Final answer:
The greatest take-home pay in a city where x% tax is levied on x thousand dollars income cannot be determined without additional details regarding the tax structure or caps. Taxation in this case increases with income, potentially reducing the benefit of higher income due to higher taxation, but without a specific tax function or more information, the point of maximum take-home income remains unknown.
Step-by-step explanation:
The question revolves around the concept of taxation and take-home pay in the context of a specific tax rule: x% tax is collected for an income of x thousand dollars. To determine what income will yield the greatest take-home pay, we can set up a simple model where the after-tax income is calculated as income minus the tax paid on that income. Given the tax rate increases with income in this scenario, there is a point where the additional income will lead to a proportionally higher tax, reducing the marginal benefit of earning more.
Considering that taxes paid = tax rate x income; for an income of x thousand dollars, the tax would be x% of x thousand dollars, which translates to x/100 × x × 1,000. To maximize take-home pay, we need to find the income level (x) where the derivative of the after-tax income with respect to 'x' equals zero, indicating the maximum point of the function, without the increasing tax rate outweighing the income gains.
However, we lack the explicit functional form of the tax rule beyond its initial description. Therefore, without additional details about how taxation scales with income in this specific context or a cap on the taxation percentage, we cannot ascertain which income level would result in the greatest take-home pay. The answer to the question is thus D. Cannot be determined.