Micro-04-SupplyDemand-Tax-Equivalence_SLIDES.pdf

ECO 101 Tax Slides

1. Tax Liability Equivalence

2. Tax Liability Equivalence
▶In a competitive market, the burden of a tax does not depend on how the tax is col-
lected. Whether the tax is levied on the demand side or on the supply side, the bur-
den of the tax is distributed according to relative elasticities.
▶Specific tax:Also known as per-unit tax. Depends on the quantity sold (but not on
the price). Example: excise taxes, gasoline tax.
▶Ad-Valorem tax:Depends on the value of the good (and not just on quantity). Ex-
amples: consumption tax, property tax, stamp duty.
“
”
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3. Tax Liability Equivalence
▶In a competitive market, the burden of a tax does not depend on how the tax is col-
lected. Whether the tax is levied on the demand side or on the supply side, the bur-
den of the tax is distributed according to relative elasticities.
▶Specific tax:Also known as per-unit tax. Depends on the quantity sold (but not on
the price). Example: excise taxes, gasoline tax.
▶Ad-Valorem tax:Depends on the value of the good (and not just on quantity). Ex-
amples: consumption tax, property tax, stamp duty.
“
”
1 / 31

4. Tax Liability Equivalence
▶In a competitive market, the burden of a tax does not depend on how the tax is col-
lected. Whether the tax is levied on the demand side or on the supply side, the bur-
den of the tax is distributed according to relative elasticities.
▶Specific tax:Also known as per-unit tax. Depends on the quantity sold (but not on
the price). Example: excise taxes, gasoline tax.
▶Ad-Valorem tax:Depends on the value of the good (and not just on quantity). Ex-
amples: consumption tax, property tax, stamp duty.
“
”
1 / 31

5. Specific Tax

6. Demand Side

7. Specific Tax on the Demand SideSDQP
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8. Specific Tax on the Demand SideSDQP
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9. Specific Tax on the Demand SideSDQP
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10. Specific Tax on the Demand SideDSTTTQP
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11. Specific Tax on the Demand SideDSD−TQP
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12. Specific Tax on the Demand SideDSD−TTQP
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13. Supply Side

14. Specific Tax on the Supply SideDSQP
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15. Specific Tax on the Supply SideDSQP
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16. Specific Tax on the Supply SideDSQP
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17. Specific Tax on the Supply SideDSTTTQP
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18. Specific Tax on the Supply SideDSS+TQP
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19. Specific Tax on the Supply SideDSS+TTQP
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20. Equivalence

21. Tax Liability Equivalence: Case of a Specific TaxDSD−TTQP DSS+TTQP
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22. Ad-Valorem Tax

23. Demand Side

24. Ad-Valorem Tax on the Demand SideSDQP
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25. Ad-Valorem Tax on the Demand SideSDQP
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26. Ad-Valorem Tax on the Demand SideSDQP
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27. Ad-Valorem Tax on the Demand SideDSTTTQP
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28. Ad-Valorem Tax on the Demand SideDSD−TQP
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29. Ad-Valorem Tax on the Demand SideDSD−TTQP
20 / 31

30. Supply Side

31. Ad-Valorem Tax on the Supply SideDSQP
21 / 31

32. Ad-Valorem Tax on the Supply SideDSQP
22 / 31

33. Ad-Valorem Tax on the Supply SideDSQP
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34. Ad-Valorem Tax on the Supply SideDSTTTQP
24 / 31

35. Ad-Valorem Tax on the Supply SideDSS+TQP
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36. Ad-Valorem Tax on the Supply SideDSS+TTQP
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37. Equivalence

38. Tax Liability Equivalence: Case of the Ad-Valorem TaxDSD−TTQP DSS+TTQP
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39. Linear Systems

40. Tax Liability Equivalence: Linear System
▶The incidence of the tax does not depend on which side of the market makes the tax pay-
ments. Consider the demand-supply system:
Q
D
=1−P
Q
S
=P
▶Suppose a per-unit taxTis placed on buyers (the demand side):
Q
D
=1−(P
S
+T)
Q
S
=P
S
whereP
S
denotes the price received by sellers (the supply side).
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−(P
S
+T) =P
S
=⇒ P
S
=
1−T
2
=⇒ P
D
=P
S
+T=
1+T
2
28 / 31

