<p>Inflation <strong>by definition</strong> is a positive change in price level. You do not need to introduce money stock <span class="math-container">$M$</span> into a model for it to have inflation.</p>
<p>Note prices exist independently of money. Prices are fundamentally, as Bertrand pointed out, just exchange rates of one goods or service into another.</p>
<p>For example, a simple Philips curve is a model of inflation given by:</p>
<p><span class="math-container">$$\pi = \pi_e - \beta (Y-Y_n)+u$$</span></p>
<p>Where <span class="math-container">$\pi$</span> is inflation <span class="math-container">$\pi_e$</span> expected inflation, <span class="math-container">$Y$</span> is a real output, <span class="math-container">$Y_n$</span> is natural rate of output and finally <span class="math-container">$\beta$</span> is some parameter to be estimated and <span class="math-container">$u$</span> is some error.</p>
<p>While most economists believe money supply is one of several important factors that determines inflation (see Mankiw Macroeconomics pp 92), it is not necessary to include it in every model of inflation.</p>

CC BY-SA 4.0
2021-11-23T10:38:23.227Z
Most definitions of the price available on the web use the term "money". It would be helpful to mention that the meaning of a price here, is a rate of exchange of one commodity into another (so even barter economies have prices).
Bertrand
CC BY-SA 4.0
2021-11-23T11:58:14.650Z
@Bertrand thanks for pointing that out I will add that in
1muflon1
CC BY-SA 4.0
2021-11-23T13:13:07.073Z
@user253751 you can always pick some numeaire good, prices in economics do not require money. Measuring CPI for sure does but you can have theoretical concept of price level, where CPI would be some practical measure using for example US dollar as a numeaire good
1muflon1
CC BY-SA 4.0
2021-11-23T14:09:22.737Z
Thank you for your answer, muflon. I still have some confusion about the example in the video lecture, and I've edited my question accordingly.
user141240
CC BY-SA 4.0
2021-11-27T08:24:11.023Z
I read @user253751's comment as reasonable. Given changing prices, there exists a numeraire good such that all prices are weakly inflationary and also a numeraire good such that all prices are weakly deflationary. To claim inflation is therefore to make a claim on a numeraire good. We can argue "how money" is this good, but if it's denominating prices... In other words, the current concern about inflation in the US disappears if you denominate prices in used cars.
kyle
CC BY-SA 4.0
2021-11-23T08:09:24.763Z
2021-11-23T12:02:53.893Z
2021-11-23T12:02:53.893Z
1muflon1
<p>&quot;Price&quot; implicitly refers to money. The price of a good is the amount of money you exchange for it.</p>
<p>&quot;Price&quot; <em>could</em> refer to how much of good A you exchange for good B. <em>However,</em>  then it makes no sense to talk about inflation, because the situation is symmetrical. If good B is getting more expensive measured in units of good A (inflation), then we could just as well say that good A is getting cheaper measured in units of good B (deflation), cancelling it out. To break the symmetry, and define an inflation amount that isn't zero, we'd need to select <em>one</em> good to measure all our prices in, and that good would be called money.</p>

