what is the optimal incidence of taxation in coupled markets
TRANSCRIPT
![Page 1: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/1.jpg)
What is the Optimal Incidence of Taxation inCoupled Markets?
Stephen Kinsella David Ramsey
University of Limerick
Irish Economic Association, April 25–27, 2008
![Page 2: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/2.jpg)
Today
Idea
Model
Derivation
Numerical Examples
Further Work
![Page 3: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/3.jpg)
This Paper in one slide
Question What happens to coupled markets when one getstaxed?
Method Study imposition of the tax under more and morecomplex market arrangements
Results As markets become more coupled, firm relationshipsreally matter for the imposition of the tax
Practical application Environmental taxes; tourism subsidies.
Further Work Econometric testing of cross price elasticities: neednatural/computational experiment
![Page 4: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/4.jpg)
This Paper in one slide
Question What happens to coupled markets when one getstaxed?
Method Study imposition of the tax under more and morecomplex market arrangements
Results As markets become more coupled, firm relationshipsreally matter for the imposition of the tax
Practical application Environmental taxes; tourism subsidies.
Further Work Econometric testing of cross price elasticities: neednatural/computational experiment
![Page 5: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/5.jpg)
This Paper in one slide
Question What happens to coupled markets when one getstaxed?
Method Study imposition of the tax under more and morecomplex market arrangements
Results As markets become more coupled, firm relationshipsreally matter for the imposition of the tax
Practical application Environmental taxes; tourism subsidies.
Further Work Econometric testing of cross price elasticities: neednatural/computational experiment
![Page 6: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/6.jpg)
This Paper in one slide
Question What happens to coupled markets when one getstaxed?
Method Study imposition of the tax under more and morecomplex market arrangements
Results As markets become more coupled, firm relationshipsreally matter for the imposition of the tax
Practical application Environmental taxes; tourism subsidies.
Further Work Econometric testing of cross price elasticities: neednatural/computational experiment
![Page 7: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/7.jpg)
Markets we study
i) the classical case of a monopoly producing one good,
ii) the case of two companies each producing a good inwhich one company is a Stackelberg leader. Weconsider the e!ect of placing a tax on a) the leaderand b) the follower,
iii) the case of two companies each producing a good inwhich there is no such hierarchy,
iv) the case of a monopoly producing two goods.
![Page 8: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/8.jpg)
Notation
!i ,j % ! in demand for good i for 1% change in price of good jW (p) ProfitpD(p) Revenuem Marginal cost of productionE fixed costs i! m = m̄p total pricet levy/tax
![Page 9: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/9.jpg)
Methodology
1. Linearise around a demand curve
2. Assume tax is small relative to total price
3. Solve Stackelberg game
4. Derive analytical expressions for e!ect on e"ciency of theimposition of tax
![Page 10: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/10.jpg)
Methodology
1. Linearise around a demand curve
2. Assume tax is small relative to total price
3. Solve Stackelberg game
4. Derive analytical expressions for e!ect on e"ciency of theimposition of tax
![Page 11: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/11.jpg)
Methodology
1. Linearise around a demand curve
2. Assume tax is small relative to total price
3. Solve Stackelberg game
4. Derive analytical expressions for e!ect on e"ciency of theimposition of tax
![Page 12: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/12.jpg)
Classical Model
W (p) = (A" Bp)(p "m)" E , (1)
p! =m
2+
A
2B. (2)
B ="!D(p!)
p!; A = (1" !)D(p!).
m =p!(1 + !)
!# p! =
!m
1 + !.
This is the monopoly (non-discrimination) pricing rule from Tirole(1993, pg. 76.)
![Page 13: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/13.jpg)
Classical Model
W (p) = (A" Bp)(p "m)" E , (1)
p! =m
2+
A
2B. (2)
B ="!D(p!)
p!; A = (1" !)D(p!).
m =p!(1 + !)
!# p! =
!m
1 + !.
This is the monopoly (non-discrimination) pricing rule from Tirole(1993, pg. 76.)
![Page 14: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/14.jpg)
Classical Model
W (p) = (A" Bp)(p "m)" E , (1)
p! =m
2+
A
2B. (2)
B ="!D(p!)
p!; A = (1" !)D(p!).
m =p!(1 + !)
!# p! =
!m
1 + !.
This is the monopoly (non-discrimination) pricing rule from Tirole(1993, pg. 76.)
