1. 5520_l_15_tax incidence © Allen C. Goodman, 2015
11/8/2018
WHO
REALLY
PAYS?
Tax Incidence
© Allen C. Goodman, 2015

2. 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.

5. Tax Bites

7. Short-Run and Long-Run Impacts
Why drawn like this? $ 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

8. Long-Run Impacts Look at LR supply elasticities?
Supply more elastic $ 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

9. Long-Run Impacts What is net impact as drawn?$ 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 ↓. Probably ↓.
D'' P2 P3
New Tax Rev.
Tot. Tax Rev. P1
Tot Sales Q3 Q2 Q1
Quantity

10. What happens in parallel markets? e.g. Michigan/Ohio
SR?
Let’s look at cigarettes.
Michigan and Ohio sellers are both price takers. Why? OH $ $ MI
D'M DM DO
PM+ t
Taxes PM PO Q q Q2 Q1 q1

11. Parallel Market e.g. Michigan/Ohio
Let’s look at cigarettes.
Michigan and Ohio are both price takers. Why?
LR? MI OH $ $
D'M DM DO
D'O
PM+ t
Taxes PM PO Q Q
Q'2 Q2 Q1 q1 q2

12. 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 p1 Q1 (t1, t2, p1, p2, y) + t2 p2 Q2 (t1, t2, p1, p2, y)
y = p1 Q1 + p2 Q2 + - + - +
What happens if we
establish (increase) taxes
on local goods, services?

13. 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?

14. 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 )
Less local goods sold!
But it Is now taxed.
Higher prices,
Less sold.
More taxes on
Substitutes.

15. 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)

16. 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!

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

18. 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) * 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