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Ratio Theory of the Price Level

Ratio Theory of the Price Level states that the price level is a relative measure of market value. More specifically, the price level measures the market value of the basket of goods in terms of the market value of money.

Mathematically, the price level is a ratio of two variables: the market value of the basket of goods divided by the market value of money.

The numerator is the market value of the basket of goods: all else remaining equal, as the market value of goods rises, the price level rises. The market value of the basket of goods can rise for all manner of reasons, but a couple of reasons might include a sudden increase in aggregate demand (“too much demand”) or a sudden decrease in aggregate supply (“supply shock”).

The denominator is the market value of money: all else remaining equal as the market value of money falls, the price level rises. The market value of money is poorly understood by modern economics because most economists don’t explicitly focus on the “value of money” as a factor in their equations. Indeed, the “market value of money” can only be isolated as a variable if market value is measured in terms of a “standard unit”, i.e. in absolute terms.

The key to appreciating Ratio Theory is understanding two microeconomic concepts: (a) the property of “market value” can be measured in both the relative and the absolute, and (b) every price is nothing more than a relative measurement of two market values, both of which can be measured in absolute terms. In this week’s post we will explore both of these microeconomic concepts and then extend them to develop a macroeconomic theory of price level determination, namely “Ratio Theory of the Price Level”.

Ratio Theory of the Price Level: A Useful Concept for Analysis

There are many competing theories regarding price level determination. Economists trained in the Keynesian school tend to believe that inflation is caused by “too much demand” and that one of the primary roles of the central bank is to manage the economy to ensure that it doesn’t “overheat”.

Monetarists tend to believe that “too much money” is the primary cause of inflation, although many monetarists seem to ascribe to a Keynesian transmission mechanism: “too much money” creates “too much demand” which leads to rising prices. Other economists believe that “too much government debt” is the primary cause of inflation, particularly severe inflation (Fiscal Theory of the Price Level).

Each of these schools of thought suffers from a rather narrow perspective regarding the way the economic world works. Economists have made countless efforts to improve these one-sided models by the inclusion of various “expectation terms”, but this has only led to more vague notions such as the idea that inflation is determined by “inflation expectations” (even if this is the case, what then determines “inflation expectations”?).

The view of The Money Enigma is that all of these schools of thought could improve their models by acknowledging what should be a simple notion: the price level is a ratio of two market values.

The price of a good, in terms of another good, is a relative expression of the market value of both goods. The price of a good, in money terms, is a relative expression of the market value of the good itself and the market value of money. Therefore, the price of the basket of goods, in money terms, (also known as “the price level”) is a relative expression of the market value of the basket of goods in terms of the market value of money.

In mathematical terms, the price level is a ratio: the price level is equal to the market value of the basket of goods (the numerator) divided by the market value of money (the denominator).

We can use this simple model of the price level to ask more probing questions about traditional theories of inflation. For example, does “too much money” create inflation because (a) it increases the level of economic activity and raises the market value of goods (V_G rises), or (b) increases the monetary base relative to economic output thereby reducing the market value of money (V_M falls)?

Similarly, does “too much government debt” lead to rising prices because the fiscal spending increases economic activity (V_G rises as there is “too much demand”) or because markets become fearful about the economic viability of society and the value of the fiat currency issued by that society falls (V_M falls)?

Ratio Theory also provides a good starting point for any “inflation versus deflation” debate. For example, does economic weakness lead to deflation? While economic weakness should put downward pressure on the market value of goods, the other side of the equation (which is often ignored by Keynesians) is what will happen to the market value of money if confidence in the long-term economic prospects of society begins to falter?

While all these questions represent interesting topics for discussion, the primary goal for this week is to explain the concepts behind Ratio Theory. In particular, most economists will probably struggle with the terms V_G and V_M in the equation above.

Both of these terms represent market value as measured in the “absolute”: V_G is the market value of the basket of goods as measured in absolute terms, and V_M is the market value of money as measured in absolute terms.

In order to understand what it means to measure the market value of a good in the absolute, we need to go back to basics and think about the different ways in which scientists can measure physical properties.

The Measurement of Market Value: Absolute versus Relative

The view of The Money Enigma is that “price” and “market value” are not the same thing. While some may believe that these terms are synonymous, there is a subtle but important distinction between the two.

“Market value” is a property possessed by an economic good. For any good to be exchanged in trade that good must be “valuable”, i.e. it must possess the property of “market value”.

