- Imagine that we live in a barter economy. What determines the price of apples in banana terms? Does the price of apples, in banana terms, depend upon (a) supply and demand for apples or (b) supply and demand for bananas?

- The correct answer is (c), “both”. The price of apples, in banana terms, depends upon both supply and demand for apples and supply and demand for bananas. In this week’s post, we will explain why this is the case and we will outline a novel method for illustrating this phenomenon.

- In last week’s post, “The Matrix of Prices in a Barter Economy”, we examined the theory that every price is a relative measurement of market value and explored the implications of this for price determination in a barter economy. In this week’s post, we will extend this concept and use a couple of simple examples to illustrate the principle that every price in a barter economy is a function of two sets of supply and demand.

- Intuitively, the notion that the price of apples in banana terms depends upon supply and demand for both apples and bananas is not that difficult: the ratio of exchange “apples for bananas” must be determined by market forces for both of the goods being exchange. The real trick with this theory of price determination is
*illustrating*the concept that every price is a function of two sets of supply and demand.

- In order to illustrate the theory that every price is a function of two sets of supply and demand, we need to appreciate the difference between the
*relative*measurement of a property and the*absolute*measurement of a property. More specifically, we need to introduce a “standard unit”, or “invariable” unit, of measurement for the property of market value. By adopting such a “standard unit” we can show, by example, how the price of one good, in terms of another, will react to changes in supply and/or demand for either of the goods.

**Two Questions, One Answer**

Let’s begin by contemplating two questions that relate to price determination in a barter economy.

*Question One*: What determines the price of *apples*, as measured in banana terms, in a barter economy?

At first glance, most students of economics will think that this is a very simple question. The vast majority of economics students would probably offer an answer along these lines: “The price of a good is determined by supply and demand for that good. Therefore, the price of apples is determined by supply and demand for apples.”

OK, let’s stick with that answer for a moment. Now, let’s ask our second question.

*Question Two*: What determines the price of *bananas*, as measured in apple terms, in a barter economy?

Once again, the most common answer to this question would be: “The price of a good is determined by supply and demand for that good. Therefore, the price of bananas is determined by supply and demand for bananas.”

At first sight, these might seem like reasonable answers to both of these questions. But if we dig a little deeper, we can see that a problem exists.

Let’s step back and think about the concept of “price”.

What exactly is the “price of apples in banana terms”? The price of apples in banana terms is merely a way of expressing the ratio of two quantities exchanged: a quantity of bananas for a quantity of apples. In essence, it is the number of bananas that must be exchanged for one apple in order for an exchange to occur in the current market environment. For example, the price of apples might be two bananas (if I want to buy an apple from you, I need to give you two bananas).

Now, let’s look at the other side of the picture. What is the “price of bananas in apple terms”? Once again, it is a ratio of exchange, “apples for bananas”. *Indeed, it is exactly the same ratio of exchange but simply stated in different terms.*

For example, if the price of apples is two bananas, then the price of bananas, in apple terms, is half an apple. Both described the same ratio of exchange: “two bananas for one apple” is exactly the same as saying “half an apple for one banana”.

**In more technical terms, the price of apples in banana terms is simply the reciprocal of the price of bananas in apple terms. Both are merely different ways of stating the same “ratio of exchange” between apples and bananas.**

Let’s return to the first question: “what determines the price of apples in banana terms?”

Is it correct to say that the price of apples, *in banana terms*, is determined solely by supply and demand for apples?

No. The market forces that determine the price of apples in banana terms must be the same as the set of market forces that determine the price of bananas in apple terms. Why? These two “different” prices are merely different ways of describing the same ratio of exchange.

So, how do we reconcile the notion that the price of apples, in banana terms, has something to with supply and demand for apples, while the price of bananas, in apple terms, has something to do with supply and demand for bananas?

There is a simple solution.

**The price of apples in banana terms depends upon both supply and demand for apples and supply and demand for bananas. Similarly, the price of bananas in apple terms depends upon both supply and demand for bananas and supply and demand for apples.**

In this way, the one ratio of exchange (apples for bananas) is determined by the same set of market forces (supply and demand for both goods). It doesn’t matter whether we state the ratio of exchange in apple terms or banana terms. The fact is that the ratio of exchange is determined by two sets of supply and demand: supply and demand for apples, *and* supply and demand for bananas.