![Page 15: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/15.jpg)
Classical Model
W (p) = (A" Bp)(p "m)" E , (1)
p! =m
2+
A
2B. (2)
B ="!D(p!)
p!; A = (1" !)D(p!).
m =p!(1 + !)
!# p! =
!m
1 + !.
This is the monopoly (non-discrimination) pricing rule from Tirole(1993, pg. 76.)
![Page 16: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/16.jpg)
Now impose a tax, t
W (p) = (p "m " t)(A" Bp)" E .
The marginal tax revenue will be D(p!)
#W = (m " p!)#D + (1"#p)D(p!) = D(p!).
#S = #pD(p!) =D(p!)
2
i.e. half of the marginal tax revenue. It follows that the marginale"ciency of this tax is 2
3 .
![Page 17: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/17.jpg)
Now impose a tax, t
W (p) = (p "m " t)(A" Bp)" E .
The marginal tax revenue will be D(p!)
#W = (m " p!)#D + (1"#p)D(p!) = D(p!).
#S = #pD(p!) =D(p!)
2
i.e. half of the marginal tax revenue. It follows that the marginale"ciency of this tax is 2
3 .
![Page 18: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/18.jpg)
Now impose a tax, t
W (p) = (p "m " t)(A" Bp)" E .
The marginal tax revenue will be D(p!)
#W = (m " p!)#D + (1"#p)D(p!) = D(p!).
#S = #pD(p!) =D(p!)
2
i.e. half of the marginal tax revenue. It follows that the marginale"ciency of this tax is 2
3 .
![Page 19: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/19.jpg)
Now impose a tax, t
W (p) = (p "m " t)(A" Bp)" E .
The marginal tax revenue will be D(p!)
#W = (m " p!)#D + (1"#p)D(p!) = D(p!).
#S = #pD(p!) =D(p!)
2
i.e. half of the marginal tax revenue. It follows that the marginale"ciency of this tax is 2
3 .
![Page 20: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/20.jpg)
Now impose a tax, t
W (p) = (p "m " t)(A" Bp)" E .
The marginal tax revenue will be D(p!)
#W = (m " p!)#D + (1"#p)D(p!) = D(p!).
#S = #pD(p!) =D(p!)
2
i.e. half of the marginal tax revenue. It follows that the marginale"ciency of this tax is 2
3 .
![Page 21: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/21.jpg)
Hierarchical Model, 2 firms, one good each
Two goods, two firms: p1, p2, Firm 1 is Stackelberg leader.Linearised Demand Functions look like
W1(p1, p2) = (p1 "m1)[A1 " B1p1 + C1p2]" E1
W2(p1, p2) = (p2 "m2)[A2 " B2p2 + C2p1]" E2.
![Page 22: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/22.jpg)
Hierarchical Model, 2 firms, one good each
Two goods, two firms: p1, p2, Firm 1 is Stackelberg leader.Linearised Demand Functions look like
W1(p1, p2) = (p1 "m1)[A1 " B1p1 + C1p2]" E1
W2(p1, p2) = (p2 "m2)[A2 " B2p2 + C2p1]" E2.
![Page 23: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/23.jpg)
Hierarchical Model, contdFirst Eqm condition
"W2
"p2 |p=(p1,p!2 (p1))= 0.
Which leads to
p!2(p1) =m
2+
A2 + C2p1
2B2.
And the second eqm condition is
"W1
"p1 |p=(p!1 ,p!2 (p!1 ))= 0.
Which leads to
p!1 =2A1B2 + C1A2 + C1B2m2 + 2B1B2m1 " C1C2m1
4B1B2 " 2C1C2(3)
![Page 24: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/24.jpg)
Hierarchical Model, contdFirst Eqm condition
"W2
"p2 |p=(p1,p!2 (p1))= 0.
Which leads to
p!2(p1) =m
2+
A2 + C2p1
2B2.
And the second eqm condition is
"W1
"p1 |p=(p!1 ,p!2 (p!1 ))= 0.
Which leads to
p!1 =2A1B2 + C1A2 + C1B2m2 + 2B1B2m1 " C1C2m1
4B1B2 " 2C1C2(3)
![Page 25: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/25.jpg)
Hierarchical Model, contdFirst Eqm condition
"W2
"p2 |p=(p1,p!2 (p1))= 0.
Which leads to
p!2(p1) =m
2+
A2 + C2p1
2B2.
And the second eqm condition is
"W1
"p1 |p=(p!1 ,p!2 (p!1 ))= 0.
