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

2 Lots of Different Taxes Income/BusinessConsumptionWealth Personal IncomeSalesProperty Corporate IncomeUseEstate Value-AddedMotor FuelInheritance LicenseAlcoholic BeverageTransfer Hotel/Motel Restaurant Meals Telephone Call Gambling Most economists Don’t like this one. Why?

3 Lots of Different Taxes Income/BusinessConsumptionWealth Personal Inc.SalesProperty Corporate Inc.UseEstate Value-AddedMotor FuelInheritance LicenseAlcoholic BeverageTransfer Hotel/Motel Restaurant Meals Telephone Call Gambling

4 Lots of Different Taxes Income/BusinessConsumptionWealth Personal Inc.SalesProperty Corporate Inc.UseEstate Value-AddedMotor FuelInheritance LicenseAlcoholic BeverageTransfer 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 ↑ Income Tax

7 Progressive Tax –Tax Burden/income ↑ as income ↑ –Slope of ray = T/Y –Mgl Tax Rate = ΔT/ΔY Example – Gas Guzzler Tax Federal Income Tax Income Tax T Y Y1Y1 Y2Y2 Y3Y3 Ave. Tax Rate Mgl. Tax Rate T ΔTΔT ΔYΔY AverageMarginal Ave  Ray to origin Mgl  slope

8 Proportional Tax –Tax Burden/income constant as income ↑ –Slope of ray = T/Y –Mgl Tax Rate = ΔT/ΔY Example – Medicare Tax Income Tax Y1Y1 Y2Y2 Y3Y3 T Y ΔTΔT ΔYΔY AverageMarginal Ave  Ray to origin Mgl  slope

9 Regressive Tax –Tax Burden/income ↓ as income ↑ –Slope of ray = T/Y –Mgl Tax Rate = ΔT/ΔY Example – FICA tax for Social SecuritySocial Security Income Tax Y1Y1 Y2Y2 Y3Y3 Mgl. Tax Rate T Y ΔTΔT ΔYΔY AverageMarginal Ave  Ray to origin Mgl  slope

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 Taxes and Efficiency 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. $ Q DS Q0Q0 P0P0 Efficient Quantity! WHY? Efficient Quantity! WHY?

13 Taxes and Efficiency Excise Tax –Tax on a particular good. –Look at a unit (as oppose to percentage) tax. $1 Tax Collected on DEMANDERS $ Q DS Q0Q0 P0P0 $1 Why is this treated as a downward shift? 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 $

14 Total Revenue Taxes and Efficiency Excise Tax –Tax on a particular good. –Look at a unit (as oppose to percentage) tax. $1 Tax Collected on DEMANDERS $ Q DS Q0Q0 P0P0 Who Pays? P1P1 Q1Q1 D' $1 3.0

15 Taxes and Efficiency Excise Tax –Tax on a particular good. –Look at a unit (as oppose to percentage) tax. $1 Tax Collected on DEMANDERS $ Q DS Q0Q0 P0P0 What’s DW$ P1P1 Q1Q1 Prod. Con. DW $1 3.0

16 Total Revenue Prod. Suppose the $1 is on Suppliers? $ Q DS Q0Q0 P0P0 Excise Tax –Tax on a particular good. –Look at a unit (as oppose to percentage) tax. $1 Tax Collected on SUPPLIERS Who Pays? Cons. EXACTLY the same result. DW P1P1 Q1Q1 3.0

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 Total (yellow) Another Gas Tax Example 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. $ Quantity D S Who Pays? Q0Q0 $1 P0P0 P1P1 Q1Q1 Price ↑ a little; Quantity ↓ a lot Most is paid by producers. S' Consumer by producer

20 Tax Collected Another Gas Tax Example 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. $ Quantity D S Who Pays? Q0Q0 $1 P0P0 P1P1 Q1Q1 Price ↑ a lot; Quantity ↓ a little Most is paid by consumers. S' WHY?

21 Excess Burden – Gen’l Eq’m 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. U0U0 U1U1 U2U2 We can’t measure U 1 – U 2, but we CAN, in principle, measure the cost in $ of this excess burden. Gasoline Other Goods Excess Burden

22 Even if Q doesn’t change! – Gen’l Eq’m 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. U0U0 U1U1 U2U2 Again we can’t measure U 1 – U 2, but we CAN, in principle, measure the cost in $ of this excess burden, even though the amount of gas did not change. Gasoline Other Goods

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

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 SpreadsheetSpreadsheet All States

26 Where does Michigan stand? Go to Spreadsheet.Spreadsheet

27 Total Sales Short-Run and Long-Run Impacts Look at SR supply elasticities? Look at SR demand elasticities? What is impact of 6% tax on services? DS $ Quantity S' Why drawn like this? Total Tax Rev. P1P1 Q1Q1 Q2Q2 P2P2 DW is small

