Textbook Problem

Taxation Schemes To raise revenues during the recent recession, the governor of your state proposed the following taxation formula:

$T\left(i\right)=0.001i^{0.5},$ where $i$ representstotal annual income earned by an individual in dollars and $T\left(i\right)$ is the income tax rate as a percentage of total annual income. (Thus, for example, an income of $50,000 per year would be taxed at about 22%, while an income of double that amount would be taxed at about 32%.)¹⁹

a. Calculate the after-tax (net) income $N\left(i\right)$ anindividual can expect to earn as a function of income $i$.

b. Calculate an individual’s marginal after-tax income at income levels of $100,000 and $500,000.

c. At what income does an individual’s marginal after-tax income become negative? What is the after-tax income at that level, and what happens at higher income levels?

d. What do you suspect is the most anyone can earn after taxes? (See the footnote.)