand for money and long-term expectations in more detail.
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The Goods-Money Framework
A Framework for Analyzing Short-Run Price Level Determination
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Price Level Analysis:
Short Term vs Long Term
• In the last section, our discussion focused on the determination
of the price level in the long term. It was argued that, in the long
term, changes in the value of money are driven primarily by
changes in real output and the monetary base and we can largely
ignore the impact of shifting long-term expectations on the
market value of money. Furthermore, in the long term, changes
in the general value level are largely irrelevant to the price level as
such changes are reflected in the market value of money.
• In the short term, none of the above analysis is appropriate.
Firstly, expectations do matter in the short term, we can’t just
ignore them. Secondly, shifts in the general value level are not
automatically reflected in the value of money.
235
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Need to Analyze Markets for
Goods and Money Separately
• This second point is critical. In the long term, we can largely
ignore the path of the general value level. But in the short term,
changes in the general value level can have an important impact
on the price level (we can not assume such changes are just
automatically reflected in the absolute market value of money).
• Therefore, in order to analyze price determination in the short
term, we need a framework that allows us to analyze the
absolute market value of money VM and the general value level
VG separately. In simple terms, if we want to understand the
impact of an exogenous shock on the price level, we need to
understand the impact of that shock on both the market for
goods and the market for money.
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A Two-Market Model for
Determination of the Price Level
• In this vein, the primary model that we will use for short-term
analysis of the price level is a basic two-market model called the
“Goods-Money Framework”.
• The Goods-Money Framework proposes that (1) the equilibrium
general value level VG is determined by aggregate demand and
aggregate supply in the market for goods/services and (2) the
equilibrium absolute market value of money VM is determined
by supply and demand for the monetary base. The key
implication of the Goods-Money Framework is that the price
level is determined, in a stylized sense, by two sets of supply and
demand, it is not determined solely by aggregate supply and
demand as represented in traditional Keynesian analysis.
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The Goods-Money Framework
Aggregate supply and demand for goods/services determines the
equilibrium general value level VG and real output q. Supply and
demand for money determines the market value of money VM .
“LEFT SIDE: GOODS”
“RIGHT SIDE: MONEY”
General Value Level (EV)
Value of Money (EV)
AS
Supply
VG
p=
VM
VG
VM
Demand
AD
q
Real Output
M
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Base Money
Gervaise R. J. Heddle, 2014
The Left Side of the Framework
LEFT SIDE OF
THE FRAMEWORK
• The Left Side of the
Framework is a short run
model of aggregate demand
and aggregate supply, where
both functions are expressed
in terms of the general value
level and real output.
“GOODS/SERVICES”
General
Value
Level
(EV)
Aggregate
Supply
VG
Aggregate
Demand
q
Real Output
239
• The intersection of aggregate
demand and aggregate supply
determines equilibrium levels
of real output and the general
value level.
Gervaise R. J. Heddle, 2014
The Right Side of the Framework
• The Right Side of the
Framework is the market for
money. The supply of money
(the monetary base) is fixed.
Demand for money is plotted
in terms of the absolute market
value of money.
THE RIGHT SIDE OF
THE FRAMEWORK
“MONEY”
Value of
Money (EV)
• The intersection of supply and
demand for money determines,
in the first instance, the
equilibrium absolute market
value of money.
Supply
VM
Demand
fn{VG ,q ,v}
M
240
Base Money
Gervaise R. J. Heddle, 2014
Example One: Increase in
Aggregate Demand
• Let’s briefly consider two
basic examples. In this
example, the aggregate
demand curve shifts to the
right. Equilibrium levels of
real output q and the general
value level VG both rise.
LEFT SIDE OF
THE FRAMEWORK
General
Value
Level
(EV)
“GOODS/SERVICES”
Aggregate
Supply
VG,2
VG,1
• All else equal, the rise in VG
will lead to a rise in the price
level:
V
AD2
AD1
q1 q2
Real Output
241
p=
G
VM
Gervaise R. J. Heddle, 2014
Example Two: Increase in
Demand For Money
• In this second example, there
is an increase in the demand
for money. The demand
curve for money moves to
the right. The equilibrium
absolute market value of
money VM rises.
• All else equal, the rise in VM
will lead to a fall in the price
level:
THE RIGHT SIDE OF
THE FRAMEWORK
“MONEY”
Value of
Money (EV)
Supply
VM,2
VM,1
VG
p=
VM
D2
D1
M
242
Base Money
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The Left Side: An Extension of
the Microeconomic Principle
• Both sides of the Goods-Money Framework are analyzed in
more detail later in this paper, but for now let’s make a few quick
observations about the left side of the framework so that we can
move on and discuss the right side of the framework.
• In simple terms, the left side of the framework represents an
extension of the microeconomic principle described earlier in
this paper that supply and demand for a good are, in the first
instance, functions of the absolute market value of that good, not
its price in money terms. Prima facie, the hypothetical aggregate
supply and demand functions should both be a function of the
overall absolute market value of goods (the general value level),
not the price level.
243
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Predictable Real Output Response to
Changes in Price Level Unlikely
• Aggregate supply and demand analysis as traditionally represented
(with the price level, not inflation, on the y-axis) posits that there are
predictable responses between the aggregate quantity of goods
supplied/demanded and the price level. This must be the case in
order for both functions (aggregate supply and demand) to be
derived in terms of the price level.
• The problem with this view is that the price level is a very noisy
signal. If Ratio Theory is correct, then the price level contains
information about both the value of goods and the value of money.
It is not clear why economic agents should respond in the same
manner to a rise in the value of goods as they do to a fall in the
value of money, even though both have the same effect on the price
level (the price level rises in both cases).
244
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A “More Predictable” Real Output
Response to General Value Level?
• Consider the aggregate supply curve. In very simple terms, if
something (the basket of goods) is absolutely more valuable, then
it may make sense for people to work harder to supply it and
hence real output will increase. If something is only relatively
more valuable, it is only more valuable in the sense that the item
received in exchange (money) is less valuable, then it is not clear
why a similar “work harder” response should be elicited.
• It is the contention of this paper that if there is any predictable
relationship between the overall market value of goods and real
output, then it is between the absolute market value of goods and
real output, not the relative market value of goods (the market
value of goods in money terms) and real output.
245
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Derivation of Aggregate
Supply and Demand Curves
• If there is a predictable response between the general value level
and real output demanded and supplied (the aggregate supply
and demand functions), then the natural question to ask is what
is the nature of that response (what is the slope of the
functions?).
• The left side of the Goods-Money Framework attempts to
capture the short-term dynamics in the “Goods Market”. In the
short term, the aggregate demand function is downward sloping
and the aggregate supply function is upward sloping. While there
are many possible arguments to justify these shapes, a later
section in this paper will argue that the respective slopes of the
short-term AD/AS functions are driven primarily by
expectations of mean reversion in the general value level.
246
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General Value Level Sensitive to
Short-Term Conditions
• Before we conclude this introductory section on the GoodsMoney Framework and move on with our initial analysis of the
right side of the framework, it is worth making one more point.
• It is the view of this paper that the general value level is highly
responsive to changes in current market conditions and shortterm expectations. This should not be a controversial point. The
reason it is highlighted is because it contrasts sharply with the
behavior of the market value of money. In the next section and
the final paper in the Series, it will be argued that, in the short
term, the absolute market value of money is driven primarily by
shifts in long-term expectations. With that point in mind, let’s
begin a more detailed analysis of each side of the framework.
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The Market for Money
The Right Side of the Goods-Money Framework
248
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The Market For Money:
Introductory Comments
• In an earlier section, we used the Simple Model to think about
the long-term determination of the absolute market value of
money and the price level. This section of the paper is designed
to provide readers with a basic introduction to the short-term
determination of the absolute market value of money.