28 Tot Sales Long-Run Impacts Look at LR supply elasticities? Look at LR demand elasticities? What is impact of 6% tax on services? DS $ Quantity S' Supply more elastic Tot. Tax Rev. P1P1 Q1Q1 Q2Q2 P2P2 S'' D'' Demand more elastic

29 Tot Sales Long-Run Impacts What is net impact as drawn? P 3 < P 2 because demand is more elastic TR? Depends on whether price ↑ (leading to ↑ in tax per unit) by greater % than quantity ↓. DS $ Quantity S' Tot. Tax Rev. P1P1 Q1Q1 Q2Q2 P2P2 S'' D'' P3P3 Q3Q3 New Tax Rev.

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 = t 1 p 1 Q 1 (t 1, t 2, p 1, p 2, y) + t 2 p 2 Q 2 (t 1, t 2, p 1, p 2, y) y = p 1 Q 1 + p 2 Q What happens if we establish (increase) taxes on local goods, services?

31 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? What will the Full Impact of a tax on local goods be?

32 dT/dt 2 = p 2 Q 2 + t 2 p 2 (dQ 2 /dt 2 ) + t 2 p 2 (dQ 2 /dp 2 ) (dp 2 /dt 2 ) + t 1 p 1 (dQ 1 /dt 2 ) What will the Full Impact of a tax on local goods be? Less Sold! But it Is now taxed. Higher prices, Less sold. More taxes on Substitutes.

33 dT/dt 2 = p 2 Q 2 + t 2 p 2 (dQ 2 /dt 2 ) + t 2 p 2 (dQ 2 /dp 2 ) (dp 2 /dt 2 ) + t 1 p 1 (dQ 1 /dt 2 ) dT/dt 2 = p 2 Q 2 + t 2 (dQ 2 /dt 2 ) (Q 2 /Q 2 ) p 2 + (Q 2 /Q 2 )(p 2 /p 2 ) t 2 p 2 (dQ 2 /dp 2 ) (dp 2 /dt 2 ) + (t 2 /t 2 ) (Q 1 /Q 1 ) t 1 p 1 (dQ 1 /dt 2 ) dT/dt 2 = p 2 Q 2 + dQ 2 /dt 2 (t 2 /Q 2 ) (p 2 Q 2 ) + p 2 Q 2 [(dQ 2 /dp 2 ) (p 2 /Q 2 )] [(dp 2 /dt 2 ) (t 2 /p 2 )] + (t 1 /t 2 )(p 1 Q 1 ) (dQ 1 /dt 2 ) (t 2 /Q 1 ) dT/dt 2 = p 2 Q 2 + Elas Q 2 t 2 (p 2 Q 2 ) + p 2 Q 2 (Elas Q 2 p 2 ) (Elas p 2 t 2 ) + (t 1 /t 2 )(p 1 Q 1 ) (Elas Q 1 t 2 ) dT/dt 2 = p 2 Q 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 )+ p 1 Q 1 (t 1 /t 2 ) (Elas Q 1 t 2 ) What will the Full Impact of a tax on local goods be?

34 dT/dt 2 = p 2 Q 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 )+ p 1 Q 1 (t 1 /t 2 ) (Elas Q 1 t 2 ) A Model of the Service Tax + or - ? KEY POINT --- There are LOTS of Impacts!

35 dT/dt 2 = p 2 Q 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 )+ p 1 Q 1 (t 1 /t 2 ) (Elas Q 1 t 2 ) 0.06* (dT/dt 2 ) = 0.06 * p 2 Q 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 ) * t 1 p 1 Q 1 (Elas Q 1 t 2 ) Elas Tt 2 = s 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 ) + s 1 * Elas Q 1 t 2 ; s 1 = t 1 p 1 Q 1 /T; s 2 = t 2 p 2 Q 2 /T. A 6% Service Tax t 2 = 0.06 This is a one UNIT  in tax. We want 0.06 of that.

36 dT/dt 2 = p 2 Q 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 )+ p 1 Q 1 (t 1 /t 2 ) (Elas Q 1 t 2 ) 0.06* (dT/dt 2 ) = 0.06 * p 2 Q 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 ) * p 1 Q 1 (t 1 ) (Elas Q 1 t 2 ) Elas Tt 2 = s 2 (1 + Elas Q 2 t 2 + Elas Q 2 p 2 Elas p 2 t 2 ) + s 1 * Elas Q 1 t 2 ; s 1 = t 1 p 1 Q 1 /T; s 2 = t 2 p 2 Q 2 /T. A 6% Service Tax t 2 = % of original sales of Q 2 Change in sales of Q 1