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If the tax system is changed so as to take more revenue from the rich and less from the poor, the benefit to the poor will be competed away by the same "market" forces that currently make them poor and keep them poor—unless, perchance, the change in the tax system strengthens the competitive position of the poor in the "market", in which case it will improve their lot even if it doesn't take any less revenue from them…
A progressive tax system is not one that collects and redistributes enough revenue to compensate for the inequity of the "market". That alone is futile. Rather: A progressive tax system is one that makes the rich compete against each other for the services and patronage of the poor, instead of the other way around. Or, in terms of incentives: A progressive tax system is one that deters anti-competitive conduct by the rich.
Now, if we have a deterrent tax on anti-competitive conduct by the rich, how much revenue does it need to raise from the rich in order to do its job? No particular amount…
If you reduce poverty without spending, you also reduce the need for poverty-alleviation programs that do involve spending, and reduce the need for spending on other problems caused by poverty. These effects reduce the total amount of tax that needs to be collected. That means progressives can get by with less tax revenue than conservatives! Low taxation is a highly strategic piece of ideological territory that progressives have needlessly ceded to conservatives. Progressives need to invade it, occupy it, annex it, fortify it, and never give it back. The key to the conquest is not to "tax the rich", but to make the rich compete…
To make the rich compete is to make them do things: get residential tenants for vacant houses; get commercial tenants for vacant shops; build accommodation on vacant lots, etc. If the rich do things in order to avoid a particular tax, they generate economic activity, thereby expanding the bases of whatever other taxes are in force, allowing lower tax rates for the same revenue. But, as we have just seen, the needed revenue doesn't stay the same, but is reduced, because there is less need to spend money in response to poverty. Thus the reduction in tax rates is compounded: less revenue is needed from a bigger base. But if the conservatives regain power and abolish the taxes that make the rich compete, then the rich do less, the economy contracts, the tax base shrinks, and revenue falls, while poverty and the related expenses increase, so that tax rates increase and/or the deficit blows out—on the conservatives' watch. That's what I mean by "fortify it"…
Which taxes are progressive?
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Full text: “Progressive tax myths” (4k words).