Malodery: The mechanisms involved with sales tax are entirely different from those involved with income tax. The effect on tax revenue and the economy are not equivelant.
But, the outcome is in the same direction. If you pay less for an item because of a sales tax decrease, you have more disposable income. More disposable income means more things are purchased. If more things are purchased, the producers' and sellers' incomes increase. As their income increases, they pay more income taxes. As they pay more taxes the tax revenue goes up. Hallelujah.
You never put any numbers on these things. I would think the Big Sibling would do the math but he doesn't. Maybe he hasn't studied math.
I'll take my earlier example of lowering sales tax from 7 cents to 2 cents and carry it a little further using your theory of how tax revenue will be increased.
To reiterate, you buy $20 worth of stuff and you've saved one dollar on sales tax. You spend your dollar and it adds 2 cents back into the sales tax revenue so you're short 98 cents.
But it's worse. People don't spend all their income on things that have sales tax. State and federal income taxes are two big items. Property taxes, medicine and groceries are others. So maybe you're really short 99 cents.
Now you present the threory that the producer of what you bought makes more product and makes more money and pays more income tax and that increases tax revenue.
OK assume a beer producer makes a 20% taxable profit. That's high but we can use it. Companies like Exxon like to keep that close to zero. Assume the producer is in the 10% income bracket. That's also high for Iowa.
He then pays 10% of the 20% which is 2 cents. Then you're still 96 or 97 cents short. But if you didn't but Amana beer and went for Bud Lite, the income goes to Missouri and you're back to 98 or 99 cents short.
I hope you consider this educational, not confrontnational.