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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

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

T ( i ) = 0.001 i 0.5 , where i representstotal annual income earned by an individual in dollars and T ( i ) 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 ( i ) 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.)

(a)

To determine

The expected after tax (net) income N(i) to be earned by an individual as a function of income i, where the taxation formula is T(i)=0.001i0.5.

Explanation

Given Information:

The taxation formula by the state governor to raise the revenue during the recession is T(i)=0.001i0.5 where, i is the total annual income (in dollars) and T(i) is income tax rate as a percentage of total annual income.

Consider the taxation formula, T(i)=0.001i0.5.

The expected value of net annual income before tax, is 1.

Evaluate the expected value of net income after tax, by subtracting the tax from net income and multiply by i for annual income

(b)

To determine

To calculate: The marginal after tax income of an individual at income levels of $1,00,000 and $5,00,000 where the taxation formula is T(i)=0.001i0.5.

(c)

To determine

To calculate: The level at which the marginal after tax income of an individual become negative and the income at the level and what about higher income levels where the taxation formula is T(i)=0.001i0.5.

(d)

To determine

The maximum income that can be earned after taxes where the taxation formula is T(i)=0.001i0.5.

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