<p>I think this question stems from misunderstanding from what inflation is. My best guess is that this happened because most macro books will say that inflation is a monetary phenomenon as in mainstream economics it is accepted that inflation over long periods of time is affected mainly by money supply. This is illustrated by equation of exchange (see Blanchard et al Macroeconomics an European Perspective) which is given by:</p>
<p><span class="math-container">$$P= MV/Y$$</span></p>
<p>This is the same equation that Brian also mentioned in his comment just solved for prices. Here <span class="math-container">$P$</span> are the average prices, <span class="math-container">$M$</span> money supply, <span class="math-container">$V$</span> velocity, and <span class="math-container">$Y$</span> real output. The standard textbook argument for inflation being monetary phenomenon goes like this. Velocity is assumed to change over business cycle but not really over long run and hence it cannot be responsible for all inflation and we can hold it constant. Moreover, real output tends to increase over time which should be deflationary. Hence the argument goes that over long run inflation should be caused by <span class="math-container">$M$</span>.</p>
<p>However, this does not mean that inflation is defined in terms of <span class="math-container">$M$</span>. The definition of inflation is simply the change in average prices for example:</p>
<p><span class="math-container">$$\pi_t= \frac{P_t-P_{t-1}}{P_{t-1}}$$</span></p>
<p>This is what inflation is. Moreover, inflation also is measure of how money looses value. The issue is that money especially in short run might not loose value just because there is more of it (i.e. by <span class="math-container">$M$</span> increasing) but also because velocity changing or real output dropping. Furthermore, <span class="math-container">$M$</span> and <span class="math-container">$V$</span> are not always independent. At zero lower bound any increase in <span class="math-container">$M$</span> will be offset by changes in <span class="math-container">$V$</span> because at zero lower bound peoples preference for holding (but not necessary spending) cash will be infinite (abstracting from issues such as storage costs for large sums of cash). What even more, models that are above simple undergraduate textbooks rely not just on actual values of <span class="math-container">$M$</span>, <span class="math-container">$V$</span> and <span class="math-container">$Y$</span> but also on peoples expectations of these (see <a href="https://www.brookings.edu/wp-content/uploads/1998/06/1998b_bpea_krugman_dominquez_rogoff.pdf" rel="nofollow noreferrer">Krugman 1998</a>).</p>
<p>Hence you simply cannot calculate how money looses its value from <span class="math-container">$M$</span>. At minimum to calculate change in <span class="math-container">$P$</span> using <span class="math-container">$M$</span>  you would need to know and control for not just what <span class="math-container">$M$</span> is but also what real output is and velocity is but here you will run into problem that real output is usually calculated by deflating nominal output by CPI - so you introduce the same problem you wanted to avoid. What even worse velocity itself is usually not directly observed but imputed from data. And this is all before we start factoring in all the expectations we should that are extremely difficult to measure. Compared to such convoluted way using CPI directly is far more sensible even if it may be imperfect measure.</p>

CC BY-SA 4.0
2020-08-18T15:36:22.493Z
2020-08-18T16:22:39.537Z
2020-08-18T16:22:39.537Z
1muflon1
<p>I gave a comment, but I just wanted to offer an intuitive example why we people normally do not use the money supply for this purpose. This is embedded in 1muflon1’s answer, but this might be easier to grasp (since there is a lot going on within P,Q).</p>
<p>Imagine that we have a country in which everyone just uses money to buy food. Food prices are constant, and everyone earns \$100/week, and everyone keeps \$10 as precautionary savings. All these numbers never change.</p>
<p>The money supply is \$10 per person.</p>
<p>The country has a 1%/year population growth rate. By implication, the money supply grows at a 1% annual rate.</p>
<p>If the prices for everything is constant, why does the expansion of the money supply imply a loss of purchasing power?</p>
<p>Closer to the real world situation, population has been growing - which is slowing now - while output per person is rising. This means that the economy can grow, even if there is no inflation. If people keep a fixed percentage of their income as money, then the money supply should grow. Once again, despite no price changes. To translate to 1muflon1’s answer, the Q term is expected to rise due to productivity and population growth, allowing for M to rise with V,P constant.</p>

CC BY-SA 4.0
2020-08-18T23:05:56.317Z
2020-08-18T23:05:56.317Z
Brian Romanchuk
<p>For example, how much is $25 million in 1790 considered today?  How do I update such value?  <strike>It doesn't make sense to me to use, say, price indices</strike>.  Shouldn't such update be done based on the expansion (or contraction) of monetary supply?</p>
<p><strong>Clarification post-comments</strong>.  My thinking --- please educate me if it is nonsensical --- is that inflation is an expansion of the monetary supply, so I would like to do a computation from the phenomenon of inflation itself, not of its effect, one of which is an increase in prices. So I would like to be able to estimate a loss of value merely from the the increase in monetary supply.  I could then compare it against real facts --- which would be the market prices.  I'd be willing to read an entire book just to learn how to do this.  So feel free to advise.  Thank you!</p>

