1. Copyright © by Houghton Mifflin Company. All rights reserved. 1 How is the Tax Applied? Tax rates, Exemptions, Deductions, and Credits Exemptions, deductions, and credits. Statutory and effective tax rates. Average and marginal tax rates. Taxation and income.

2. Copyright © by Houghton Mifflin Company. All rights reserved. 2 Tax Computation The amount of tax to be paid (T) is determined by the product of the tax rate (r) times the tax base (b): T = r b. As a result, the amount you pay in tax is a combination of the definition of the tax base and the tax rates that are applied to that base.

3. Copyright © by Houghton Mifflin Company. All rights reserved. 3 Tax Rates If we rearrange the relationship, we can write the tax rate as the ratio of the tax paid to the tax base r = T/b. For example, suppose that you are required to pay a property tax of 2% of the value of your home to the local governments in your area. If your home has a value of $100,000, your tax liability is T=(0.02)(100,000)=2,000. Thus, the tax you must pay is simply the product of the tax rate and the tax base.

4. Copyright © by Houghton Mifflin Company. All rights reserved. 4 Tax Rates [continued] We can flip the relationship, however, and discuss the tax rate as the ratio of the tax liability and the tax base. If your tax is $2,000 on your home worth $100,000, the tax rate is 2%, since 2,000/100,000=0.02.

5. Copyright © by Houghton Mifflin Company. All rights reserved. 5 Graduated Tax Rates The rate of taxation may not be constant, as was the case in the example above. An example of a tax with graduated rates is the U.S. income tax which has approximate rates of 15%, 28%, 32%, 36% and 39%. In such as case we say that the rates are graduated.

6. Copyright © by Houghton Mifflin Company. All rights reserved. 6 Figure 9.3: A Graduated Rate Structure

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9. 9 Exemption Suppose that part of the tax base is exempt from taxation. An example is the case of food (purchased at a grocery store) being exempt from a state sales tax. Of the total tax base b, we can denote the taxable part as b t and the exempt part as b x with b=b t +b x. The effect of this exemption is to reduce the effective rate of taxation.

10. Copyright © by Houghton Mifflin Company. All rights reserved. 10 Exemption [continued] If we divide the tax paid by the total base, the effective tax rate (denoted r e ) is given by Exemptions reduce effective tax rates. Since the ratio of b t to b t +b x is less than one, the effective tax rate is smaller than the nominal tax rate. The larger the exemption, the smaller the effective tax rate.

11. Copyright © by Houghton Mifflin Company. All rights reserved. 11 Deduction Deductions also reduce effective tax rates. Suppose that we provide a deduction of amount d to a taxpayer. That deduction reduces the amount of the taxable base to which we apply the tax rate in order to compute the tax.

12. Copyright © by Houghton Mifflin Company. All rights reserved. 12 Deduction The effect is to reduce the tax base T=r(b-d) The effective tax rate is then

13. Copyright © by Houghton Mifflin Company. All rights reserved. 13 Deduction Since the ratio of(b-d) over b is less than one, the effective tax rate is less than the nominal tax rate r. Deductions reduce nominal tax rates. The larger the deduction d the smaller the effective tax rate.

14. Copyright © by Houghton Mifflin Company. All rights reserved. 14 Credit A tax credit works in an entirely different way. Rather than reducing the tax base as an exemption or deduction does, a credit reduces tax liability.

15. Copyright © by Houghton Mifflin Company. All rights reserved. 15 Credit If we provide a credit (denoted c) the tax becomes T=rb - c. The effective tax rate is then

16. Copyright © by Houghton Mifflin Company. All rights reserved. 16 Credit Credits reduce effective tax rates. The larger the credit, the lower the effective tax rate. It is important to notice, however, that a credit reduces the effective tax rate in a more powerful way than an exemption or deduction does. Since the credit reduces tax liability, rather than simply reducing the base, it has a greater effect in reducing the effective tax rate

17. Copyright © by Houghton Mifflin Company. All rights reserved. 17 Statutory and Effective Tax Rates The statutory tax rate is the rate specified in statute, or law. Of course, the effective tax rate may be quite different. We are concerned with effective tax rates, since they affect behavior.

18. Copyright © by Houghton Mifflin Company. All rights reserved. 18 Average and Marginal Tax Rates The average tax rate is the tax divided by the base: The marginal tax rate is the change in the tax divided by a change in the base:

19. Copyright © by Houghton Mifflin Company. All rights reserved. 19 A Sales Tax Example Table 10 gives income and consumption information. Average and marginal tax rates are computed for a 4% sales tax.

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21. Copyright © by Houghton Mifflin Company. All rights reserved. 21 A Sales Tax Example with Exemption Suppose we introduce a $3,000 exemption in the sales tax example. The first $3,000 worth of consumption is now exempt from taxation. Notice the impact on the average tax rate.

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23. Copyright © by Houghton Mifflin Company. All rights reserved. 23 Taxation and Income We classify taxes according to the relationship between the ATR and income: A regressive tax has an ATR that falls with income. A progressive tax has an ATR that rises with income. A flat rate tax has an ATR that is independent of income.

24. Copyright © by Houghton Mifflin Company. All rights reserved. 24 Figure 9.4: Average and Marginal Tax Rates for the Sales Tax