How does the rate of a population tax change with income

People would spend a lot more time trying to steal what they need and a lot less time trying to produce what they need, as stealing something is often easier than producing it yourself. This leads to a reduction in economic growth.

If there wasn't a rate of a population tax change with income, people who have produced valuable goods would spend more time and money trying to protect what they've earned. This is not a productive activity; society would be much better off if citizens would spend more time producing productive goods.