CC BY-SA 4.0
2020-08-17T07:06:49.117Z
1. There is no "ideal" way, any method will have some problems.
Giskard
CC BY-SA 4.0
2020-08-17T07:07:32.863Z
2. Since most people use price indices (though they do not think them ideal) could you elaborate on why they do not make sense to you? Otherwise answers will probably recommend price indices.
Giskard
CC BY-SA 4.0
2020-08-17T12:35:50.070Z
If we had an imaginary equilibrium economy that had constant prices, per capita output, and product mix, yet the population was growing, the expectation (even by critics of the MV=PQ relationship, like myself) that the monetary base would grow in line with population. So even though prices are constant, your suggested measure would imply there was inflation.
Brian Romanchuk
CC BY-SA 4.0
2020-08-18T15:10:39.207Z
@Giskard, thanks for your request for clarification.  I didn't expect that you guys would think of price indices first.  I'm very inexperienced here.  My thinking is that there should be an estimation of the value of the money that's not taken by prices on the market.  I would like a price estimation merely out of the monetary supply.  Though this might be unreasonable, I would like to know a best-effort method that could be done.  I'm willing to read an entire book, so feel free to recommend.
user12406990
CC BY-SA 4.0
2020-08-18T15:14:07.320Z
@Giskard, let me elaborate on why it doesn't make sense to me.  Instead of saying "it doesn't make sense to me", I should've said it's not the only information I would like to see.  I would like to see a direct computation from the phenomenon of inflation itself, not of its effect.  I think of prices as an effect of inflation, not as inflation per se.  I would like to do a calculation that updates the value of an amount (say $25 million) merely based on the monetary supply.
user12406990
CC BY-SA 4.0
2020-08-18T15:18:16.740Z
"I would like to see a direct computation from the phenomenon of inflation itself, not of its effect." But inflation by definition is the change in average prices in time - thats not the 'effect' of inflation that is the inflation - its not like inflation is some sort of different concpet that then changes prices. Inflation $\pi$ is simply $\pi_t= \frac{P_t-P_{t-1}}{P_t}$ we can debate that CPI which is supposed to measure average prices $P$ is bad measure of $P$ and we can discuss different measures that we could use but that is what inflation is
1muflon1
CC BY-SA 4.0
2020-08-18T15:24:45.253Z
@1muflon1  In that case I'm using the wrong word.  Instead of trying to find a new one or correct my use of words, I can explain that I am assuming that an increase in monetary supply always causes a loss of currency-value and I would like to compute a measure of this loss from only the change in monetary supply.  Has any book ever done this?  I would like to see how they do it and what can be learned about it.  Thank you for your attention.
user12406990
<inflation>
What is the ideal way to update an old value to today's currency value?
user12406990
# What is the ideal way to update an old value to today's currency value?

(Asked by: username_0 on 2020-08-17)

For example, how much is $25 million in 1790 considered today? How do I update such value? It doesn't make sense to me to use, say, price indices. Shouldn't such update be done based on the expansion (or contraction) of monetary supply?

**Clarification post-comments**. My thinking --- please educate me if it is nonsensical --- is that inflation is an expansion of the monetary supply, so I would like to do a computation from the phenomenon of inflation itself, not of its effect, one of which is an increase in prices. So I would like to be able to estimate a loss of value merely from the the increase in monetary supply. I could then compare it against real facts --- which would be the market prices. I'd be willing to read an entire book just to learn how to do this. So feel free to advise. Thank you!

