# How come there is inflation in a model with no money?

I'm watching the video lectures of Financial Theory (ECON 251) by John Geanakoplos, Yale University. In Lesson 5, Chapter 4 at 33:41, 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?

• A model is a stand-in for reality. A ratio is just a measurement. Nov 23 '21 at 7:41
• 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? Nov 23 '21 at 7:50
• @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. Nov 23 '21 at 11:03
• If there's no preferred "money" good in which you measure prices, then if the price of bananas measured in coconuts goes up then the price of coconuts measured in bananas goes down, so the overall price level of "everything measured in everything" is the same. You would need to pick a good to be money and then you would have inflation or deflation depending on which good you picked. Nov 23 '21 at 12:48
• 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. Nov 23 '21 at 19:06

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.

• 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). Nov 23 '21 at 10:38
• @Bertrand thanks for pointing that out I will add that in
– 1muflon1
Nov 23 '21 at 11:58
• Exchange rates of which goods into other goods? You'll measure a different change in price level depending on which one you pick! Nov 23 '21 at 12:48
• @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
Nov 23 '21 at 13:13
• 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. Nov 23 '21 at 14:09

"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.

• “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
Nov 23 '21 at 13:26
• 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! Nov 23 '21 at 14:01