**Illustrating Supply and Demand in a Barter Economy**

It is easier to understand the notion that price is determined by two sets of supply and demand if we illustrate the general concept and then perform a couple of simple examples. The general principle is illustrated in the slide below.

In simple terms, we can say:

- Supply and demand for apples determines the market value of apples;
- Supply and demand for bananas determines the market value of bananas;
- The price of apples, in banana terms, is the determined by the ratio of the two market values (the market value of apples divided by the market value of bananas);
- Therefore, the price of apples, in banana terms, is determined by both supply and demand for apples and supply and demand for bananas;
- [While it is not explicitly illustrated above, we can also say that the price of bananas, in apple terms, is determined by the ratio of the two market values (the market value of bananas divided by the market value of apples) and consequently by both supply and demand for apples and supply and demand for bananas.]

All else remaining equal, if the market value of apples *V(A)* rises, then the price of apples, in banana terms, will rise. Conversely, if the market value of bananas *V(B)* rises, the price of apples, in banana terms, will fall. (If bananas become more valuable, then you need fewer bananas to acquire the same number of apples).

This concept will become clearer as we explain it by use of example. But before we do, let’s quickly think about how it is possible to represent price as a function of two sets of supply and demand.

*The key is the unit of measurement used on the y-axis. More specifically, the diagram above measures market value on the y-axis in “absolute terms”, that is to say, in terms of a “standard” or “invariable” unit of market value.*

In nearly every supply and demand diagram, the y-axis unit of measurement is “price”. Price is a relative measure of market value: a price measures the market value of a primary good in terms of the market value of a measurement good.

If it is possible to measure a property on a *relative* basis, then it is also possible to the measure that same property on an *absolute* basis: if we can measure the property market value on a relative basis (as a “price”), then we can also measure the property of market value on an absolute basis.

What does it mean to measure something in the “absolute”?

This is a long subject that was addressed in detail in a recent post titled “The Measurement of Market Value: Absolute, Relative and Real”.

In simple terms, a measurement is considered to be “absolute” if we measure something compared to a “standard unit” of measurement. This begs the question, what is a “standard unit” of measurement?

In order for something to act as a standard unit of measurement it must possess two properties. First, it must possess the property that is being measured. Second, it must be invariable in the property that is being measured. (For example, “inches” are a standard unit for the measurement of length).

In the slide above, we assume that there is a “standard unit” for the measurement of market value. Once we have adopted this standard unit, we can illustrate supply and demand for apples in terms of this standard unit. As the market value of apples rises, the quantity of apples demanded falls and the quantity of apples supplied rises. The “equilibrium market value” of apples, *V(A)*, is determined by the intersection of supply and demand for apples.

Similarly, on the right hand side of our slide, we can illustrate supply and demand for bananas in terms of this standard unit. As the market value of bananas rises, the quantity of bananas demand falls and the quantity of bananas supplied rises. The “equilibrium market value” of bananas, *V(B)*, is determined by the intersection of supply and demand for bananas.

**The Price of Apples in Banana Terms**

Once we have illustrated supply and demand for both apples and bananas in terms of our standard unit for the measurement of market value, we can assemble a clearer picture regarding how the price of apples in banana terms is determined (or conversely, the price of bananas in apple terms).

We discussed the basic concept of “price” in a couple of recent posts, “The Matrix of Prices in a Barter Economy” and “A New Economic Theory of Price Determination”.

In essence, every “price” is nothing more than a relative measurement of market value. The price of one good (“the primary good”) in terms of another good (“the measurement good”) is determined by the market value of the primary good relative to the market value of the measurement good.

For example, suppose that I told you that one apple was twice as valuable as one banana. Question: what is the price of apples in terms of bananas?

If one apple is twice as valuable as one banana (in a “market value” sense), then someone must offer two bananas to purchase one apple. Therefore, the price of apples, in banana terms, is two bananas.