**Tags:** inflation
> **Comments:**
> **username_1**: 1. There is no "ideal" way, any method will have some problems.  
> **username_1**: 2. Since most people use price indices (though they do not think them ideal) could you elaborate on why they do not make sense to you? Otherwise answers will probably recommend price indices.  
> **username_2**: If we had an imaginary equilibrium economy that had constant prices, per capita output, and product mix, yet the population was growing, the expectation (even by critics of the MV=PQ relationship, like myself) that the monetary base would grow in line with population. So even though prices are constant, your suggested measure would imply there was inflation.  
> **username_0**: @Giskard, thanks for your request for clarification.  I didn't expect that you guys would think of price indices first.  I'm very inexperienced here.  My thinking is that there should be an estimation of the value of the money that's not taken by prices on the market.  I would like a price estimation merely out of the monetary supply.  Though this might be unreasonable, I would like to know a best-effort method that could be done.  I'm willing to read an entire book, so feel free to recommend.  
> **username_0**: @Giskard, let me elaborate on why it doesn't make sense to me.  Instead of saying "it doesn't make sense to me", I should've said it's not the only information I would like to see.  I would like to see a direct computation from the phenomenon of inflation itself, not of its effect.  I think of prices as an effect of inflation, not as inflation per se.  I would like to do a calculation that updates the value of an amount (say $25 million) merely based on the monetary supply.  
> **username_3**: "I would like to see a direct computation from the phenomenon of inflation itself, not of its effect." But inflation by definition is the change in average prices in time - thats not the 'effect' of inflation that is the inflation - its not like inflation is some sort of different concpet that then changes prices. Inflation $\pi$ is simply $\pi_t= \frac{P_t-P_{t-1}}{P_t}$ we can debate that CPI which is supposed to measure average prices $P$ is bad measure of $P$ and we can discuss different measures that we could use but that is what inflation is  
> **username_0**: @1muflon1  In that case I'm using the wrong word.  Instead of trying to find a new one or correct my use of words, I can explain that I am assuming that an increase in monetary supply always causes a loss of currency-value and I would like to compute a measure of this loss from only the change in monetary supply.  Has any book ever done this?  I would like to see how they do it and what can be learned about it.  Thank you for your attention.  

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## 2 answers

### Answer by username_3 on 2020-08-18. Score: 1

I think this question stems from misunderstanding from what inflation is. My best guess is that this happened because most macro books will say that inflation is a monetary phenomenon as in mainstream economics it is accepted that inflation over long periods of time is affected mainly by money supply. This is illustrated by equation of exchange (see Blanchard et al Macroeconomics an European Perspective) which is given by:

$$P= MV/Y$$

This is the same equation that Brian also mentioned in his comment just solved for prices. Here $P$ are the average prices, $M$ money supply, $V$ velocity, and $Y$ real output. The standard textbook argument for inflation being monetary phenomenon goes like this. Velocity is assumed to change over business cycle but not really over long run and hence it cannot be responsible for all inflation and we can hold it constant. Moreover, real output tends to increase over time which should be deflationary. Hence the argument goes that over long run inflation should be caused by $M$.

However, this does not mean that inflation is defined in terms of $M$. The definition of inflation is simply the change in average prices for example:

$$\pi\_t= \frac{P\_t-P\_{t-1}}{P\_{t-1}}$$

This is what inflation is. Moreover, inflation also is measure of how money looses value. The issue is that money especially in short run might not loose value just because there is more of it (i.e. by $M$ increasing) but also because velocity changing or real output dropping. Furthermore, $M$ and $V$ are not always independent. At zero lower bound any increase in $M$ will be offset by changes in $V$ because at zero lower bound peoples preference for holding (but not necessary spending) cash will be infinite (abstracting from issues such as storage costs for large sums of cash). What even more, models that are above simple undergraduate textbooks rely not just on actual values of $M$, $V$ and $Y$ but also on peoples expectations of these (see [Krugman 1998](https://www.brookings.edu/wp-content/uploads/1998/06/1998b_bpea_krugman_dominquez_rogoff.pdf)).

Hence you simply cannot calculate how money looses its value from $M$. At minimum to calculate change in $P$ using $M$ you would need to know and control for not just what $M$ is but also what real output is and velocity is but here you will run into problem that real output is usually calculated by deflating nominal output by CPI - so you introduce the same problem you wanted to avoid. What even worse velocity itself is usually not directly observed but imputed from data. And this is all before we start factoring in all the expectations we should that are extremely difficult to measure. Compared to such convoluted way using CPI directly is far more sensible even if it may be imperfect measure.


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### Answer by username_2 on 2020-08-18. Score: 0

I gave a comment, but I just wanted to offer an intuitive example why we people normally do not use the money supply for this purpose. This is embedded in 1muflon1’s answer, but this might be easier to grasp (since there is a lot going on within P,Q).

Imagine that we have a country in which everyone just uses money to buy food. Food prices are constant, and everyone earns \$100/week, and everyone keeps \$10 as precautionary savings. All these numbers never change.

The money supply is \$10 per person.

The country has a 1%/year population growth rate. By implication, the money supply grows at a 1% annual rate.

If the prices for everything is constant, why does the expansion of the money supply imply a loss of purchasing power?

Closer to the real world situation, population has been growing - which is slowing now - while output per person is rising. This means that the economy can grow, even if there is no inflation. If people keep a fixed percentage of their income as money, then the money supply should grow. Once again, despite no price changes. To translate to 1muflon1’s answer, the Q term is expected to rise due to productivity and population growth, allowing for M to rise with V,P constant.


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