The “price” of a good is not a property of that good. Rather, the price of the good is a way of measuring the property of “market value”. More specifically, price is a relative measure of the market value of a good: a price measures the market value of one good (the primary good) in terms of the market value of another good (the measurement good).

If price is a relative measure of market value, then this raises an interesting question: “Is it possible to measure market value in the absolute?”

In order to answer this question, we need to go back one more step and answer a more general question: “What does it mean to measure any property in the absolute?”

Fortunately, science has a well-established paradigm that distinguishes between the absolute measurement of a property and the relative measurement of a property.

The act of measurement is, by definition, an act of comparison. In this sense, all measurements could be considered to be “relative”. However, even though all measurements involve an act of comparison, scientists designated some measurements as being absolute while others are relative.

So, what does it mean to say that a measurement is “absolute”?

A measurement is considered to be “absolute” if we measure something compared to a “standard unit” of measurement.

What makes something a “standard unit” of measurement?

In order for something to perform as a standard unit for the measurement for a certain property, there are two key characteristics that thing must possess. First, it must possess that property. Second, it must be invariable in that property.

These are the two key characteristics of a standard unit of measurement, but there is a third characteristic that most standard units possess: most “standard units” of measurement are theoretical.

Let’s think about this in the context of a simple example: the measurement of height.

We can measure the height of a building in absolute or relative terms. For example, we can say that one building is twice as tall as another building. This is a relative measurement of height.

In contrast, we can measure the height of the building in absolute terms. In order to do this, we need a standard unit for the measurement of height, such as “feet and inches”. Feet and inches are standard units of height: they posses the property of height and they are invariable in that property. Therefore, if we measure the height of the building in feet and say it is 250 feet tall, then that is an absolute measurement of the height of the building.

What we should also note about this example is that feet and inches are theoretical units of measure. The length of one “inch” is not something that exists in nature. We made it up. We decided, on a fairly arbitrary basis, that the length of one inch is “about that much”.

This is true of most standard units of measure: one hour, one mile, one kilogram – they are all theoretical measures of a particular property that we made up to help us measure various physical properties.

Why are most standard units of measurement theoretical? The reason we use theoretical entities as standard units of measure is because nearly everything in nature is variable. By definition, we can’t use objects that are variable in a property as “standard units” of measurement for that property.

In summary, the key difference between an “absolute” and a “relative” measurement is the unit of measure being used. In the case of an absolute measurement, we use a “standard unit” of measure. Most standard units are theoretical units of measure and, importantly, they must be invariable in the property that they are measuring.

In contrast, a relative measurement is merely a comparison of one object (the primary object) with another (the measurement object): it does not require that the second object (the measurement object) is invariable in the property being measured.

Now, let’s return to the main topic at hand: the measurement of market value.

Can we measure the property of “market value” in the absolute? The answer is yes, at least theoretically. But in order to measure market value in the absolute, we need to create a standard unit for the measurement of market value.

Unfortunately, a standard unit for the measurement of market value must be theoretical in nature. Why? It must be theoretical because there is no real-life good that is invariable in the property of market value.

So, what is the key advantage of measuring market value in the absolute? By adopting a standard unit for the measurement of market value, we can now measure the market value of each good independently of the market value of other goods.

Let’s use a simple example: the price of apples in money terms. Let’s assume that the current price of apples is two dollars per apple. This ratio exchange implies that one apple is worth twice as much as one dollar.

Now, let’s assume that next year the price of apples rises to three dollars per apple. What can we say about the market value of apples and the market value of dollars?

What we can say for certain is that the value of one apple has risen relative to the value of one dollar. One apple is now worth three times as much as one dollar.

But what can we say about the value of apples? Has the value of apples risen or fallen? From the facts provided, we can’t answer this question. We know that the relative value of apples has risen, but we can’t say whether the absolute value of apples has risen or fallen.

The price of apples could have risen either because (a) the market value of apples rose, or (b) because the market value of money fell.

In order to know whether the price of apples rose because of (a) or (b) above, we need some way to measure the market value of each good independently from other goods. Our standard unit for the measurement of market value gives us a means to make this type of absolute measurement.

Price as a Ratio of Two Market Values

Introducing a standard unit for market value for the property of market value allows us to measure the market value of goods independently of each other. The key advantage of this approach is that it allows us to express price as a ratio of two market values.

