Define "save for a rainy day". Are you talking about permanently putting it under your matress, leaving it in your checking account, or investing it? It will eventually be spent, and the only thing that is changing is the velocity. Either way, that is not necessarily correct.

GDP has multiple different calculations:

Y = C + I + G + NX

or

GDP = Consumption + Investment + Government Spending + Net Exports

Another calculation is

Y = C + S + T

GDP = Consumption + Saving + Net Taxes

Saving either through investment and cash hoarding both count toward GDP. The percentage of GDP that is Saving is the Gross National Savings or National Savings Rate.

tldr; In isolation, scenario 1, Investment is $10 as inventory and Savings is $10. Both add toward GDP

https://en.wikipedia.org/wiki/National_saving

The issue is the next sentence:

> Thus income can not be treated as equivalent to GDP.

GDP is defined as total income, calculated in a certain way. There are also other equivalent definitions.

Income is the endpoint of economic activity. Your income contributes to the GDP when you earn it.

Your spending is largely unrelated to your income. In any period of time, you can spend more than you earn or less than that. Spending creates new economic activity. That activity contributes to the GDP, which by definition means creating new income.

But since, once you spent the $10, they are now somebody else’s income, namely for the person/company you bought from. Which means that now, by simply summing everyone’s incomes, you have an accurate count of GDP, without ever considering how individuals spend their money. I think the main problem of contention is, confusion about personal income v. national income, the latter of which includes institutions and is the one being used for GDP calculations. Money cannot be spent without being received by anyone, and the moment it is, GDP goes up in the country it’s received in.

I think you missed why I am failing to understand this one. The full context there is:

> If I earn a dollar and don't spend it, it results in a lower GDP than if I spent it. Thus income can not be treated as equivalent to GDP.

It's the second part that I don't understand. Those two sentences read to me like: "Spending decisions impact GDP, therefore income is not equivalent to GDP."

I don't think anyone is claiming that spending would fail to increase GDP. But I still don't see how income is disconnected from GDP, since that spending would be someone else's income.