Principles of Tax Analysis

1. Principles of Tax Analysis © Allen C. Goodman, 2009

2. Lots of Different Taxes Income/BusinessConsumptionWealth Personal Income Sales Property Corporate Income Use Estate Value-Added Motor Fuel Inheritance License Alcoholic Beverage Transfer Hotel/Motel Restaurant Meals Telephone Call Gambling Most economists Don’t like this one. Why?

3. Lots of Different Taxes Income/BusinessConsumptionWealth Personal Inc. Sales Property Corporate Inc. Use Estate Value-Added Motor Fuel Inheritance License Alcoholic Beverage Transfer Hotel/Motel Restaurant Meals Telephone Call Gambling

4. Lots of Different Taxes Income/BusinessConsumptionWealth Personal Inc. Sales Property Corporate Inc. Use Estate Value-Added Motor Fuel Inheritance License Alcoholic Beverage Transfer Hotel/Motel Restaurant Meals Telephone Call Gambling Why good? Why bad?

5. Tax Incidence • Who REALLY pays the tax • If you buy something at the store, you give $ to the clerk, and the store pays $ to the gov’t, but who really pays? • If you rent an apartment and property taxes in your city rise, what happens to the rent that you pay? Who really pays?

6. Tax Incidence and Burden • Progressive Tax • Tax Burden/income ↑ as income ↑ • Proportional Tax • Tax Burden/income is constant as income ↑ • Regressive Tax • Tax Burden/income ↓ as income ↑ Tax Income

7. Ave  Ray to origin Progressive Tax Mgl  slope Average Marginal T ΔT • Progressive Tax • Tax Burden/income ↑ as income ↑ • Slope of ray = T/Y • Mgl Tax Rate = ΔT/ΔY • Example – Gas Guzzler Tax • Federal Income Tax Y ΔY Mgl. Tax Rate Ave. Tax Rate Tax T Income Y1 Y2 Y3

8. Ave  Ray to origin Proportional Tax Mgl  slope Average Marginal T ΔT • Proportional Tax • Tax Burden/income constant as income ↑ • Slope of ray = T/Y • Mgl Tax Rate = ΔT/ΔY • Example – Medicare Tax Y ΔY Tax Income Y1 Y2 Y3

9. Ave  Ray to origin Regressive Tax Mgl  slope Average Marginal T ΔT • Regressive Tax • Tax Burden/income ↓ as income ↑ • Slope of ray = T/Y • Mgl Tax Rate = ΔT/ΔY • Example – FICA tax for Social Security Y ΔY Tax Mgl. Tax Rate Income Y2 Y1 Y3

10. FICA and Medicare

11. General Rules for Taxes • Only way (legally) to avoid taxes is to change behavior. • The more that one agent can avoid the tax • the less is collected • the more someone else pays

12. Efficient Quantity! WHY? Taxes and Efficiency D S • Excise Tax • Tax on a particular good. • Look at a unit (as oppose to percentage) tax. • Partial eq’m analysis looks at a single market. $ P0 Q0 Q

13. Taxes and Efficiency D S • Excise Tax • Tax on a particular good. • Look at a unit (as oppose to percentage) tax. • $1 Tax Collected on DEMANDERS $ Why is this treated as a downward shift? P0 3.0 Suppose you buy gasoline at $3.00 per gallon. Your state imposes a $1.00/gallon tax. You keep your receipts and pay tax. You demand based on $2.00 per gallon, because you know you’ll have to pay an additional $1.00. Your demand curve shifts DOWN by $1.00. $1 Q0 Q

14. Taxes and Efficiency D S • Excise Tax • Tax on a particular good. • Look at a unit (as oppose to percentage) tax. • $1 Tax Collected on DEMANDERS $ D' P1 Total Revenue P0 3.0 $1 Who Pays? Q1 Q0 Q

15. Taxes and Efficiency D S • Excise Tax • Tax on a particular good. • Look at a unit (as oppose to percentage) tax. • $1 Tax Collected on DEMANDERS $ P1 Con. P0 3.0 DW Prod. $1 What’s DW$ Q1 Q0 Q

16. Suppose the $1 is on Suppliers? EXACTLY the same result. D S • Excise Tax • Tax on a particular good. • Look at a unit (as oppose to percentage) tax. • $1 Tax Collected on SUPPLIERS $ P1 Cons. Total Revenue P0 3.0 DW Prod. Who Pays? Q1 Q0 Q

17. If result is same … • Why do we usually collect sales taxes from the sellers? • Do we ever try to collect it from the buyers? • What happens when we do?

18. Important Concepts! • DW loss relates to the change in quantity. Remember, we saw that efficiency related to quantity. The more behavioral change that a tax makes, the more DW loss. • Incidence relates to elasticity of demand and supply. Remember elasticity addresses whether quantity changes a little or lot. If you can change your behavior a lot, and avoid the tax, its incidence on you is small. • If you can’t change your behavior and avoid it, its incidence is a lot! Does it matter how we collect the tax?