The view of The Money Enigma is that price is a relative measurement of market value. This is hardly a new concept. Adam Smith in “The Wealth of Nations” (1776) seeks to explore the rules that “determine what may be called the relative or exchangeable value of goods”. While Smith may not have explicitly stated that “price is a relative expression of market value”, it was clear that Smith considered price to be “relative” in nature.

Nevertheless, what does it mean to say, “Price is a relative measure”?

In simple terms, if the price of an apple is two dollars, then this implies that the market value of one apple is twice that of one dollar. The money price of an apple is merely a measure of the market value of an apple relative to the market value of a dollar.

This is simple concept, but how do we express this in mathematical terms? The key is measuring the market value of apples and money independently using the standard unit of market value that we discussed earlier.

Let’s think about this in general terms.

If the market value of good A as measured in terms of our standard unit is denoted as V(A) and the market value of good B as measured in terms of the standard unit is denoted as V(B), then the price of good A, in good B terms, is merely the ratio of V(A) divided by V(B). The price of A, in B terms, can rise either because (1) the market value of A rises, or (2) the market value of B falls.

If “good A = apples” and “good B = money”, then we can say that the price of apples, in terms of money, depends on both the market value of apples and the market value of money.

Importantly, the market value of money is the denominator of the price of apples. All else remaining equal, if the market value of money falls, the price of apples, as measured in money terms, will rise.

Moreover, this is observation is true for every “money price” in the economy: the market value of money is the denominator of every money price in the economy.

The price of apples, the price of bananas, the price of milk… all of these prices, as expressed in money terms, are determined by both the market value of the good itself (apples/bananas/milk) and the market value of money. All else remaining equal, if the market value of money falls, then the price of all these goods, as measured in money terms, will rise.

We can take this one step further.

The price level is a hypothetical measure of the price of the “basket of goods”. In a simplified sense, the price level is an index of prices. If every price in that index is a function of a numerator (the market value of the good) and a denominator (the market value of money), then it follows that the price level itself is a function of a numerator (the market value of the basket of goods, denoted V_G) and a common denominator (the market value of money, denoted V_M). [The market value of the basket of goods V_G can be thought of as an output-weighted index of market values for the goods contained in the basket of goods, where market value is measured in terms of the standard unit.]

The Market Value of Money

Ratio Theory raises an interesting question. Namely, what determines the market value of money, the denominator of the price level?

Economics has largely failed to answer this question because most economists have failed to ask it. Mainstream economics does not have any variable called the “value of money” or the “market value of money” in its equations.

The reason for may not be obvious, but in essence, if you don’t recognize that market value can be measured in the absolute using a standard unit for the measurement of market value, then you can’t isolate the “value of money” as a variable.

Economists will talk about the “purchasing power of money”, but the purchasing power of money is a relative expression of the market value of money. The purchasing power of money is merely the inverse of the price level, itself a relative measure of market value.

The Enigma Series develops a theory of money that might be used to help think about the determination of the market value of money called “Proportional Claim Theory”. In essence, the view of The Enigma Series is that money is a long-duration, special-form equity instrument that represents a proportional claim on the future output of society.

Moreover, The Enigma Series uses this theory to develop a “valuation model” for money. Importantly, this valuation model is expressed in “standard unit” terms and is the first model to solve for the value of money as measured in the absolute. This valuation model for money can also be used to create expectations-based solutions for the price level, the velocity of money and foreign exchange rates.

Readers who are interested in exploring these concepts further should read “Money as the Equity of Society” and “What Factors Influence the Value of Fiat Money?”

If you would like to learn more about Ratio Theory, then please visit the Price Determination section of The Money Enigma or read The Inflation Enigma, the second paper in The Enigma Series.

Author: Gervaise Heddle, heddle@bletchleyeconomics.com

Supply and Demand for Money: Where Keynes Went Wrong

The notion that “supply and demand for money determines the interest rate” is an idea that seems innocuous and entirely plausible. In fact, it is a very dangerous and misleading idea: an idea that has sent the science of economics on an 80-year journey down the wrong path.

The fundamental problem with this Keynesian theory is that it implicitly denies a role for the market value of money in the determination of “money prices”. The view of The Money Enigma is that supply and demand for money determines the market value of money. In turn, the market value of money is the denominator of every “money price” in the economy. (As the market value of money falls, prices rise).

Let’s start with what should be a simple concept: “every price is a relative expression of the market value of the two items being exchanged”. Think about a simple trade in which two items are exchanged, for example, a certain amount of money for a certain number of apples. Both items being exchanged (apples and money) must possess the property of market value in order for a trade to occur (no is going to part with something of value for something that has no value).

