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In the case of a public utility or not for profit exactly what I said is true.
"Because public services like healthcare, national defense, and education are rarely sold at a market price, Statistics Canada measures their output by calculating the cost to produce them. Therefore, the value of government output is deemed to be exactly equal to the total cost of the wages paid to public servants plus the cost of intermediate inputs."
So wages in such cases directly increase the GDP. If you pay a nurse or a police officer $50 per hour then for that hour the GDP goes up by $50
In the case where a corporation distributes profits it absolutely is relevant. You made the statement that the corporation is retaining the profits and that's not accurate. Dividends are akin to repayment of a loan. They are cost of doing business.
Sure. In such a case GDP and income would be equal pre-tax.
For public services and non profit, here you say you think wages are the only component included: "But in many cases those services represent the value. So what winds up being included is just the wage." When you say "just the wage" it means you don't think other costs are included (materials, overhead).
I speculated that the total cost must be used. Then you say the truth is exactly like you say but the quote you provide says this "the value of government output is deemed to be exactly equal to the total cost of the wages paid to public servants plus the cost of intermediate inputs."
If you look up the definition of intermediate inputs you'll see it includes other services, goods, and energy. So in the case of nursing they include medical supplies, electricity, and office costs like payroll services. It doesn't seem like that's what you said in your first post.
Regarding dividends, they are a distribution of profit. They are not a cost. Shareholders own a portion of the company. In a privately owned company the owner may transfer money from the company account to his personal account. This is not a cost for the business. In the same way, payments of dividends is a distribution of profit to shareholders.
I have never said anything remotely close to "The wages are the only component" If you have to be dishonest about what I've said in order to make your point then you probably don't have a very good point. What I have said is that the wages are 100% included in the calculation. So if $50 is paid in wages then GDP goes up by $50 and that is absolutely true
And you fundamentally misunderstand the point I'm making. I never said anything about wages being the only cost. What I said originally was that the entirety of their wages are included in the value of the GDP and nothing about the fact that other costs are also included changes that fact. Which demonstrates that your original claim is false considering all wages are included with regards to those calculations in those sectors
I'm feeling like perhaps this is a little bit beyond your grasp. The original claim is that gDP minus income means something and my counterpoint which you are not getting is that gDP actually includes income for a significant portion of the sector therefore your statement is wrong. It doesn't have to be the only input for that to be true
You can say anything is a distribution of profit. Wages are in distribution of profit, the company makes money and uses a portion of it to pay its employees. The company pays the shareholders in exchange for the money that the shareholders have paid to own a portion of the company. An employee transfers money from the company account to his personal account. This is absolutely a cost of doing business. Just like repaying a loan is a cost of doing business