The price of the primary good (apples) in terms of the measurement good (bananas) is determined by the relative market value of the two goods. In this case, the market value of the primary good (apples) is twice that of the market value of the measurement good (bananas). Therefore, the price of the primary good (apples), in terms of the measurement good (bananas), is two units of the measurement good (bananas).

Mathematically, we can illustrate this as shown in the slide below. If we assume that *V(A)* is the market value of apples as measured in terms of our “standard unit” of market value, and *V(B)* is the market value of bananas as measured in terms of that same standard unit, then the price of apples in banana terms, *P(A _{B})*, is merely the ratio of

*V(A)*divided by

*V(B)*.

Now, let’s return to our earlier supply and demand diagram. Supply and demand for apples determines the market value of apples. Supply and demand for bananas determines the market value of bananas. *The price of apples, in banana terms, is simply the ratio of the market value of apples divided by the market value of bananas.*

**Two Simple Examples**

The theory that every price is a function of two sets of supply and demand is more easily explained by way of example. In this final section, let’s consider two scenarios and the impact of each on the price of apples, in banana terms, in our barter economy

** Scenario One:** what happens to the price of apples, in banana terms, if there is an increase in demand for apples?

If there is an increase in the demand for apples, then the demand curve for apples moves to the right. The *market value* of apples rises from *V(A) _{0}* to

*V(A)*. Furthermore, the price of apples, in banana terms, rises. In simple terms, if apples become more valuable relative to bananas, then the price of apples, in terms of bananas, will rise. (It will require more bananas to purchase the same amount of apples).

_{1}In the slide above, supply and demand in the apple market is measured in terms of our standard unit (in terms of “units of economic value” or “EV terms”). However, we can illustrate the market for apples in both “standard unit” terms (in terms of the *absolute* market value of apples) and in “price” terms (in terms of the *relative* market value of apples). In this example, we can see that we end up with the same type of result, no matter what unit of measurement we use on the y-axis: the demand curve for apples moves to the right as measured in both absolute and relative market value terms.

So far, so good: but what happens if there is a change in the banana market? How does a change in the banana market impact the price of apples?

** Scenario Two:** what happens to the price of apples, in banana terms, if there is an increase in demand for bananas?

If there is an increase in the demand for bananas, then the demand curve for bananas moves to the right. The *market value* of bananas rises from *V(B) _{0}* to

*V(B)*. Bananas are, to put it simply, “more valuable”.

_{1}Now, what happens to the price of apples where the price of apples is expressed in banana terms?

If there is no change in market value of an apple, *V(A)* is constant, then the price of apples, in banana terms, must fall. In simple terms, if apples become less valuable *relative* to bananas, then the price of apples, in terms of bananas, will fall. (It will require fewer bananas to purchase the same amount of apples because bananas are now “more valuable”).

Traditional supply and demand analysis (with “price” on the y-axis) struggles with this scenario. If there is “no change” in the market for apples, then how is possible for the price of apples to fall?

The answer to this question is illustrated below. Although there is no change in the *absolute* market value of apples, the *relative* market value of apples falls (the market value of apples relative to the market value of bananas falls). If apple prices are expressed in banana terms, then a rise in the market value of bananas will have the effect of shifting down both the supply curve for apples and the demand curve for apples.

The fact is that while there has been “no change” in the market for apples when measured in terms of a “standard” or “invariable” unit of market value, there has been a significant change in the market for apples when measured in terms of bananas.

**One Final Word**

The view of The Money Enigma is that *every* price is a function of two sets of supply and demand. The model we have discussed above applies not only to the determination of barter prices (“good/good prices”), but also applies to the determination of money prices (“good/money prices”) and foreign exchange rates (“money/money prices”).

Consider this point. What happens if instead of using bananas to buy apples in the examples above, we use money. Should the principle be any different? The answer is “no”: a good theory of price determination should be able to describe the determination of any type of price.

The view of The Money Enigma is that supply and demand for money (the monetary base) 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, all else remaining equal, the price level rise. This view sits in direct opposition to the traditional Keynesian view that supply and demand for money determines the interest rate.

This theory is covered in more detail in the Price Determination section.