The ratio of exchange of one item for another (also known as the “price” of the trade) depends upon the market value of the first good (apples) relative to the market value of the second good (money). For example, if an apple is three times as valuable as one dollar, then the price of an apple is three dollars.

If this theory of price determination is correct, then something must determine the market value of money. By far the best candidate for this role is supply and demand for money (or, more specifically, supply and demand for the monetary base).

Where Keynes went wrong is that he assumed that every price is determined by only one set of supply and demand. For example, he assumed that the price of apples is determined solely by supply and demand for apples. Therefore, supply and demand for money, to Keynes’ mind, doesn’t have a direct role to play in the determination of the price of apples.

The view of The Money Enigma is that this traditional model is wrong: every price is a function of not one, but two sets of supply and demand. In terms of our example, this means that the price of apples, in money terms, is determined by both supply and demand for apples and supply and demand for money.

In summary, supply and demand for money can determine only one of two things: either it can determine the interest rate (Keynesian view), or it can determine the market value of money (Money Enigma view). It can’t determine both. If you choose “the interest rate”, then implicitly you are denying any role for the value of money in the determination of money prices.

Liquidity Preference Theory: a Naïve and Dangerous Idea

Keynes’s liquidity preference theory states that supply and demand for money determines the interest rate. It is one of the core theories of modern economics and stands largely unchallenged in orthodox economics circles to this day.

The view of The Money Enigma is that liquidity preference theory represents a naïve and dangerous view about the nature of money and the role of money in the price determination process. Moreover, liquidity preference theory has only survived because microeconomics has failed to develop a sensible theory of universal price determination (a theory of price determination that can be applied to the determination of all prices, not just money prices).

We will explore these assertions in more detail in a moment. But first, let’s step back to the year 1935, the year John Maynard Keynes wrote “The General Theory of Employment, Interest, and Money” and think about why Keynes might have come up with the notion that supply and demand for money determines the interest rate.

Keynes was a student of the great economist Alfred Marshall. Although Keynes never officially graduated with an economics degree, he did do one term of postgraduate work with Marshall and it was Marshall that gave Keynes the job lecturing in monetary economics at Cambridge when Keynes finished his short 18-month stint as a clerk at the India Office. (See Robert Skidelsky’s fawning biography of Keynes titled “John Maynard Keynes: Economist, Philosopher, Statesmen”, page 125).

You might think that someone with such limited qualifications shouldn’t be teaching economics at Cambridge. But, as fairly noted by Skidelsky, there really wasn’t much economics to teach at that point in time. [Or at least there wasn’t much “English” economics: there was quite a bit of “German/Austrian” economics that had been written but most respectable English gentlemen in the 1930s weren’t that interested in what the Germans had to say].

For those studying economics at Oxford or Cambridge in the 1930s, there were only a small number of books that would have been considered “required reading”. One of those books was Alfred Marshall’s “Principles of Economics”.

Marshall’s “Principles of Economics” is an important book in the history of economics because that book, more than any other, was instrumental in popularizing the supply and demand diagram that we use today. Marshall’s supply and demand diagram, with “price” on the y-axis, remains one of the most fundamental concepts in economics today and Keynes would have been well versed in this theory.

The problem is that the modern-day interpretation of Marshall’s work presents a very one-sided view of the price determination process. Marshall appreciated that his representation of price determination, the standard supply and demand diagram that we use today, implicitly assumes a constant or uniform value for money.

In Chapter III.IV.17-19, Marshall discusses the issues with his derivation of the standard demand curve: “So far we have taken no account of the difficulties in getting an exact list of demand prices… To begin with, the purchasing power of money is constantly changing, and rendering necessary a correction of the results obtained on our assumption that money retains a uniform value” (my emphasis added in italics).

At least superficially, Marshall seemed to appreciate that the standard supply and demand diagram that we use today assumes a constant market value for money. However, a naïve view of Marshall “scissors analysis” is that the price of a good is determined solely by supply and demand for that good.

The naïve view of Marshall’s work leaves open an obvious question: if supply and demand for a good determines the price of a good, then what does supply and demand for money determine?

For Keynes, the most obvious answer to this question was “supply and demand for money determines the interest rate”. It’s the obvious answer and it is wrong.

The problem is that Keynes has implicitly assumed that a price is determined by only one set of supply and demand. For instance, if supply and demand for apples determines the price of apples, then supply and demand for money must determine something else.