• I would like to stress that this section is merely an introduction to
the complicated issues involved and is really just a preview of key
ideas discussed in the final paper of the series, The Velocity
Enigma. This section of the paper will discuss, at a high level,
some of the basic issues involved, but it is not a substitute for the
Discounted Future Benefits Model of Money and the more
detailed analysis contained in The Velocity Enigma.
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The Parties to the
Moneyholders’ Agreement
Let’s begin our analysis of the market for money by going back to the
basic principles discussed in The Money Enigma. Money is a financial
instrument. Money is a liability of society (issued on its behalf by
government as trust and trustee) and an asset to its holder.
“MONEYHOLDERS’ AGREEMENT”
SOCIETY
{GOVERNMENT
AS TRUST &
TRUSTEE}
MONEYHOLDER
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Money as a Proportional Claim
on the Output of Society
Money is created by society in order to fund certain public activities.
Society authorizes government to issue claims on the future output of
society. Money represents a proportional claim to that future output.
AUTHORIZES
GOVERNMENT
“THE TRUST”
SOCIETY
“BENEFICIARY”
PRODUCES
TO ISSUE CLAIMS ON
“LEGAL LIABILITY”
GOVERNMENT
LIABILITIES
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“ECONOMIC LIABILITY”
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The Supply of Money
• The view of The Enigma Series is that money is a financial
instrument. More specifically, money is a special-form equity
instrument issued by government, as trust and trustee on behalf
of society, in order to finance communal activities and programs.
• The supply of this “equity finance” is determined by what is
essentially a political process. We create special institutions that
are authorized to issue money (the central banks), we give them
special rules (mandates) and we seek to make them
“independent” from party politics. But ultimately, it is society,
through the combination of its cultural and political imperatives,
that determines how much of this special-form equity financing is
created.
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The Demand for Money
• Demand for money depends entirely upon its status as a financial
instrument: it derives value from its contractual, not its physical
properties. Money represents an implied contract between
society and the holder of money: it is a liability to society and an
asset to its holder. More specifically, money is a proportional
claim on the output of society.
• Demand for any financial instrument is a function of the
expected discounted future benefits of that instrument. Demand
for money is not an exception to this rule. Demand for money is
determined by the discounted future benefits that someone in the
immediate possession of money expects to receive from its
ultimate use as a claim on the output of society.
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Demand for Money is Driven by
Long-Term Expectations
• Financial instruments are, by their nature, contracts for the
exchange of future economic benefits. The market value of a
financial instrument depends primarily upon market
expectations regarding those future economic benefits. All else
equal, the market value of an asset with longer duration will be
more sensitive to changes in those expectations than an asset
with shorter duration.
• Money is a long-duration financial instrument. It is the view of
The Enigma Series that, in the short term, changes in the
absolute market value of money are driven primarily by shifts in
long-term expectations of important economic variables such as
long-term output and money supply growth.
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Money is a Long-Duration Asset
• We briefly discussed one argument for the long-duration nature
of money in The Money Enigma. It was argued that if it was
declared that, one year from now, money would no longer be
recognized as a claim on the output of society, then the value of
money would immediately collapse. This “benefits cut off test”
is a simple test for the duration of any asset.
• The Velocity Enigma discusses the long-duration nature of
money in great detail. In particular, the paper argues that if the
economy is in a state of intertemporal equilibrium, then most of
the present value of money reflects the expected value of money
in distant future periods. For now, let’s assume that the “longduration” thesis is correct and return to the discussion at hand.
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Common Stock Analogy
Revisited
• In an earlier section of this paper, we compared money with a
share of common stock: both are equity instruments (in the
broadest sense of that term) and both are long-duration assets. A
share of common stock is a proportional claim on the residual
cash flows of a company; money is a proportional claim on the
output of society.
• Long-term, the key driver of share price performance is the
change in earnings per share: similarly, the main driver of the
absolute market value of money is the change in the “real
output per unit of money” ratio. In the short-term, long-duration
equity instruments are highly sensitive to shifts in expectations
regarding their respective set of future economic benefits.
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Long-Term Expectations Matter
More than Current Conditions
• By definition, much of the value of a long-duration asset depends
upon expectations regarding long dated future economic benefits.
For example, if investors suddenly believe the earnings growth of
a company will slow, (maybe due to a new technology entering
the market), then that will have an immediate and significant
effect on the stock price of that company.
• In contrast, changes in current conditions that are perceived to be
“temporary” can have little to no impact on the share price. For
example, a slump in current earnings per share due to bad
weather will, in most circumstance, have little impact on the
share price. Theoretically, long-term expectations, not short-term
conditions, are the primary driver of share prices.
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Same Principle
Applies to Money
• It is the contention of The Enigma Series that money is a longduration asset and most of the current market value of money, as
measured in “units of economic value” terms, depends upon
expectations of long dated future benefits. In other words, much
of the market value of money is tied up in claims on output that
will be made not now or next year, but in 20 or 30 years time.
• Just as a stock price is highly sensitive to changes in long-term
EPS growth expectations, so money is highly sensitive to changes
in long-term expectations regarding the growth of real output per
unit of base money. Furthermore, the value of money is
relatively insensitive to changes in current economic conditions,
particularly if those changes are perceived to be “temporary”.
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Long Term vs Short Term:
The Market Value of Money
• Let’s contrast this view with the long-term determination of the
absolute market value of money as discussed earlier in this paper.
Long-term, we can assume that the velocity of money is relatively
stable and use the Simple Model to determine changes in the value
of money:
VG × q
VM =
M ×v
• However, in the short term, changes in current levels of real output
and money supply may have little to no impact on the value of
money. This creates an issue: if M changes and VM is constant then
one of the other terms in the equation above must change. Short
term, the velocity of money is not constant, but adapts to reflect the
relative absolute market value of goods (VG q) and money (VM M).
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The Right Side of the Framework
• The theory just described can
be better understood by
example. We will use our basic
supply and demand framework
to illustrate how the value of
money may react in various
economic circumstances.
THE RIGHT SIDE OF
THE FRAMEWORK
“MONEY”
Value of
Money (EV)
• The supply of money (the
monetary base) is fixed.
Demand for money is plotted in
terms of the absolute market
value of money.
260
Supply
VM
Demand
fn{VG ,q ,v}
M
Base Money
Gervaise R. J. Heddle, 2014
Supply & Demand is
“Second Best” Solution
• Before we begin our scenario analysis, it is important to note that
supply and demand analysis is really a “second best” solution for
analyzing the market for money. The better model for analyzing
the equilibrium absolute market value of money is the discounted
future benefits model developed in The Velocity Enigma.
• As a general rule, the analysis of a long-duration equity
instrument (such as money) is better performed and understood in
the context of a discounted future benefit model, not supply and
demand. We can use supply and demand analysis, but such
analysis is not ideal (particularly when expressed in stock, not
flow, terms). Nevertheless, we will press on and do the best we can
with the supply and demand framework we have at our disposal.
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Simple Scenario:
Lull in Economic Activity
• Let’s illustrate the general point with the following scenario:
imagine that there is an exogenous fall in aggregate demand, but
that fall is considered by most people to be temporary in nature
(for example, three months of terrible winter storms).
• According the Goods-Money Framework, we should expect a
fall (albeit temporary) in the general value level VG and real
output q as the aggregate demand curve shifts to the left. But
what about the value of money? Should this temporary lull in
economic activity lead to reduced demand for money and a fall
in the absolute market value of money? The view of The Enigma
Series is “no”. Money is a long-duration asset and the lull in
economic activity should have almost no impact on its value.
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What Happens to the Value of
the Financial Instrument?
• Let’s think back to the discussion in The Money Enigma about
causality between demand for money and its functions. The
traditional view suggests that demand for money is derived from
its functions: in this example, demand for money should fall as
there is less transaction demand for money. But this is a circular
view: “there is demand for money because it serves as a medium
of exchange, it is a medium of exchange because there is
demand for it”.
• Demand for money comes from its nature as a proportional
claim on output. In this scenario, the question that must be
asked is does the value of the financial instrument (money)
change significantly due to a temporary change in conditions.