CC BY-SA 4.0
2021-11-23T13:26:17.270Z
“we’d need to select one good to measure all our prices in, and that good would be called money”. - this is incorrect that good would not be called money **in economics**. That would just be a numeaire good. A money **in economics** has to be simultaneously: 1. Medium of exchange 2. Unit of account and 3. Store of value. **by definition of money** money has to satisfy 1-3, not just one. Using a good as a numeaire just satisfies 2 not 1, and 3 so **by definition you are not describing money**.
1muflon1
CC BY-SA 4.0
2021-11-23T14:01:04.757Z
Inflation in *relative* prices against numeaire good does make sense. But in the example in the video lecture, there is only one good. The confusing part is, he defined inflation in terms of prices of that one good!
user141240
CC BY-SA 4.0
2021-11-23T12:53:54.173Z
2021-11-23T12:53:54.173Z
Criticize SE actions means ban
<p>I'm watching the video lectures of <a href="https://www.youtube.com/playlist?list=PLEDC55106E0BA18FC" rel="nofollow noreferrer">Financial Theory (ECON 251)</a> by John Geanakoplos, Yale University. In <a href="https://www.youtube.com/watch?v=IVxmtb3zTlk&amp;list=PLEDC55106E0BA18FC&amp;index=6&amp;t=2021s" rel="nofollow noreferrer">Lesson 5, Chapter 4 at 33:41</a>, Geanakoplos defined inflation as the ratio of prices between two periods. There was no metion of money in his model whatsoever.</p>
<p>On the other hand, macroeconomic theory textbooks usually introduce money first before inflation. Only after incorporating money into macroeconomic models would they start to discuss about inflation. They then would go on to derive the <em>relation between inflation and money supply</em>.</p>
<p>What happened to money in Geanakoplos' model? How come there was inflation in a model with no money? Did I misunderstand something?</p>
<p><strong>Edit:</strong>
I know that we can talk about inflation in terms of <em>relative</em> prices against some numeraire good when there is no money. However, in the example provided by Geanakoplos in the video lecture, there was a single good, which is called &quot;apple&quot; by Geanakoplos. The confusing thing is, he defined inflation as the two-period ratio of the prices of an &quot;apple&quot;, the only good in the economy! In such case, what is this ratio measuring? What is inflating exactly against what?</p>

CC BY-SA 4.0
2021-11-23T07:41:44.677Z
A model is a stand-in for reality. A ratio is just a measurement.
H2ONaCl
CC BY-SA 4.0
2021-11-23T07:50:18.787Z
I am not sure I understand what you are asking here. A phenomenon can be described without theorizing about its cause, so what exactly is surprising?
Giskard
CC BY-SA 4.0
2021-11-23T11:03:14.937Z
@Giskard If there is no money, prices can only be measured in units of goods, but then what exactly is inflating? I'm quite confused.
user141240
CC BY-SA 4.0
2021-11-23T19:06:40.347Z
Hyman Minsky, Stabilizing an Unstable Economy, argues that there are two classes of workers in the economy: consumption goods workers and investment goods workers. In non-monetary terms the investment goods workers take consumption goods output as their "wages" and/or "borrowing". If the production possibility frontier forces a tradeoff of C and I, for example C + I = CONSTANT, then a shift of employment from making C to making I will cause inflation or relative shortage of goods C for consumption by workers making C + I. This would be inflation without monetary allocation of output via wages.
SystemTheory
<macroeconomics><inflation><money-supply><financial-economics>
How come there is inflation in a model with no money?
user141240
# How come there is inflation in a model with no money?

(Asked by: username_0 on 2021-11-23)

I'm watching the video lectures of [Financial Theory (ECON 251)](https://www.youtube.com/playlist?list=PLEDC55106E0BA18FC) by John Geanakoplos, Yale University. In [Lesson 5, Chapter 4 at 33:41](https://www.youtube.com/watch?v=IVxmtb3zTlk&list=PLEDC55106E0BA18FC&index=6&t=2021s), Geanakoplos defined inflation as the ratio of prices between two periods. There was no metion of money in his model whatsoever.

On the other hand, macroeconomic theory textbooks usually introduce money first before inflation. Only after incorporating money into macroeconomic models would they start to discuss about inflation. They then would go on to derive the *relation between inflation and money supply*.

What happened to money in Geanakoplos' model? How come there was inflation in a model with no money? Did I misunderstand something?

**Edit:**
I know that we can talk about inflation in terms of *relative* prices against some numeraire good when there is no money. However, in the example provided by Geanakoplos in the video lecture, there was a single good, which is called "apple" by Geanakoplos. The confusing thing is, he defined inflation as the two-period ratio of the prices of an "apple", the only good in the economy! In such case, what is this ratio measuring? What is inflating exactly against what?