The problem with this theory is that it does not recognize the notion, as implicitly acknowledged by Marshall, that every price depends on not only the market value of the good in question, but also the market value of money.

Unfortunately, Marshall failed to take his work one step further. Namely, if price is a relative expression of the market value and market value is determined by supply and demand, then every price must be determined by two sets of supply and demand.

Keynes never entertained the notion that price is determined by not one, but two sets of supply and demand. Therefore, he never considered the idea that supply and demand for money determines the market value of money, which, in turn, is the denominator of every money price in the economy.

The view of The Money Enigma is that the “money price” of a good (the price of a good in money terms) is a function of both supply and demand for the good itself and supply and demand for the monetary base. This concept is illustrated in the slide opposite.

The key to this diagram, as we will discuss in a moment, is the y-axis unit of measurement. “Market value” on the y-axis is measured in absolute terms, using a “standard unit” for the measurement of market value.

Every Price is Determined by Two Sets of Supply and Demand

As young economists, we are all taught the price of a good is determined by supply and demand for that good. So, how is it possible for a price to be determined by two sets of supply and demand? This is a good question and one that we have discussed in several previous posts including “A New Economic Theory of Price Determination”, “Every Price is a Function of Two Sets of Supply and Demand” and “Is the Price of Apples Determined by Supply and Demand for Bananas?”

I find that the easiest way to explain this theory is to use a simple example.

Consider the following question: “In a barter economy, what determines the price of apples, where the price of apples is measured in terms of bananas?”

Is it (a) supply and demand for apples, or (b) supply and demand for bananas?

The answer is (c), “both”.

Clearly, the price of apples, in banana terms, depends upon supply and demand for apples: if there is a supply shortage of apples, then the market value of apples will rise and the price of apples, as measured in banana terms, will rise.

But what about supply and demand for bananas? Does supply and demand for bananas have any impact on the price of apples as measured in banana terms?

The short answer is “yes”. Imagine you live in that barter economy and then think about what happens if there is a supply shortage of bananas.

If there is a supply shortage of bananas, then bananas become “more valuable”. If you have bananas and bananas become more valuable, then you would expect more apples for every banana that you sell.

The ratio of exchange, apples for bananas, will shift such that there are more apples required for one banana. One way to say this is that the price of bananas, in apple terms, would rise. The other way to say this is that the price of apples, in banana terms, would fall. A decrease in banana supply will, all else remaining, lead to a fall in the price of apples, where that price is measured in banana terms.

The general principle is illustrated in the slide opposite. The market value of the “primary good”, denoted as “V(A)”, is determined by supply and demand for the primary good. The market value of the “measurement good”, denoted as “V(B)”, is determined by supply and demand for the measurement good. The price of the primary good, in terms of a measurement good, is determined by the market value of the primary good relative to the market value of the measurement good.

What Keynes missed is that this principle also applies to the determination of “money prices”. The price of a good, in money terms, depends upon both the market value of the good (as determined by supply and demand for that good) and the market value of money (as determined by supply and demand for money).

On the left hand side, supply and demand for the good determines the market value of the good. On the right hand side, supply and demand for the monetary base determines the market value of money. The price of the good, in money terms, depends upon the numerator (the market value of the good) and the denominator (the market value of money). If the market value of money falls, then, all else remaining equal, the price of a good, in money terms, will rise.

First time readers may have trouble interpreting some of these diagrams. The key to appreciating these diagrams is getting your head around the y-axis unit of measurement.

Traditional supply and demand diagrams use price on the y-axis: “price” is a relative measure of market value. The diagrams above use a “standard unit” for the measurement of market value: in this sense, supply and demand in the diagrams above are plotted in terms of “absolute market value”.

This is a complex subject that is addressed in detail in “The Measurement of Market Value: Absolute, Relative and Real”. Please read this post if you really care about this subject.

Conclusion

So, where did Keynes go wrong?

The short answer is that Keynes assumed that a price is determined by only one set of supply and demand.

By assuming that supply and demand for money can have no direct role in the determination of “money prices”, Keynes was forced to look for something that supply and demand for money could determine. The obvious candidate may seem to be “the interest rate”, but this doesn’t make it right.

The view of The Money Enigma is that every price is a function of two sets of supply and demand. The price of a good in money terms is a relative expression of both the market value of the good and the market value of money. Therefore, the price of a good in money terms is determined by two sets of supply and demand: supply and demand for the good and supply and demand for money.

Supply and demand for money determines the market value of money, the denominator of every money price in the economy.

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