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Yes, I think that it's close to an identity, but that wasn't my point. In your previous post, you said,

> There is a vast quantity of new money being created, and it isn't appearing in household incomes. Something should be done.

You seemed to be implying that things were out of control on the money supply. My point was that this is not so. The money supply has to grow as much as the growth of real GDP, or it's deflationary, and deflation is much more damaging than inflation. Money supply growth on top of that results in inflation, but 3% inflation isn't the kind of level that causes real problems.

I don't think that gold is a good metric. Yes, it rose in price from 2000 to 2018, but it fell from 2015-2018, and we still had growth in the money supply and inflation. The price of gold is basically a measure of distrust in fiat currencies. It reflects inflation, true, but it also incorporates sentiment, which can change much faster than the money supply.

I think that invalidates the premise of your third paragraph. (Somewhat: I don't totally buy the official inflation statistics either. But measuring by gold isn't the answer.)

> You seemed to be implying that things were out of control on the money supply.

I absolutely was, and still am.

> The money supply has to grow as much as the growth of real GDP, or it's deflationary, and deflation is much more damaging than inflation. Money supply growth on top of that results in inflation, but 3% inflation isn't the kind of level that causes real problems.

There is an assumption there though, and that was what I was excited about. The assumption is that everything that isn't a consumer good increases in cost by (inflation_CPI + real growth).

If that assumption is wrong, and I take my prior (ie, out of control money supply) then the result is that real GDP growth is decoupled from the growth of the underlying economy, and now I have a formula to play with.

So the next step is for me to go and look up why they think that, eg, change in the price of gold (or anything not measured as part of the CPI) is equal to (inflation_CPI + real) instead of (inflation_asset_markets + real). Because I think that the way the money supply is being expanded would cause the rate of change in expected price of assets (sans real changes in value) to differ from the inflation rate of consumer goods.

EDIT I'll just add my reasoning for why - we can establish that new money isn't going to median households by looking at the average median household wage (and growth in household numbers isn't high enough to make up the difference). Therefore, the money is likely being directed towards people who already have lots of it, and businesses. At this point, assuming that this is spent on and causes inflation first and foremost in consumer prices seems like unclear thinking. It isn't going to entities who compete for consumer goods, it is going to entities who compete for assets and business supplies.

Here I am going to mostly agree with you. When new money enters the economy, it enters the financial system. Then prices rise. Then wages rise. The financial system gets the extra money before prices rise; the workers get it after the prices rise.

The extra money goes to raise prices of financial assets, not just of consumer goods. Those financial assets may go up more than consumer goods do.

> because if the impact of monetary supply increases on business and asset prices is different

This is why we have https://en.wikipedia.org/wiki/Consumer_price_index vs https://en.wikipedia.org/wiki/Producer_price_index vs https://en.wikipedia.org/wiki/GDP_deflator and chained vs non-chained versions of some of these. Measuring "inflation" is hard.

The price of gold is not defined according to some fixed utility function. There's a demand component, yes (which is not fixed). But there's also a supply component.

Inflation is an indication, it's not actually measuring anything, because it has so many parameters you can literally make it whatever value you want.