**Tags:** macroeconomics, inflation, money-supply, financial-economics
> **Comments:**
> **username_1**: A model is a stand-in for reality. A ratio is just a measurement.  
> **username_2**: I am not sure I understand what you are asking here. A phenomenon can be described without theorizing about its cause, so what exactly is surprising?  
> **username_0**: @Giskard If there is no money, prices can only be measured in units of goods, but then what exactly is inflating? I'm quite confused.  
> **username_3**: Hyman Minsky, Stabilizing an Unstable Economy, argues that there are two classes of workers in the economy: consumption goods workers and investment goods workers. In non-monetary terms the investment goods workers take consumption goods output as their "wages" and/or "borrowing". If the production possibility frontier forces a tradeoff of C and I, for example C + I = CONSTANT, then a shift of employment from making C to making I will cause inflation or relative shortage of goods C for consumption by workers making C + I. This would be inflation without monetary allocation of output via wages.  

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## 2 answers

### Answer by username_4 on 2021-11-23. Score: 3

Inflation **by definition** is a positive change in price level. You do not need to introduce money stock $M$ into a model for it to have inflation.

Note prices exist independently of money. Prices are fundamentally, as Bertrand pointed out, just exchange rates of one goods or service into another.

For example, a simple Philips curve is a model of inflation given by:

$$\pi = \pi\_e - \beta (Y-Y\_n)+u$$

Where $\pi$ is inflation $\pi\_e$ expected inflation, $Y$ is a real output, $Y\_n$ is natural rate of output and finally $\beta$ is some parameter to be estimated and $u$ is some error.

While most economists believe money supply is one of several important factors that determines inflation (see Mankiw Macroeconomics pp 92), it is not necessary to include it in every model of inflation.

> **Comments:**
> **username_5**: Most definitions of the price available on the web use the term "money". It would be helpful to mention that the meaning of a price here, is a rate of exchange of one commodity into another (so even barter economies have prices).  
> **username_4**: @Bertrand thanks for pointing that out I will add that in  
> **username_4**: @user253751 you can always pick some numeaire good, prices in economics do not require money. Measuring CPI for sure does but you can have theoretical concept of price level, where CPI would be some practical measure using for example US dollar as a numeaire good  
> **username_0**: Thank you for your answer, muflon. I still have some confusion about the example in the video lecture, and I've edited my question accordingly.  
> **username_6**: I read @user253751's comment as reasonable. Given changing prices, there exists a numeraire good such that all prices are weakly inflationary and also a numeraire good such that all prices are weakly deflationary. To claim inflation is therefore to make a claim on a numeraire good. We can argue "how money" is this good, but if it's denominating prices... In other words, the current concern about inflation in the US disappears if you denominate prices in used cars.  

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### Answer by username_7 on 2021-11-23. Score: 2

"Price" implicitly refers to money. The price of a good is the amount of money you exchange for it.

"Price" *could* refer to how much of good A you exchange for good B. *However,* then it makes no sense to talk about inflation, because the situation is symmetrical. If good B is getting more expensive measured in units of good A (inflation), then we could just as well say that good A is getting cheaper measured in units of good B (deflation), cancelling it out. To break the symmetry, and define an inflation amount that isn't zero, we'd need to select *one* good to measure all our prices in, and that good would be called money.

> **Comments:**
> **username_4**: “we’d need to select one good to measure all our prices in, and that good would be called money”. - this is incorrect that good would not be called money **in economics**. That would just be a numeaire good. A money **in economics** has to be simultaneously: 1. Medium of exchange 2. Unit of account and 3. Store of value. **by definition of money** money has to satisfy 1-3, not just one. Using a good as a numeaire just satisfies 2 not 1, and 3 so **by definition you are not describing money**.  
> **username_0**: Inflation in *relative* prices against numeaire good does make sense. But in the example in the video lecture, there is only one good. The confusing part is, he defined inflation in terms of prices of that one good!  

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