41. Tax Liability Equivalence: Linear System
▶The incidence of the tax does not depend on which side of the market makes the tax pay-
ments. Consider the demand-supply system:
Q
D
=1−P
Q
S
=P
▶Suppose a per-unit taxTis placed on buyers (the demand side):
Q
D
=1−(P
S
+T)
Q
S
=P
S
whereP
S
denotes the price received by sellers (the supply side).
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−(P
S
+T) =P
S
=⇒ P
S
=
1−T
2
=⇒ P
D
=P
S
+T=
1+T
2
28 / 31

42. Tax Liability Equivalence: Linear System
▶The incidence of the tax does not depend on which side of the market makes the tax pay-
ments. Consider the demand-supply system:
Q
D
=1−P
Q
S
=P
▶Suppose a per-unit taxTis placed on buyers (the demand side):
Q
D
=1−(P
S
+T)
Q
S
=P
S
whereP
S
denotes the price received by sellers (the supply side).
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−(P
S
+T) =P
S
=⇒ P
S
=
1−T
2
=⇒ P
D
=P
S
+T=
1+T
2
28 / 31

43. Tax Liability Equivalence: Linear System
▶Suppose a per-unit taxTis placed on sellers (the supply side):
Q
D
=1−P
D
Q
S
=P
D
−T
whereP
D
the price paid by buyers (the demand side)
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−P
D
=P
D
−T=⇒ P
D
=
1+T
2
=⇒ P
S
=P
D
−T=
1−T
2
▶Comparing the expressions shows that whether the buyers or the sellers pay the tax, the in-
cidence is equivalent: The quantity traded is reduced by the same amount, the buyers’ price
rises by the same amount, the sellers’ price falls by the same amount.
▶Tax liability equivalence holds for any tax schedule and any kind of demand and supply curves.
29 / 31

44. Tax Liability Equivalence: Linear System
▶Suppose a per-unit taxTis placed on sellers (the supply side):
Q
D
=1−P
D
Q
S
=P
D
−T
whereP
D
the price paid by buyers (the demand side)
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−P
D
=P
D
−T=⇒ P
D
=
1+T
2
=⇒ P
S
=P
D
−T=
1−T
2
▶Comparing the expressions shows that whether the buyers or the sellers pay the tax, the in-
cidence is equivalent: The quantity traded is reduced by the same amount, the buyers’ price
rises by the same amount, the sellers’ price falls by the same amount.
▶Tax liability equivalence holds for any tax schedule and any kind of demand and supply curves.
29 / 31

45. Tax Liability Equivalence: Linear System
▶Suppose a per-unit taxTis placed on sellers (the supply side):
Q
D
=1−P
D
Q
S
=P
D
−T
whereP
D
the price paid by buyers (the demand side)
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−P
D
=P
D
−T=⇒ P
D
=
1+T
2
=⇒ P
S
=P
D
−T=
1−T
2
▶Comparing the expressions shows that whether the buyers or the sellers pay the tax, the in-
cidence is equivalent: The quantity traded is reduced by the same amount, the buyers’ price
rises by the same amount, the sellers’ price falls by the same amount.
▶Tax liability equivalence holds for any tax schedule and any kind of demand and supply curves.
29 / 31

46. Tax Liability Equivalence: Linear System
▶Suppose a per-unit taxTis placed on sellers (the supply side):
Q
D
=1−P
D
Q
S
=P
D
−T
whereP
D
the price paid by buyers (the demand side)
▶In equilibrium, market clearingQ
D
=Q
S
implies:
1−P
D
=P
D
−T=⇒ P
D
=
1+T
2
=⇒ P
S
=P
D
−T=
1−T
2
▶Comparing the expressions shows that whether the buyers or the sellers pay the tax, the in-
cidence is equivalent: The quantity traded is reduced by the same amount, the buyers’ price
rises by the same amount, the sellers’ price falls by the same amount.
▶Tax liability equivalence holds for any tax schedule and any kind of demand and supply curves.
29 / 31

47. Tax Liability Equivalence: Linear System
▶The incidence of the tax does not depend on which side of the market makes the tax pay-
ments. The following tax schedules are equivalent:
{
Q
D
=c−a(P
S
+T)
Q
S
=d+bP
S
⇐⇒
{
Q
D
=c−aP
D
Q
S
=d+b(P
D
−T)
whereP
S
denotes the price received by sellers (the supply side) andP
D
the price paid by buy-
ers (the demand side), and wherea,b,c,dare parameters of the linear system.
▶In equilibrium,Q
D
=Q
S
yields:
c−a(P
S
+T) =d+bP
S
=⇒ P
S
=
c−d−a·T
a+b
c−aP
D
=d+b(P
D
−T) =⇒ P
D
=
c−d+b·T
a+b
▶Example:a=1,b=1,c=1,d=0
{
Q
D
=1−(P
S
+T)
Q
S
=P
S
⇐⇒
{
Q
D
=1−P
D
Q
S
=P
D
−T
=⇒ P
D
=
1+T
2
,P
S
=
1−T
2
30 / 31