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Reaction to a Temporary Decline
in Aggregate Demand
A fall in aggregate demand is perceived to be temporary. Real output
and the general value level fall. Money is a long-duration asset: there is
no change in long-term expectations and hence negligible change in VM .
The end result is the price level falls (p = VG /VM )
General Value Level
Value of Money
AS
Supply
VG,0
VM
VG,1
AD1
q1 q0
“No Change”
AD0
Real Output
264
D0 = D1
M
Money
Gervaise R. J. Heddle, 2014
Velocity of Money Falls as
Predicted by Keynesian Analysis
• So, what just happened? A naïve reading of the Simple Model
would suggest that the absolute market value of money should
move in lockstep with the general value level and real output:
VG × q
VM =
M ×v
• But in this scenario, the fall in the current levels of VG and q has
no impact on the value of money. Why? Because money is a
long-duration asset: most of its value is tied up in claims that are
expected to be made many years into the future. Rather, the
velocity of money term must adjust to “solve” the Simple Model:
the velocity of money falls as predicted by Keynesian analysis.
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Second Scenario:
A Nation at War
• In summary, traditional Keynesian analysis works well when
there is a change in economic conditions but little change in longterm expectations. But what about a reverse scenario where is no
change in current economic conditions, but a major shift in longterm expectations?
• Imagine this scenario: a country has been at war for six months,
people expect the war to finish soon but then a key battle is lost
and it becomes clear the war will rage on for several years to
come, a situation which will require a significant acceleration of
the growth rate in the monetary base (money is being printed to
finance the war). How will both sides of the framework react to
this scenario and what will be the impact on the price level?
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The Value of Money Falls as
Long-Term Expectations Shift
• On the left side of the framework, we will assume that there is
little impact on current economic activity: people at home keep
going about their daily business while the war rages on.
• What would you expect to happen on the right side of the
framework? While expectations of money base growth have
increased, there has been no actual increase in the monetary
base. Furthermore, there has been no change in real output or
the general value level. And yet, the market value of money
should decline. Why? Because the present value of money begins
to discount the lower expected future values of money: more
money in the future reduces the future proportional claim of
each unit of money and hence reduces money’s present value.
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Expected Money Growth Rate
Rises: The Value of Money Falls
The shift in long-term expectations has no impact on the goods market
(VG and q are unchanged). However, the shift in long-term expectations
drives down demand for money and the absolute market value of money
falls. As a result, the price level rises (p = VG /VM ).
General Value Level
Value of Money
Supply
AS
VM,0
VG
VM,1
D0
AD
q0
D1
Real Output
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M
Money
Gervaise R. J. Heddle, 2014
Using “Inflation Expectations”
to Explain the Result
• This second scenario is more difficult for traditional Keynesian
analysis to explain. However, it is a result that can be explained
by “expectations augmented” Keynesianism. In particular, it is a
result that can be explained by the New Keynesian “expectations
augmented Phillips curve”. From a New Keynesian (“NK”)
perspective, it could be argued that an expected increase in the
growth rate of money leads to an increase in inflationary
expectations which in turn leads to a higher level of inflation.
• While NK may get the same end result, it is the view of this
series that Keynesianism has been forced to adopt the rather
nebulous “inflation expectations” concept in order to adjust for
the fact that it doesn’t explicitly recognize the “value of money”.
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“Less Attractive as a Store of Value”
A Circular Argument
• The problem with “inflation expectations” analysis is that it
implicitly relies on a circular argument. In this scenario, the
traditional explanation would be something like this:
expectations of higher money growth lead to higher inflation
expectations which make money less attractive as a store of
value, therefore demand for money falls.
• Once again, the demand for money relies on one of its functions
(store of value). But money can only perform its functions
(including acting as a store of value) because there is demand for
it. The demand for money comes not from its functions, but from
its nature as a financial instrument. In this case, demand for the
financial instrument falls as its set of future values falls.
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Review of Scenarios
• Let’s quickly review our two scenarios. In the first scenario, there
is a change in current economic conditions (VG and q both fall),
but no change in the market value of money. In the second
scenario, there is a no change in current economic conditions,
but a significant fall in the absolute market value of money.
• The key takeaway from this analysis should be that any analysis
of the right side of the framework begins with an analysis of
long-term expectations. If there is no change in expectations,
then there is probably little change in the market value of money.
Alternatively, a small shift in expectations can have a big impact
on the value of money, even if there is no change in important
current variables such as real output q and base money M.
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The Value of Money Determined by
A Chain of Expected Future Values
• Admittedly, all of the preceding analysis is a bit high level, but it
is does serve to illustrate an important principle. Money is a longduration asset: the absolute market value of money depends on
perceptions of what the market value of money will be in the
distant future. More specifically, the value of a unit of money
today depends in large part upon how much output that unit of
money will be able to claim in various distant future periods.
• In essence, the current absolute market value of money
represents a chain of future values: if the expected future value of
money falls, then the current value falls. There are two related
ways to understand this concept, both of which are explored in
The Velocity Enigma.
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Section Review
• In summary, the view of The Enigma Series is that money is a
long-duration asset. In the short term, demand for money is
highly sensitive to changes in long-term expectations and
relatively insensitive to changes in current economic conditions.
The goal of the next paper in the series, The Velocity Enigma, is
to illustrate this theory by building a valuation model for money.
• More specifically, The Velocity Enigma develops an
expectations-based model for the market value of money: the
Discounted Future Benefits Model. The Discounted Future
Benefits Model can be used to demonstrate that the velocity of
money is, essentially, an “expectations term”: it is a variable that
is determined by a complex set of expectations.
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The Market for Goods
The Left Side of the Goods-Money Framework
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The Market for Goods:
Introductory Comments
• While the primary focus of The Enigma Series is the nature of
money and its role in price level determination, it is not possible
to explain short-term price level determination without some
understanding of the short-term behavior of the general value
level. The general value level VG is the critical numerator in the
Ratio Theory of the price level:
VG
p=
VM
• This final section of the paper proposes that the impact of
various economic shocks on the general value level can be
analyzed using an aggregate supply and demand framework.
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The Left Side of the Framework
LEFT SIDE OF
THE FRAMEWORK
• The Left Side of the
Framework is a short run
model of aggregate demand
and aggregate supply, where
both functions are expressed
in terms of the general value
level and real output.
“GOODS/SERVICES”
General
Value
Level
(EV)
Aggregate
Supply
VG
q
• The intersection of
aggregate demand and
aggregate supply determines
Aggregate
equilibrium levels of real
Demand
output and the general value
level.
Real Output
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Predictable Relationships Break
Down at the Macro Level
• Before we begin, let’s discuss the inherent problems of aggregate
supply and demand analysis. Frankly, it’s not clear whether
supply and demand diagrams should have any role in
macroeconomic analysis. The process of adapting the simple
and elegant microeconomic concept of supply and demand to an
aggregate level is a tortuous one at the best of times.
• The generic problem common to all aggregate supply and
demand schedules is that they imply the existence of consistent
and predictable relationships between macroeconomic variables.
Microeconomic supply & demand analysis “works” because the
relationships between price and quantity are “predictable”. But
these relationships are much more complex at the macro level.
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A Review of the the
Microeconomic Relationship
• As a reminder, the reason the relationships between price and
quantity supplied/demanded are predictable at a microeconomic
level is because, and only because, microeconomic supply and
demand analysis assumes the value of money to be constant.
Alfred Marshall, the developer of “scissors analysis”, explicitly
notes the constant value of money assumption in his Principles
of Economics [see Marshall (1890), Chapter III.IV.17-19].
• The true nature of the predictable relationship observed by
microeconomic analysis is not between the price of the good and
quantity, but rather between the absolute market value of the good
and quantity. Only by holding the value of money constant is the
price/quantity relationship in any sense “predictable”.
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Market Value vs Real Output:
A Predictable Relationship?
