A huge number of towns in America are basically run by one or two corporations. Cupertino is not unique in the slightest, aside from the fact that Apple is just a larger company.
But it really doesn't matter if you "only" have a $1 Billion market cap company headquartered in your small 30,000 town, or a $600 Billion behemoth like Apple. Its all basically the same: all your taxes are basically going to come from only one source.
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In either cases, you can run the town independently of the corporation. True: a lot of the corporation's workers will be your citizens, but keep the issues separate and keep things fair... and you ought to get what you need done.
The German city of Wolfsburg, and the state of Niedersachsen have done it with VW.
The solution: You just buy a large amount of shares of the companies that are started in your city. Municipalities get a far larger share of the profits directly, politicians have an incentive to ensure companies are profitable, and companies can’t avoid paying for the infrastructure they use.
Don't have an American bias when people share their cultures from around the world.
There are a lot of governments, and all of our experience with the American government basically means jack diddly with respect to the German government.
With that said, I do share your concerns, but I'm not going to make claims about a government I never visited and never worked with in my life that's roughly 10 time-zones away.
The German government, for example, owns several large banking groups, which act like any normal banking group – but their dividends directly go into the tax budget. (And they have to give loans at lower interest rates to the governments).
Normal bankers, in normal environment, and they’d probably never notice it was government owned.
The German government has done it for several decades, with great success – you should take a look at their model.
In all other cases, cities investing in companies are either going to take on a VC role which I'd very much argue that they are not capable of performing well (and introduces so much room for corruption) or will be investing in mature companies and likely without the balance sheet to make a dent as far as voting power goes. I don't see how either leads to anything productive.
Property taxes are based on the value of (and in some cases the type of use of) local property, that's reasonable because the costs incurred by the local government to build and maintain infrastructure is related to their use of land.
His argument seems to be that because Apple makes a lot of money they should also pay more taxes, luckily for him that's the way the system works! Apple also pays corporation tax on their income.
Unfortunately for him that tax is federal and not local so he doesn't get any more than any other local government does in federal contributions.
Edit: I don't want to sound like I'm saying "the town should be grateful for these scraps and nothing more", these are benefits to the town on top of the taxes that it pays.