Explaining why government factors big in private savings

I got this email from a viewer of one of my videos...

Saving is the opposite of consumption, not only in monetary terms, but also in resources and production. Resources and production not consumed are saved. But If Govt doesn't produce anything or acquire resources, how can it supply savings? Govt can only redirect or consume what is already or being produced or acquired by printing, borrowing, taxing, legislating or confiscation. Capitalists have to have previously produced and saved in order to provide capital. They supply savings.

Here's what I wrote back to him...

You can define savings anyway you like, but it doesn't mean it's right. The basic definition of savings is total income minus total outlays. Income is equal to all private wages and salaries, plus net foreign income (what we get in income from abroad) plus Government transfer payments (unemployment insurance, health and social benefits, etc), interest the government pays on its debt minus taxes the government collects. Consumption is the sum total of all that households and businesses consume. The equation looks like this:

P = (Y + NFI + TR + Int -T) - C

Where...

P = Private savings
Y = All wages and salaries
TR = Government transfer payments (unemployment insurance, health and social benefits, etc.)
IR = Interest the gov't pays on its debt
T = All taxes collected
C = Total consumption of households and businesses

We can rearrange the equation to look like this:

P + C = (Y + NFI + TR + Int -T)

You can state this as, "Private savings plus consumption equals total income"

or...

P + C = Total income

In the examples above you can see that if the government pays more interest on its debt, increases transfer payments and collects less in taxes, the amount of private savings will rise, all else being equal. Therefore, Three of the five elements of total income, are related to government. And three of the six elements of savings are related to what government does. Another way to say this is, half of all the things that determine the level of private savings are affected by government.