And, in this case, the dollar-amount increase in GDP serves as a virtual quantitative proxy for the increase in mowed lawns (and the value thereof). In other words, the participants in this economy are collectively ~$200 richer with their mowed lawns than they were without them.
If everyone goes around mowing lawns for each other, the economy is richer in lawn mowing at the expense of all the other things that would have been funded had everyone mowed their own lawns and purchased different services instead.
I am confused with this, if "everyone mowed their own lawns" then the net result will be exactly the same, everyone will be busy the same and not poorer, just without money movement.
This is not the same. If everyone wants mowed lawns, and everyone is busy working on that, there is no opportunity cost, everyone is working on their top priorities. The broken window fallacy is a fallacy because the headline gdp figure doesn't account for the destruction of the window which cancels out the benefit. In the grass mowing analogy nothing has been destroyed, useful and priority work has been done all around.
If the pricing is fair and at arms' length. What's happening in reality is as if they are mowing each others' lawns at wink wink nudge nudge $1000. Not a good proxy for actual value created.
In the real world, you have to pay taxes. So people are incentivized to claim less value for the lawns mowed, or even just do it themselves, instead of benefiting from the division of labour.
Leverage doesn't work that way. (If it were so easy, it would load up my investment portfolio with a lot more leverage than I currently do. And I don't live in the US where regulation T would keep me to a puny 2x leverage.)
But also importantly the government of the residents' country is about 39% ($78) richer, if say the participants are honest in reporting this and the country is the UK and the participants are people like you and me in the tech industry who frequent HN and would think to do something like this.