48. Tax Liability Equivalence: Linear System
▶The incidence of the tax does not depend on which side of the market makes the tax pay-
ments. The following tax schedules are equivalent:
{
Q
D
=c−a(P
S
+T)
Q
S
=d+bP
S
⇐⇒
{
Q
D
=c−aP
D
Q
S
=d+b(P
D
−T)
whereP
S
denotes the price received by sellers (the supply side) andP
D
the price paid by buy-
ers (the demand side), and wherea,b,c,dare parameters of the linear system.
▶In equilibrium,Q
D
=Q
S
yields:
c−a(P
S
+T) =d+bP
S
=⇒ P
S
=
c−d−a·T
a+b
c−aP
D
=d+b(P
D
−T) =⇒ P
D
=
c−d+b·T
a+b
▶Example:a=1,b=1,c=1,d=0
{
Q
D
=1−(P
S
+T)
Q
S
=P
S
⇐⇒
{
Q
D
=1−P
D
Q
S
=P
D
−T
=⇒ P
D
=
1+T
2
,P
S
=
1−T
2
30 / 31

49. Tax Liability Equivalence: Linear System
▶The incidence of the tax does not depend on which side of the market makes the tax pay-
ments. The following tax schedules are equivalent:
{
Q
D
=c−a(P
S
+T)
Q
S
=d+bP
S
⇐⇒
{
Q
D
=c−aP
D
Q
S
=d+b(P
D
−T)
whereP
S
denotes the price received by sellers (the supply side) andP
D
the price paid by buy-
ers (the demand side), and wherea,b,c,dare parameters of the linear system.
▶In equilibrium,Q
D
=Q
S
yields:
c−a(P
S
+T) =d+bP
S
=⇒ P
S
=
c−d−a·T
a+b
c−aP
D
=d+b(P
D
−T) =⇒ P
D
=
c−d+b·T
a+b
▶Example:a=1,b=1,c=1,d=0
{
Q
D
=1−(P
S
+T)
Q
S
=P
S
⇐⇒
{
Q
D
=1−P
D
Q
S
=P
D
−T
=⇒ P
D
=
1+T
2
,P
S
=
1−T
2
30 / 31

50. Tax Liability Equivalence: Linear System
▶In general, letαbe share of tax paid by the demand side, andβthe share paid by the supply
side, whereα+β=1. The following system is equivalent to the previous one:
{
Q
D
=c−a(P+αT)
Q
S
=d+b(P−βT)
wherePis the vertical coordinate of the intersection of the post-tax schedules, i.e.
P=P
D
−αTandP=P
S
+βT. In equilibrium,Q
D
=Q
S
yields:
c−a(P+αT) =d+b(P−βT) =⇒ P=
c−d
a+b
+
bβ−aα
a+b
·T
Substituting and simplifying yields:
P
D
=P+αT=
c−d+b·T
a+b
P
S
=P−βT=
c−d−a·T
a+b
▶The tax allocation parametersαandβhave no effect on prices and quantity. Only the pa-
rameters of the demand and supply curves affect the distribution of tax incidence.
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51. Tax Liability Equivalence: Linear System
▶In general, letαbe share of tax paid by the demand side, andβthe share paid by the supply
side, whereα+β=1. The following system is equivalent to the previous one:
{
Q
D
=c−a(P+αT)
Q
S
=d+b(P−βT)
wherePis the vertical coordinate of the intersection of the post-tax schedules, i.e.
P=P
D
−αTandP=P
S
+βT. In equilibrium,Q
D
=Q
S
yields:
c−a(P+αT) =d+b(P−βT) =⇒ P=
c−d
a+b
+
bβ−aα
a+b
·T
Substituting and simplifying yields:
P
D
=P+αT=
c−d+b·T
a+b
P
S
=P−βT=
c−d−a·T
a+b
▶The tax allocation parametersαandβhave no effect on prices and quantity. Only the pa-
rameters of the demand and supply curves affect the distribution of tax incidence.
31 / 31