19. Another Gas Tax Example S' S • Suppose that Southfield puts a $1/gallon tax on gas. • Let’s look at demand and supply. • Why did I draw demand and supply like I did. $ $1 P1 Consumer Total (yellow) P0 D Who Pays? Price ↑ a little; Quantity ↓ a lot Most is paid by producers. by producer Q1 Q0 Quantity

20. Another Gas Tax Example S' S • Suppose that the US puts a $1/gallon tax on gas. • Let’s look at demand and supply. • Why did I draw demand and supply like I did. $ P1 Tax Collected $1 P0 D Who Pays? Price ↑ a lot; Quantity ↓ a little Most is paid by consumers. WHY? Q1 Q0 Quantity

21. Excess Burden – Gen’l Eq’m Other Goods • Previously, we looked only at a single market. Even if a tax doesn’t change quantity in a given market it may change behavior in other markets. U1 U2 U0 • We can’t measure U1 – U2, but we CAN, in principle, measure the cost in $ of this excess burden. Excess Burden Gasoline

22. Even if Q doesn’t change! – Gen’l Eq’m Other Goods • Previously, we looked only at a single market. Even if a tax doesn’t change quantity in a given market (again, suppose it’s gasoline) it may change behavior in other markets. U0 • Again we can’t measure U1 – U2, but we CAN, in principle, measure the cost in $ of this excess burden, even though the amount of gas did not change. U1 U2 Gasoline

23. WHO REALLY PAYS? Tax Incidence © Allen C. Goodman, 2009

24. What has been happening • Over time, the share of output generated from the relatively less cyclically sensitive service-producing industries has risen modestly in comparison with relatively larger cyclically sensitive goods-producing industries. • So, as the share of services has risen the share (and possibly the amount) of goods-based sales taxes has fallen.

25. Sources of State Revenues • Go to Spreadsheet All States http://www.census.gov/compendia/statab/cats/state_local_govt_finances_employment/state_government_finances.html

26. Where does Michigan stand? • Go to Spreadsheet. http://www.census.gov/compendia/statab/cats/state_local_govt_finances_employment/state_government_finances.html

27. Why drawn like this? Short-Run and Long-Run Impacts D S $ S' • Look at SR supply elasticities? • Look at SR demand elasticities? • What is impact of 6% tax on services? P2 Total Tax Rev. DW is small P1 Total Sales Q2 Q1 Quantity

28. Supply more elastic Long-Run Impacts D S $ S'' S' • Look at LR supply elasticities? • Look at LR demand elasticities? • What is impact of 6% tax on services? D'' Demand more elastic P2 Tot. Tax Rev. P1 Tot Sales Q2 Q1 Quantity

29. Long-Run Impacts D S $ S'' S' • What is net impact as drawn? • P3 < P2 because demand is more elastic • TR? Depends on whether price ↑ (leading to ↑ in tax per unit) by greater % than quantity ↓. D'' P2 P3 Tot. Tax Rev. New Tax Rev. P1 Tot Sales Q3 Q2 Q1 Quantity

30. A Model of a Michigan Service Tax 1 = goods produced nationally– examples? 2 = goods produced locally – examples? T = Taxes Collected by Michigan T = National sector taxes + Local Sector taxes T = t1 p1Q1 (t1, t2, p1, p2, y) + t2 p2Q2 (t1, t2, p1, p2, y) y = p1 Q1 + p2 Q2 + - + - + What happens if we establish (increase) taxes on local goods, services?

31. What will the Full Impact of a tax on local goods be? • Lots of things happen!! • Prices of local goods ,   in quantity demanded of local goods. •  in demand for national goods. • What will be the TAX IMPACT and who will pay it?

32. What will the Full Impact of a tax on local goods be? dT/dt2 = p2 Q2 + t2 p2 (dQ2/dt2) + t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + t1 p1 (dQ1/dt2 ) Higher prices, Less sold. Less Sold! But it Is now taxed. More taxes on Substitutes.

33. What will the Full Impact of a tax on local goods be? dT/dt2 = p2 Q2 + t2 p2 (dQ2/dt2) + t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + t1 p1 (dQ1/dt2 ) dT/dt2 = p2 Q2 + t2 (dQ2/dt2 ) (Q2/Q2) p2 + (Q2/Q2)(p2/p2) t2 p2 (dQ2/dp2 ) (dp2/dt2 ) + (t2/t2) (Q1/Q1) t1 p1 (dQ1/dt2) dT/dt2 = p2 Q2 + dQ2/dt2 (t2 /Q2) (p2 Q2) + p2 Q2 [(dQ2/dp2)(p2/Q2)] [(dp2/dt2) (t2/p2)] + (t1/t2)(p1Q1) (dQ1/dt2) (t2/Q1) dT/dt2 = p2 Q2 + Elas Q2t2 (p2 Q2) + p2 Q2(Elas Q2p2)(Elas p2t2) + (t1/t2)(p1Q1) (Elas Q1t2) dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2)

34. A Model of the Service Tax + or - ? + or - ? + or - ? dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2) + or - ? KEY POINT --- There are LOTS of Impacts!

35. This is a one UNIT  in tax. We want 0.06 of that. A 6% Service Tax t2 = 0.06 dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2) 0.06* (dT/dt2) = 0.06 * p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ 0.06 * t1p1Q1 (Elas Q1t2) Elas Tt2 = s2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+s1* Elas Q1t2 ; s1 = t1p1Q1/T; s2 = t2p2Q2/T.

36. A 6% Service Tax t2 = 0.06 dT/dt2 = p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ p1Q1 (t1/t2) (Elas Q1t2) 0.06* (dT/dt2) = 0.06 * p2 Q2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+ 0.06 * p1Q1 (t1) (Elas Q1t2) Elas Tt2 = s2 (1 + Elas Q2t2 + Elas Q2p2 Elas p2t2)+s1* Elas Q1t2 ; s1 = t1p1Q1/T; s2 = t2p2Q2/T. 6% of original sales of Q2 Change in sales of Q1