• Turning back to macroeconomics, aggregate supply and demand
analysis only “works” if there are consistent and predictable
relationships between the variable used on the y-axis (typically,
the price level or the inflation rate) and the variable used on the
x-axis (typically, real output).
• Macroeconomists have spent decades arguing for and against the
existence of such predictable relationships. In this regard, the
view of this paper is simple: such relationships are, at best,
tenuous. If there is any consistent relationship between the
overall market value of goods and real output, then it is between
the absolute market value of goods and real output, not the relative
market value of goods (the price level) and real output
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Towards a Better Model
• In a moment, we will begin to analyze why there might be
predictable relationships between the overall absolute market
value of goods (the general value level) and the quantity of real
output supplied and/or demanded. [This is not a straightforward
process: the fact that there is a predictable microeconomic
relationship between absolute market value and quantity
demanded/supplied does not automatically imply that this
relationship extends to the macroeconomic level.]
• However, before we begin that task, we will spend a little more
time considering why the traditional aggregate supply & demand
diagram (with the price level on the y-axis) is very limited in its
application and, frankly, somewhat misleading.
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The Price Level is a Noisy Signal
• Aggregate supply and demand as traditionally represented posits
that there are predictable relationships between the aggregate
quantity of goods demanded/supplied and the price level. This
must be the case in order for both functions (AD and AS) to be
derived in terms of the price level. The problem with this view is
that the price level is a very noisy signal.
• The price level contains an extraordinary amount of information
regarding not only present conditions in the goods market, but
information regarding future levels of money supply, real output,
expected nominal investment returns and other important
variables. Any of these disparate factors can influence the price
level.
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Aggregate Supply and Demand:
A Traditional View
• The aggregate supply &
demand diagram as
traditionally presented
implies that there is a
predictable relationship
between the price level and
both (1) the quantity of real
output supplied, and (2) the
quantity of real output
demanded.
TRADITIONAL REPRESENTATION
(“Old” Keynesian, not “New” Keynesian)
Price Level
AS
p
• The problem with this
traditional view is that not all
changes in the price level are
created equal.
AD
q
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Real Output
Gervaise R. J. Heddle, 2014
An Identical Response?
• We will further discuss the “noise” in the price level later in this
section of the paper, but for now we can break it down into one
simple observation: the price level contains information about
both the absolute market value of goods and the absolute market
value of money.
• The key question that needs to be answered is why economic
agents should respond in the same manner to a rise in the value
of goods as they do to a fall in the value of money? Both of these
events cause the price level to rise. But, prima facie, there is no
obvious reason to expect an identical set of macroeconomic
responses to these two very different events. Let’s illustrate this
point by considering both aggregate functions.
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Aggregate Demand:
Price and Real Output
• In regard to the aggregate demand function, traditional analysis
has a reasonable story to tell: the “wealth effect”. As the price
level rises, people feel less wealthy (assets such as money and
bonds are now less valuable in real terms) and spend less.
• Arguably, it doesn’t matter whether the price level rises due a
higher market value for goods or a lower market value for money:
either way, people feel less wealthy. But it does matter if one
impact is generally assumed to be “cyclical” while the other is
assumed to be “trending”. If changes in the general value are
generally assumed to be cyclical (temporary in nature), while
changes in the value of money are assumed to be trending, then
we might expect very different reactions to changes in each.
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Aggregate Supply:
Price and Real Output
• This rather difficult point is more easily illustrated in relation to
the aggregate supply curve. The traditional short-term aggregate
supply curve states that as the price level rises, economic agents
will supply a greater level of real output. (Traditional analysis
has always struggled with the derivation of the short run AS
function, inevitably relying on inefficient market explanations.)
• Philosophically, if output is absolutely more valuable, then it
makes sense for people to work harder to supply it and hence
real output will increase. But if something is only relatively more
valuable, it is only more valuable in the sense that the item
received in exchange (money) is less valuable, then it is not clear
why a similar “work harder” response should be elicited.
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The New IS-LM Model:
Brief Comments
• Clearly, these are difficult and contentious issues. Furthermore,
modern macroeconomics no longer posits such relationships
between the price level and real output. Rather, the modern
representation of aggregate supply and demand has the rate of
inflation, not the price level, on the y-axis.
• We are not going to spend much time discussing the “New ISLM Model” (King, 2000) interpretation of AD/AS in this paper.
The validity of the New IS-LM Model as a model of inflation is
touched on in the final section of The Velocity Enigma.
However, the view of The Enigma Series is that the relationships
between inflation and real output as described by the New ISLM Model are tenuous at best.
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Microeconomics Provides a
Good Starting Point
• It is the contention of this paper that if there is any predictable or
consistent relationship between the overall market value of goods
and real output, then it is between the absolute market value of
goods and real output, not the relative market value of goods (the
price level) and real output. [Nor is there a consistent
relationships between the rate of change in the relative market
value of goods (inflation) and real output].
• This notion starts from a simple observation: there is more likely
to be a consistent macroeconomic relationship between two
aggregate variables if there is a consistent microeconomic
relationship between similar non-aggregated variables. At the
very least, this seems like a reasonable starting point.
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Towards an Alternative
Aggregate Supply/Demand Model
• As discussed, the predictable microeconomic relationships
between price and quantity supplied/demanded only exist to the
degree that the value of money is assumed to be constant. The
better way to represent these relationships is to remove the value
of money altogether and express the analysis solely in terms of
the absolute market value of the good (the y-axis measure is
“units of economic value”, not dollars).
• Similarly, in a macroeconomic context, our starting point for
aggregate supply and demand analysis should be removing the
value of money from the analysis and exploring whether both
aggregate functions can be expressed in terms of absolute market
value (the general value level) and real output.
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The Left Side of the Framework
• The view of this paper is
that there are consistent and
predictable short-term
relationships between the
general value level and the
level of real output
demanded and supplied.
LEFT SIDE OF
THE FRAMEWORK
“GOODS/SERVICES”
General
Value
Level
(EV)
Aggregate
Supply
VG
q
• In the short term, an
increase in the general value
level will lead to a reduction
Aggregate
in real output demanded and
Demand
an increase in real output
supplied.
Real Output
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Derivation of AD/AS Functions
in General Value Level Terms
• There are several possible reasons for the respective slopes of the
short-term aggregate supply and demand functions. Rather than
addressing all of these arguments, this paper will focus on one
explanation that has potentially interesting implications. In
particular, it will be argued that the respective slopes of these
aggregate functions may be explained by rational expectations of
cyclicality and mean reversion in the general value level.
• The view of this paper is that people tend to regard sudden
short-term changes in the general value level as “temporary” in
nature and behave accordingly. In order to understand this, it
helps to consider and contrast the potential sources of volatility
in both the price level and the general value level.
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The Two Components of
the Price Level
• In order to begin this exercise, let’s start by trying to analyze
potential sources of volatility in the price level. Ratio theory
states that the general price level can be calculated as:
p = VG / VM
Where
p is the general price level
VG is the general value level
VM is the absolute market value of money
• As discussed earlier, the price level is a noisy signal that contains
information about both the value of goods and the value of
money. Furthermore, the volatility in the price level is a function
of not two, but three variables.
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The Three Components of
Variance in the Price Level
• Technically, the variance of the price level can be broken down
into three components:
• The variance of the general value level Var(VG );
• The variance of the abs. market value of money Var(VM ); and
• The covariance of the two variables Cov(VG ,VM ).
• In simple terms, volatility in the price level is caused by both
volatility in the general value level and volatility in the value of
money. To the degree that these two variables (VG and VM ) are
positively correlated, then the volatility in one series may
somewhat offset the volatility in the other series such that the
overall volatility of the price level is not as high as it would be if
both were completely independent variables.
