Are you sure of this example? It does look like GDP is 200k in both cases. The first case looks wrong, if he pulls 25k from his savings, there will be -25k in savings (or investments as they are the same) and +25k in spendings. Effect is 0...
When the maid gets married, money is no longer spent on consuming her services, and that's the end of the story. Everything else is just accounting. In this example, the 25k of spending in the first case is counted one time extra because it passes through the maid on the way to some other saving or spending.
In the first case he has 175 of investments (I) and 25 of consume (C).
In the second case he has 200 of investments.
If some of the downvoters can please explain in those terms where I am wrong, it would be nice. Please, show me where the +25 come from in the 1st case.
Before marriage: 175 I + 50 of consume (the man consumes 25 in the form of a clean home, his maid consumes 25 to buy shoes) = 225.
After marriage: 175I + 25 of consume (the 25 consumed by the wife to buy shoes) = 200.
By the way, your question is good, and I really wish HN wouldn't reflexively downvote stuff they don't agree with.
When they get married, the man's income stays the same. The woman's income evaporates. She's not getting paid anymore. So their combined income is now 200K.
But the situation is exactly the same! The same amount of work is being done.
GDP works exactly the same way. It's an account of money flows, not production or actual economic activity.
Again, you are looking at the GDP of the man, not of the pair of people.
Because the man first spends 25k, and then the maid spends 25k again, the 25k is counted twice in GDP statistics. In the second case, it is counted once.
This is why GDP != Income.