If we barter it the economy doesn’t notice.
If we do the wood/fence ourselves the economy diesnt notice
If we charge $1000 each the economy booms more than charging $100 each.
In the first example there are various taxes that you will pay. Income tax. VAT or sales tax. Maybe license fees.
These taxes go to the government, who in turn uses that money in some way.
In the latter two examples tax revenue does not go up.
I don’t have the stats handy, but I am fairly confident that a large portion of the barter income is not reported.
It does. Of course it might not be properly reflected in the statistics but it still creates additional value in the economy.
Now you're thinking with Line Go Up!
The first economist says to the other “I’ll pay you $100 to eat that pile of shit.” The second economist takes the $100 and eats the pile of shit.
They continue walking until they come across a second pile of shit. The second economist turns to the first and says “I’ll pay you $100 to eat that pile of shit.” The first economist takes the $100 and eats a pile of shit.
Walking a little more, the first economist looks at the second and says, "You know, I gave you $100 to eat shit, then you gave me back the same $100 to eat shit. I can't help but feel like we both just ate shit for nothing."
"That's not true", responded the second economist. "We increased the GDP by $200!"