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Price Level Volatility
• It is the view of this paper that by extending Ratio Theory
[p=VG /VM ], we can say that volatility in the price level is due
to a combination of a relatively low volatility numerator (the
general value level) and a possibly higher volatility
denominator (the market value of money), with the overall
volatility dampened somewhat by a positive correlation
between the numerator and the denominator as suggested by
the Simple Model.
• While this may be interesting in and of itself, the question we
need to address is how do economic agents react to volatility in
the general value level. To answer this question, we need to
isolate the probable source of such volatility.
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Volatility in the Value of Money
• In order to isolate the source of volatility in the general value
level, it helps to think about the probable sources of volatility in
the price level and the market value of money so that we can
separate these from our discussion on the general value level.
While this exercise is a little premature, we can make a few
preliminary observation regarding possible drivers of volatility
in the absolute market value of money from our earlier
discussions regarding the nature of money.
• As discussed earlier, money is a long-duration financial
instrument. Long-duration financial instruments are more
volatile than short-duration instruments (i.e., small shifts in
long-term expectations have a big impact on their value).
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Current Conditions Have Little
Impact on Value of Money
• In simple terms, the absolute market value of money should be
driven primarily by expectations of long-term growth in both
real output and the money supply. Short-term changes in the
levels of real output and money supply should, in theory, have
little impact on the value of money. Indeed, such short-term
changes in these levels should only significantly impact the value
of money if they alter future expectations.
• Since price level volatility is driven, in large part, by volatility in
the market value of money, we can begin to see how “noisy” the
price level signal is. Volatility in the price level signal is driven in
no small part by changing expectations about distant future
levels of real output and money supply.
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General Value Level is a
“Clean Signal”
• In contrast, volatility in the general value level is driven primarily
by current conditions and short-term expectations. In general
terms, volatility in the absolute market value of any particular
good today has very little do with distant expectations of supply
and demnad for that good. If an apple crop fails, the market
value of apples rises. It doesn’t matter that next year there may
be an abundance of apples: the absolute market value of the
good is largely determined by the “here and now”.
• Unlike the price level, the general value level provides a clear
signal of current “tightness” in goods and services markets.
Volatility in the value level is driven solely by changes in supply
and demand for goods, not supply and demand for money.
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What Drives the Correlation
Between Individual Goods Markets?
• While changes in the general value level may provide a clean
signal of changes in the overall demand and supply for
goods/services, it is important to note that the level of volatility
in the general value level does not reflect the volatility in the
individual markets. Rather, volatility at the general value level is
primarily driven by correlation (covariance) between the
individual goods and services markets.
• In simple terms, an increase in the general value level is not
driven by a rise in the market value of apples or the market value
of oranges: it is driven by a rise in both. Major shifts in the
general value level only occur when the absolute market values
of many goods move in the same direction at the same time.
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Possible Sources of Volatility
in the General Value Level
• Finally, we come to the crux of the issue. Why should the
absolute market value of a large number of individual goods rise
or fall together at the same time? We have ruled out changes in
the value of money (these impact the price level, not the general
value level). So what are the other possible causes of this
correlation between individual goods/services markets?
• While not an exhaustive list, the obvious factors that could drive
an overall increase/decrease in the absolute market value of
many goods at the same time are:
• Economy Wide Productivity Gains (or Losses);
• Economic Shocks and Business Cycles; and
• Fiscal/Monetary Policy Cycles.
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Productivity May Drive Longer
Term Trend in Value Level
• One potential source of permanent adjustments in the general
value level is widespread productivity gains (or losses).
However, it is not clear whether such gains, in practice, really
make much impact on the general value level.
• In principle, broad based productivity gains should drive the
absolute market value of many individual goods lower over
time. However, this does not mean that the general value level
trends lower over time. Why? Firstly, new (high value) products
are continually entering the market. Secondly, economy wide
productivity improvements may lead to greater consumption of
high value products relative to low value products. (As the value
of goods falls, consumption “reweights” to higher value goods).
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Productivity Gains Are Not
a Major Source of Volatility
• It’s not clear whether the general value level should trend lower
or higher over time based on economy wide productivity
improvements. However, it does seem reasonable to suppose that
productivity improvements account for very little of the volatility
in the general value level.
• In general, economy wide productivity improvements occur at a
glacial pace. While it may be possible for any individual firm to
make a “step function” improvement in productivity in a short
period of time, general evidence would suggest that economy
wide productivity improvements tend to occur in continuous
small increments. Hence, it is unlikely that productivity accounts
for sudden gains or falls in the general value level.
300
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Shocks and Economic Cycles
Drive Value Level Volatility
• If productivity gains/losses are not a major source of volatility in
the general value level, then this leaves us with economic shocks,
economic cycles and policy cycles to explain the volatility in the
general value level.
• All three of these possible sources of volatility share one
important characteristic: the economic effects of each tend to be
regarded by rational economic agents as temporary in nature.
• While it is true that some shocks are permanent and some cycles
persist, the “economic world view” of most people is that the
economy moves in cycles (alternating periods of broad economic
strength and broad economic weakness).
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If Uncertain, the Expectations
Bias is “Temporary”
• If economic agents reasonably believe that much of the volatility
in the general value level is driven by temporary factors (shocks
and economic cycles), then this may impact the way they react to
movements in the general value level.
• For example, when there is a significant short-term rise in the
general value level it may be impossible for people to determine
with certainty whether the rise is due to temporary factors or
permanent factors. However, if the dominant expectation is that
movements in the general value level are primarily caused by
temporary factors, then people may respond ex ante as if the
variation is temporary adjustment, even if ex post it can be
demonstrated that the variation was permanent.
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General Value Level:
Mean Reversion Expectation
• If people rationally believe that changes in the general value level
are driven by temporary factors and react accordingly (even if there
is a level of uncertainty regarding whether changes in the general
value are temporary or permanent), then we can say that economic
agents respond to short-term changes in the general value level as if
it is a mean reverting series.
• In simple terms, if the general value level rises above recent
historical levels, then people expect that it will fall (revert to the
mean) in the near future. Conversely, if the general value level falls
significantly in a short period of time, then people expect that it will
rise in the near future. This set of rational expectations should have
a key role in shaping how people respond to changes in the general
value level.
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The General Value Level as a
Mean Reverting Series
Rational economic agents may expect most of the volatility in the
general value level to be driven by economic shocks and
investment/policy cycles. In that case, these agents may respond to
changes in the general value level as if it is a mean reverting series.
General
Value Level
Time
304
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Price Level Not Considered to be
a Mean Reverting Series
• It should be noted that the same analysis can not be directly applied
to fluctuations in the price level. As discussed, the price level is a
noisy signal. In particular, it is proposed that most of the volatility
in the price level is a result of volatility in the value of money, not
the value of goods.
• When the price level rises, it is just as likely (if not more likely) to be
due to a decline in the absolute market value of money rather than
any temporary cyclical/shock increase in the overall market value of
goods. Therefore, we can’t say that rational economic agents will
respond in the same manner to a rise in the price level as they would
to a rise in the general value level. More specifically, it seems very
unlikely that economic agents view the price level as a mean
reverting series.
305
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Derivation of Aggregate
Demand & Supply Functions
• Let’s return to the key objective of this section of the paper
which is the derivation of the aggregate demand and aggregate
supply functions as expressed in terms of the general value level
VG and real output q.
• If economic agents believe that the general value level is a mean
reverting series, then this has important implications for the
shape of both short run aggregate functions. Furthermore, not
only may it explain the respective slopes of the two functions,
but it might also explain why wages are “sticky” in an efficient
market. We will discuss this second point shortly as part of our
analysis of aggregate supply, but before we do this lets proceed
with the derivation of the aggregate demand function.
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Aggregate Demand
LEFT SIDE OF
THE FRAMEWORK
AGGREGATE DEMAND
General
Value
Level
(EV)
• It is proposed that the quantity
of real output demanded at any
point in time is a function of
the overall absolute market
value of goods (the general
value level).
• In the short term, as the overall
absolute market value of goods
Aggregate
falls, the quantity of real output
Demand
demanded increases. Hence, the
aggregate demand curve is
downward sloping.
