Is it correct to say that just because a single unit of a country's currency has less value, doesn't necessarily mean that there was inflation?

Question

Casual student of economics here, I believe I share the layman understanding of Inflation (and even then I think there are still gaps in my logic)

When you hold public shares of a company, you hold a percentage of the equity. So if a $100 company has 1000 shares outstanding, and you own 10, you have 1%, or $1 of value. If the company issues 1000 more shares, and the value of the company remains fixed, well now your 10 shares is only 0.5%. So you now have less value ($0.50)

So following that logic, I imagine inflation to be a similar situation: If a country has 1000 units of a currency in circulation, and I have 10 of those units, they are worth 1% of the country's wealth (assuming countries have market caps like publicly traded companies). If the country prints 1000 more units of currency, well now I only have 0.5% of the country's wealth. Assuming the country's market cap remains fixed like in the previous example, that would mean I effectively now wield less buying power.

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Assuming that is roughly how inflation works, it makes sense that countries would want to avoid inflation because it would decrease the effective wealth of all of it's citizens.

So here is my big question...

With stocks, when there is a split, they aren't issuing any NEW shares, but rather multiplying all existing shares. So in the previous example if I had 10 shares, now I own 100 shares. But total outstanding shares is now 10000, so I still own 1% of the value.

What if countries did a similar thing?

I remember a long time ago Zimbabwe had some sort of "hyper inflation", and what could've been a single dollar for a water became like a billion instead. So we look at this, and it seems like we correlate the increase of the cost of a water to a billion dollars as inflation

But what if the US just printed one billion the amount of outstanding USD, and gave that all to holders of USD to multiply their holdings by one billion?

Then the cost of a water bottle in the US would be one billion right? But just because single unit of USD is worth significantly less, doesn't mean that inflation occurred right? So if we cannot look at how many units of currency a bottle of water costs to determine inflation, how can we actually determine when inflation has occurred in a country?

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I think I'm missing some big concepts here, I've been trying to work through it on my own but I would really appreciate if anyone could follow my reasoning and help me determine what's missing

Answer 1

Is it correct to say that just because a single unit of a country's currency has less value, doesn't necessarily mean that there was inflation?

Depends on what you mean here by value of that currency. If by value of currency you mean inverse of price level $1/P$, then decrease in value of money does mean there had to be inflation.

If you mean value of currency in terms of other currencies (i.e. exchange rate), then currency can appreciate or depreciate in value regardless of inflation. For example, increase in domestic interest rate (ceteris paribus) would lead to currency appreciation under standard monetary model of exchange rate, and vice versa drop in domestic interest rate (ceteris paribus) would lead to depreciation of a currency even if there is no inflation.

But what if the US just printed one billion the amount of outstanding USD, and gave that all to holders of USD to multiply their holdings by one billion? Then the cost of a water bottle in the US would be one billion right?

No, inflation does not work automatically like that. Inflation is change in the price level. Price level depends on what money market equilibrium is which can be described in a simple IS-LM model as:

$$M/P=L(Y,i) \implies P = M/L(Y,i)$$

where $P$ is price level, $M$ money supply, $L$ money demand which is function of real output $Y$ and interest rates $i$. Price level is thus ratio of money supply and money demand. Printing that extra money would not affect the long run level of real output $Y$ but we still do not know what interest rates are. Moreover, we would also need to figure out the intensity with which $L$ responds to interest rates. So you can't just automatically claim that giving everyone billion dollars would make 1 dollar bottle of water worth billion dollars. It would almost certainly lead to massive inflation but price level would for sure not raise exactly proportionally.

So if we cannot look at how many units of currency a bottle of water costs to determine inflation, how can we actually determine when inflation has occurred in a country?

Inflation is by definition positive change in price level $P$ over time so whenever:

$$\frac{P_t - P_{t-1}}{P_{t-1}}>0$$

we have inflation. $P_t$ can be estimated by sampling some representative prices in economy and constructing consumer price index. When change in CPI is positive and we are confident there is no significant measurement error we know that country experienced inflation.