Real Output
307
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Microeconomic Assumptions
No Longer Valid
• The first point that should be made is that micro assumptions
don’t apply at the macro level. The derivation of the demand
curve for an individual good in absolute market value terms relies
on two key assumptions, namely:
• The absolute market values of related goods are constant; and
• The absolute market value of labor (income) is constant.
• In the case of an aggregate demand curve, the first assumption
no longer applies: there is no substitution effect between goods
as the overall absolute market value of goods rises/falls.
Furthermore, we will no longer use the second assumption,
even though there is some basis for doing so. [It will be argued
later in this section that the absolute market value of labor is
sticky].
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Applying the Mean Reversion
Expectations Model
• While we can no longer use the microeconomic assumptions, we
can use our mean reversion expectations assumption to derive
the aggregate demand curve. Simply put, economic agents
respond to short-term changes in the general value level as if the
general value level is a mean reverting series.
• Let’s consider what the response of aggregate demand will be if
the general value level falls. We will assume that the absolute
market value of labor falls proportionally with the absolute
market value of goods/services (there is no change in real
wages). What is the response of consumers likely to be if they
believe the general value level is a mean reverting series and the
decline is temporary?
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Real Output Demanded Increases as
General Value Level Falls
• If consumers believe that the decline in the general value level is
temporary (or amidst uncertainty about whether the fall
represents a new permanent plateau, “hedge their bets” and treat
it to some degree as a temporary adjustment), then we should
expect the quantity of real output demanded to increase, even if
real wages have not changed.
• If economic agents believe that the general value level is mean
reverting and the absolute market value of goods, services and
labor will all rise again in the near future, then we should expect
an intertemporal substitution effect. All else equal, consumers
(and firms) should pull forward purchases of goods and services,
either drawing on their wealth balances or by accessing credit.
310
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Response to Discounting
• In response to a decline in the general value level, economic
agents will respond (at least for a while and all else equal) as if
the broader economy is “on sale”. Clearly, this is a short-term
response. At a microeconomic level, we know that consumers
respond strongly to genuine discounting. But if the discounting
becomes “permanent” (the store always has a “sale” sign in the
window), then the response may be negligible.
• Clearly, the “all else equal” assumption is critical to deriving the
slope of the function. If the decline in the general value level is
accompanied by a drop in consumer confidence or a fall in job
security, then these factors would shift the entire demand curve
to the left, which may negate the overall response of real output.
311
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A Rise in the Value Level
Reduces Real Output Demanded
• In the case of a rise in the general value level, we should expect
consumers to reduce the quantity of real output demanded in
the short term: why buy something now (in particular, a durable
good) if it’s market value is going to be lower in the near future.
• The most obvious case in point would be a supply shock (oil
crisis) that sends the absolute market value of all goods higher.
Even if we assume the absolute market value of labor rises such
that there is no change in real wages, it is reasonable to expect
that people will defer purchases if they believe that the situation
is temporary and the general value level will fall in the near
future. In summary, the aggregate demand curve is downward
sloping. Let’s now consider aggregate supply.
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Aggregate Supply
LEFT SIDE OF
THE FRAMEWORK
AGGREGATE SUPPLY
General
Value
Level
(EV)
Aggregate
Supply
• It is proposed that the quantity
of real output supplied at any
point in time is a function of
the overall absolute market
value of goods (the general
value level).
• In the short term, as the overall
absolute market value of
goods rises, the quantity of
real output supplied increases.
Hence, the aggregate supply
curve is upward sloping.
Real Output
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Should There Be Any Supply
Response to Higher Price Level?
• The microeconomic derivation of a supply curve for an individual
good is made easy by a raft of simplifying assumptions. Most
notably, the market value of inputs (labor and raw materials) are
constant. At a macroeconomic level, we simply can not assume
that the market value of inputs remains constant as the market
value of goods (the general value level) rises.
• This has always created a problem for macroeconomics. In
traditional terms, why should there be any supply response (any
increase in real output) if all prices rise simultaneously? If the
price level rises, the price of all inputs (including labor) should
rise by a similar amount: but if this happens, then there is no
incentive for firms to increase production.
314
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Attempts to Explain the
Upward Slope of SRAS Curve
• Inevitably, traditional macroeconomics has been forced to come
up with reasons for why, in the short term, the price of inputs
don’t rise (or rise as much as the price level). Ultimately, these
arguments would always have to resort to some sort of
“inefficient markets” view: either there were “timing lags” (input
prices didn’t rise as quickly), input prices were sticky due to
“nominal rigidities” or people were fooled by some sort of
“money illusion” (people didn’t realize that the higher prices
simply reflected a lower value of money).
• “Let’s assume that markets don’t work…” is not an ideal starting
point for economic analysis. So, let’s assume markets are efficient
and see if we can explain why some input prices are “sticky”.
315
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Workers May Not Respond To
The “Real Wage”
• One implication of the mean reversion expectations thesis of the
general value level is that, short term, the quantity of labor
supplied may not be responsive to changes in the real wage
(wage relative to the price of goods). Rather, the quantity of
labor supplied will highly responsive to the absolute market
value of labor. Why? Because the absolute market value of labor
is a better proxy for workers of the true value of their labor, as
measured in a long-term context, than the current “real” wage.
• The “real wage” is determined by the absolute market value of
labor today relative to the absolute market value of goods today.
But, how do workers adjust their behavior for the fact that the
absolute market value of goods is highly cyclical?
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The Real Wage is Not
Forward Looking
• The real wage w can be determined in either price or absolute
market value terms as:
w = pL p = VL VG
where
p is the current price level (nominal)
pL is the current wage level (nominal)
VG is the current general value level
VL is the current absolute market value of labor
• In either case, the real wage level is always determined by either the
current price level or current general value level. By definition, the
denominator is solely a measure of current conditions and does not
reflect expectations of future conditions. But workers make
decisions about how much labor to supply based not only on
current conditions but also expectations.
317
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Labor Responds to Changes in
Expectations Adjusted Real Wage
• If workers believe that the general value level is mean reverting,
then, in the short term, workers may effectively treat VG as a
constant. In this case, the “expectations adjusted real wage” w*
is calculated as:
w = VL VG
*
where
VG is the expected general value mean level
VL is the current absolute market value of labor
• In simple terms, the quantity of labor supplied may be far more
responsive to w* (the expectations adjusted real wage) than w
(the real wage). When the expectations adjusted real wage rises,
workers may be induced to work more hours (savings will have
greater purchasing power when the general value level returns to
the mean level).
318
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Temporary vs Permanent:
Perceptions Matter
• For the sake of simplicity, let’s assume the value of money is
constant and discuss the issue in dollar terms. Let’s consider the
possible reaction of labor to two alternative scenarios.
• In the first scenario, the price level rises and everyone believes
that it is a permanent rise in the price level (very unlikely to be
reversed). What would be the natural response by labor?
Obviously, it would be to demand higher nominal wages.
• However, if the price level rises and everyone believes that it is
only a temporary rise (it will be reversed in the near future), then
what is the response of labor? Clearly, there would be much less
pressure for wage rises in this second scenario.
319
Gervaise R. J. Heddle, 2014
Different Reactions
to Wage Rise
• Now, what would be the impact of offering higher wages in both
scenarios on the quantity of labor supplied (assume wages rise by
half as much as the rise in the price level, say 5% vs 10%)? In the
first scenario, workers would be discouraged from working. Real
wages have fallen and, more importantly, they have fallen
permanently.
• What about in the second scenario? The price level has risen
10%, but workers expect it to fall back to the original level.
Would the 5% rise in nominal wages lead to an increase in the
quantity labor supplied? Quite possibly. Workers can work harder
now at the higher wage rate, save and spend it later once the price
level falls back to the original level.
320
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Supply and Demand for Labor in
Absolute Market Value Terms
• There is a better way to illustrate this rather difficult concept and
that is by using a supply and demand diagram for labor where
supply and demand are expressed as functions of the absolute
market value of labor (in “units of economic value” terms).
• When expressed in absolute market value terms, the supply
function for labor assumes a certain future path for the general
value level. If the general value level rises, then we should expect
workers to demand higher wages, in absolute market value
terms, in order to compensate for this and the supply curve for
labor should shift upwards. However, the degree to which the
supply curve shifts upwards will depend upon whether workers
believe the change in the general value level is permanent or
temporary.
321
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Temporary vs Permanent:
Supply of Labor Responses
THE LABOR MARKET
• Let’s consider the labor market in
SP
absolute market value terms. Each Market
supply curve for labor assumes a Value (EV)
ST
certain future path for the general
S0
value level VG .
VL,1
• If there is a permanent increase in
VG , then the supply curve shifts to
VL,0
D1
SP . If there is a perceived
temporary increase in VG , the
supply curve shifts to ST . In the
D0
second scenario, the quantity of
labor rises (L0 to L1) even as real
Quantity
L0 L1
wages fall (%ΔVG > %ΔVL ).
of Labor
322
Gervaise R. J. Heddle, 2014
The Impact of Future Expectations
on Slope of Aggregate Supply Curve
We can see the impact on the slope of the AS curve if changes in the
general value level VG are generally perceived to be temporary (AST)
versus permanent (ASP). In rough terms, if the rise in VG is treated as
“permanent”, there is no opportunity for real output to increase.
General Value
Level (EV)
Market Value
of Labor (EV)
ASP
SP
S0
VG,1
VL,1
VG,0
VL,0
D1
AD
q0 = q1
D0
Real Output
323
L0 = L 1
Labor
Gervaise R. J. Heddle, 2014
Expectations of VG Mean Reversion
Allows SRAS to be Upward Sloping
If labor perceives that the given rise in the general value level VG is
temporary, then the labor supply curve shifts only modestly, allowing for
a more modest increase in the absolute market value of labor VL and
allowing real output q and the quantity of labor employed L to rise.
Market Value
of Labor (EV)
General Value
Level (EV)
ST
AST
VG,1
S0
VL,1
VG,0
VL,0
D1
AD
q0 q1
D0
Real Output
324
L0 L1
Labor
Gervaise R. J. Heddle, 2014
A Review of the Argument
• Let’s review the argument again. As the general value level rises,
the demand curve for labor shifts upwards (D0 to D1) as firms
seek to increase production. A simplistic “classical view” would
say that the supply curve for labor also shifts upwards by a
similar amount (S0 to SP): goods are more expensive (in EV
terms) and labor seeks to be compensated for this (in EV terms).
• This simple analysis ignores the impact of expectations. If
workers believe the increase in VG is permanent, then the
classical reading is probably correct. However, if workers believe
the rise in VG is temporary, then S0 moves only to ST . This opens
the door to an increase in the quantity of labor supplied and
higher real output, even though real wages have fallen.
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Two Important Implications
• This analysis of the labor market response to an increase in the
general value level has two important implications.
• The first implication is that the short run aggregate supply curve
is likely to be upward sloping. As the general value level rises, the
absolute market value of labor may rise by a smaller percentage
amount, allowing firms to increase production (real output rises).
• The second implication is that, in an efficient market, the absolute
market value of wages should fluctuate less than the general
value level. Translated back into dollar terms, this means that
nominal wages should appear to be “sticky” (the price level
should be more volatile than nominal wages).
326
Gervaise R. J. Heddle, 2014
Wages Appear to be Sticky
If workers believe the general value level VG is mean reverting, then the
labor supply function may only adjust modestly to variations in the
general value level, creating the impression that wages VL are “sticky”.
Economic
Value
Goods
Labor
VG
VL
Time
327
Gervaise R. J. Heddle, 2014
Labor Responds to Absolute Market
Value of Labor, Not Real Wage
If workers believe the general value level VG is mean reverting, then the
quantity of labor they supply may be more responsive to the absolute
market value of labor VL than the real wage (w = VL /VG ).
Economic
Value
WORK
LESS
WORK
MORE
VG
VL
Time
328
Gervaise R. J. Heddle, 2014
Labor’s Response to a Fall in the
General Value Level
• Before we discuss these implications in more detail, let’s consider
the response of the labor market and aggregate supply to a fall in
the general value level.
• When the general value level falls, the demand curve for labor
shift to the left (firms need to cut back on labor expenses in order
to remain profitable).
• The supply curve for labor shifts downwards: workers are willing
to accept lower “absolute market value wages” VL because the
overall absolute market value of goods VG has fallen. However,
the extent to which the labor supply curve shifts depends upon
whether workers believe the fall in VG is permanent or temporary.
329
Gervaise R. J. Heddle, 2014
General Value Level Falls:
Possible Labor Market Responses
• In response to a fall in VG
“classical” analysis might suggest
EV
that the supply curve for labor
moves to from S0 to SP . This may
VL,0
be the case if the fall in VG is
believed to be permanent.
VL,1
• However, if workers believe the
fall in VG is only temporary, then
the supply curve shifts to ST . The
quantity of labor supplied falls
(L0 to L1) even as real wages rise
(%ΔVG > %ΔVL ).
330
THE LABOR MARKET
S0
ST
SP
D0
D1
L1 L0
Quantity
of Labor
Gervaise R. J. Heddle, 2014
Shift in the Labor Supply Curve
May be Minimal
• The view of this paper is that workers will nearly always treat a
sudden shift in the general value level as a temporary event. In
other words, they believe that the general value level is a mean
reverting series.
• Therefore, when the general value level declines, they believe the
decline is only temporary (it will be reversed in the near future).
As a result, workers may offer their services at a slightly lower
rate (as measured in absolute market value terms), but they will
not offer their services at a much lower rate (as classical analysis
might suggest), especially if they know that they will have to fight
for a pay increase only a few months or years later when the
general value level reverses the recent fall.
331
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Side Note:
Lucas & Rapping (2001)
• It is worth noting that the preceding labor market analysis has
similarities with the labor market theory discussed in Lucas and
Rapping (2001). Lucas and Rapping propose that labor supply is
a function of both the real wage and the expected future real
wage (which is a function of the expected future nominal wage
and the expected future price level).
• In simple terms, their argument is that if the real wage is below
the expected or normalized real wage, then less labor is supplied
than might be suggested by the long run supply curve for labor.
This thesis is very similar to the view of this paper that, in the
short term, the supply of labor is more responsive to the
expectations adjusted real wage w* than the real wage w.
332
Gervaise R. J. Heddle, 2014
Short Run Aggregate Supply
Curve is Upward Sloping
• Let’s return to the derivation of the aggregate supply curve. If
workers believe that the decline in the general value level is only
temporary, then the labor supply response will be limited (the
labor supply curve shifts only slightly) and firms will be forced to
cut back on both employment and production. Therefore, as the
general value level falls, real output falls and the short run
aggregate supply curve is upward sloping.
• Wages appear to be “sticky”: the absolute market value of labor
does not fall as much as the general value level (with value of
money constant, nominal wages don’t fall as much as the price
level). Wages don’t fall to the degree that they would need to in
order to allow firms to maintain production at previous levels.
333
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Sticky Wages are a Result of
an Efficient Market Process
• Given that this paper is meant to be part of a thesis regarding the
nature and value of money (and not a treatise on labor
economics), this doesn’t seem like the right time to go into a
review of the historic literature on sticky wages and launch into
an entirely different discussion regarding the nature and causes
of “wage rigidity”.
• All that I will say for now is that the preceding analysis suggests
that sticky wages could simply be a result of a set of rational
expectations held by workers regarding the cyclical or mean
reverting nature of the general value level. The “nominal
rigidities” so often observed may simply be a reflection of an
efficient market process and not market inefficiencies per se.
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Gervaise R. J. Heddle, 2014
Relationship Between Real Wages
and Quantity of Labor Supplied
• Before we leave this topic, we need to consider an important
qualification to the analysis just presented. It is the view of this
paper that, all else equal, a negative demand shock will lead to a
shift along the supply curve which is upward sloping: the
quantity of labor supplied falls even as the real wage rises.
• This inverse relationship between the quantity of labor supplied
and the real wage is not “universal”. Remember, our analysis so
far has (implicitly) only focused on the response to a demand
shock (a shift along the aggregate supply curve). But what
happens if there is a negative supply shock? If there is a supply
shock, the quantity of labor supplied will fall as the real wage
also falls (the two variables are now positively correlated).
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Gervaise R. J. Heddle, 2014
Labor Market Response to
A Supply Shock (Oil Crisis)
• If there is an oil price shock, VG
will move higher as the aggregate
supply curve shifts upwards (not
illustrated).
• In the labor market, demand for
labor falls (D0 to D1). Also, the
supply curve for labor will shift
upwards (S0 to S1), even if only
slightly, due to the perceived
“temporary” rise in VG . The
quantity of labor supplied falls (L0
to L1) and the real wage falls (VL
falls slightly as VG rises).
336
THE LABOR MARKET
EV
S1
S0
D0
D1
L1
L0
Quantity
of Labor
Gervaise R. J. Heddle, 2014
The Cyclical Behavior of Real
Wages: Demand vs Supply Shocks
• To summarize, if people believe the general value level is mean
reverting, then this could help explain why (1) in the case of a
demand shock, real wages and the quantity of labor supplied are
inversely correlated, and (2) in the case of a supply shock, real
wages and the quantity of labor supplied are positively correlated.
• There is strong empirical evidence to support the notion that the
real wage “flip flops” from being countercyclical to procyclical.
Basu and Taylor (1999) find such evidence and discuss it in
broadly similar terms: “perhaps demand shocks lead to
countercyclical changes in real wages, in the spirit of traditional
Keynesian models, while supply shocks lead to procyclical
changes, in the spirit of real business cycle models” (pg. 19).
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Gervaise R. J. Heddle, 2014
The Output Gap and the
Aggregate Supply Curve
• Let’s return to our discussion regarding the nature of the aggregate
supply curve (as expressed in general value level and real output
terms). So far we have discussed a thesis regarding why the short run
aggregate supply curve is upward sloping as opposed to vertical.
However, we have not discussed the second derivative nature of the
aggregate supply curve. Is it reasonable to believe that the SRAS
curve steepens as real output increases?
• The view of this paper is that the output gap does have a role to play
in determining the shape of the aggregate supply curve. In
particular, the aggregate supply curve steepens as the economy
approaches “full employment”. The output gap plays a very
prominent role in most mainstream theories of inflation, so let’s take
one moment to consider its role in our analysis.
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Gervaise R. J. Heddle, 2014
Impact of the Output Gap on
The Left Side of the Framework
• The “output gap” impacts the
shape of supply curves for
underlying input goods (labor
“GOODS/SERVICES”
etc.). If underlying input supply
General
curves steepen as quantity
Value
Aggregate
Level
supplied increases, then the
Supply
(EV)
aggregate supply curve will also
steepen as real output increases.
LEFT SIDE OF
THE FRAMEWORK
VG
q
• The diagram opposite
incorporates the impact of the
Aggregate
output gap and provides a
Demand
possibly more realistic view of
the left side of the framework.
Real Output
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Gervaise R. J. Heddle, 2014
Output Gap Matters: Responses of Labor
to Increase in General Value Level
The diagram below illustrates how the slope of the labor supply curve
impacts the aggregate supply curve. In both cases, a rise in VG is considered
to be “temporary” and there is only a small shift in the labor supply curve
(S0 to S1). However, the slope of the supply curve does have an impact (as
labor supply curve becomes steeper, so AS curve must be steeper).
OUTPUT GAP: LARGE
EV
OUTPUT GAP: SMALL
Labor Market
EV
S1
S0
Labor Market
S1
S0
VL,1
VL,1
VL,0
D0
L0 L1
VL,0
D1
D0
L0 L1
Q(Labor)
340
D1
Q(Labor)
Gervaise R. J. Heddle, 2014
Aggregate Supply Curve Steepens as
Input Markets Tighten
• If labor supply is relatively elastic, then an increase in the general
value level and the accompanied increase in labor demand (as firms
try to take advantage of the higher general value level) will have the
net effect of a significant increase in the quantity of labor supplied,
a minimal effect on the absolute market value of labor (relative to
the general value level) and, consequently, a significant increase in
real output.
• However, if the labor supply curve steepens (becomes more
inelastic) as the labor market approaches “full employment”, then
the aggregate supply curve must also steepen (the increase in the
quantity of labor supplied in response to rise in VG is minimal and,
therefore, expansion in real output is constrained). This is still the
case even if the rise in VG is considered to be “temporary”.
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Gervaise R. J. Heddle, 2014
Concluding Remarks
• It’s time to draw this paper to a close. While we have covered a lot
of ground in this paper, we are still missing one final piece of the
puzzle. In order to fully understand the determination of the price
level, we need a better model for the market value of money.
• The problem with the right side of the Goods-Money Framework is
that supply and demand analysis is a “second best” solution for
analyzing the determination of the absolute market value of money.
Money is a financial instrument and, in common with all financial
instruments, its present market value is determined by a set of
discounted expected future benefits. The final paper in the series,
The Velocity Enigma, will derive a discounted future benefits model
for money and then we shall use all the tools at our disposal to
revisit the issue of inflation.
342
Gervaise R. J. Heddle, 2014
End of Paper
Next and final paper in the series: The Velocity Enigma
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Gervaise R. J. Heddle, 2014
References
• Anderson, Benjamin M., (1917), “The Value of Money”, New
York: Macmillan Company.
• Basu, Susanto, Alan M. Taylor, (1999), “Business Cycles in
International Historical Perspectives”, National Bureau of
Economic Research, Working Paper No. 7090, Cambridge MA.
• Jehle, Geoffrey A., Philip J. Reny, (2011), “Advanced
Microeconomic Theory”, Third Edition, Prentice Hall.
• Jevons, William Stanley, (1875), “Money and the Mechanism of
Exchange”, D. Appleton & Co., Chapter II “Exchange”.
• Keynes, John Maynard, (1935), “The General Theory of
Employment , Interest, and Money”.
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Gervaise R. J. Heddle, 2014
References
• King, Mervyn, (2001), “No Money, No Inflation – The Role of
Money in the Economy”, Economie Internationale, 4/2001 (no. 88),
p. 111-131.
• King, Robert G., (2000), “The New IS-LM Model: Language, Logic
and Limits”, Federal Reserve Bank of Richmond, Economic
Quarterly, Volume 86/3, Summer 2000
• Lucas, Robert E., Leonard A. Rapping, (2001), “Real Wages,
Employment, and Inflation”, Journal of Political Economy: 721-754.
• Marshall, Alfred, (1890), “Principles of Economics”, London:
Macmillan and Co., 8th edition, 1920.
• Mishkin, Frederic, (2012), “Economics of Money, Banking, and
Financial Markets”, 10th Edition, Prentice Hall.
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Gervaise R. J. Heddle, 2014
References
• Ricardo, David, (1823), “Note on ‘Absolute Value and Exchangeable
Value’, as published in “The Works and Correspondence of David
Ricardo, Vol. 4, Pamphlets and Papers 1815-1823, ed. Piero Sraffa
with the Collaboration of M.H. Dobb”, Indianapolis: Liberty Fund,
2005.
• Smith, Adam, (1776), “The Wealth of Nations”, Simon & Brown
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the Paper Credit of Great Britain”, Chapter II “Of Trade By Barter”,
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• Wallace, Neil, (2008), “The Classical Dichotomy”, Notes for
Undergraduate Monetary Theory, PennState, Department of
Economics website.
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