Which leads to
p!1 =2A1B2 + C1A2 + C1B2m2 + 2B1B2m1 " C1C2m1
4B1B2 " 2C1C2(3)
![Page 26: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/26.jpg)
Hierarchical Model, contdFirst Eqm condition
"W2
"p2 |p=(p1,p!2 (p1))= 0.
Which leads to
p!2(p1) =m
2+
A2 + C2p1
2B2.
And the second eqm condition is
"W1
"p1 |p=(p!1 ,p!2 (p!1 ))= 0.
Which leads to
p!1 =2A1B2 + C1A2 + C1B2m2 + 2B1B2m1 " C1C2m1
4B1B2 " 2C1C2(3)
![Page 27: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/27.jpg)
Hierarchical Model, contd.
p!2 =4A2B1B2 " A2C1C2 + 2C2A1B2 " C1C2B2m2 + 2C2m1B1B2 "m1C1C 2
2 + 4B1B22m2
4B2(2B1B2 " C1C2).
(4)From the definition of the cross-price elasticities, we have
B1 = "!11D1(p!1 , p!2)
p!1; B2 = "!22D2(p!1 , p
!2)
p!2(5)
C1 =!12D1(p!1 , p
!2)
p!2; C2 =
!21D2(p!1 , p!2)
p!1(6)
A1 = D1(p!1 , p
!2)(1" !11 " !12); A2 = D2(p
!1 , p
!2)(1" !22 " !21). (7)
![Page 28: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/28.jpg)
Hierarchical Model, contd.
p!2 =4A2B1B2 " A2C1C2 + 2C2A1B2 " C1C2B2m2 + 2C2m1B1B2 "m1C1C 2
2 + 4B1B22m2
4B2(2B1B2 " C1C2).
(4)From the definition of the cross-price elasticities, we have
B1 = "!11D1(p!1 , p!2)
p!1; B2 = "!22D2(p!1 , p
!2)
p!2(5)
C1 =!12D1(p!1 , p
!2)
p!2; C2 =
!21D2(p!1 , p!2)
p!1(6)
A1 = D1(p!1 , p
!2)(1" !11 " !12); A2 = D2(p
!1 , p
!2)(1" !22 " !21). (7)
![Page 29: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/29.jpg)
Hierarchical Model, contd.Using these relationships, together with Equations (3) and (4), we obtain
p!1 =m1(2!11!22 " !12!21)
2!22(!11 + 1)" !12!21; p!2 =
!22m2
1 + !22.
![Page 30: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/30.jpg)
Message
Although the structure of the market a!ects the price set by thefollower, this is not apparent when the price is written in terms ofthe cross-price elasticities and marginal costs (the formula isanalogous to the classical model). This is due to the fact that thecross-price elasticity depends on the equilibrium price.
![Page 31: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/31.jpg)
Numerical Examples
! When goods are substitutes
! When goods are complements
![Page 32: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/32.jpg)
Other Results
Market Structure Marginal E"ciency of Taxation1 firm, 1 good 2
3
2 firms, 1 good (Stackelberg leader) 23 "
2!2,1p!2 D2(p!1 ,p!2 )18!2,2p!1 D1(p!1 ,p!2 )+3!2,1p!2 D2(p!1 ,p!2 )
2 firms, 1 good (Stackelberg follower) 23 "
2!1,2[2p!1 !2,2D1(p!1 ,p!2 )"p!2 !2,1D2(p!1 ,p!2 )]p!2 D2(p!1 ,p!2 )[36!2,2!1,1"21!1,2!2,1]+6p!1 !2,2!1,2D1(p!1 ,p!2 )
2 firms, 1 good, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
1 firm, 2 goods, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
2 firms, 1 good, hierarchy 23 "
H1H2
Table: Summary of results on marginal e"ciency of taxation by market structure.
![Page 33: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/33.jpg)
Other Results
Market Structure Marginal E"ciency of Taxation1 firm, 1 good 2
3
2 firms, 1 good (Stackelberg leader) 23 "
2!2,1p!2 D2(p!1 ,p!2 )18!2,2p!1 D1(p!1 ,p!2 )+3!2,1p!2 D2(p!1 ,p!2 )
2 firms, 1 good (Stackelberg follower) 23 "
2!1,2[2p!1 !2,2D1(p!1 ,p!2 )"p!2 !2,1D2(p!1 ,p!2 )]p!2 D2(p!1 ,p!2 )[36!2,2!1,1"21!1,2!2,1]+6p!1 !2,2!1,2D1(p!1 ,p!2 )
2 firms, 1 good, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
1 firm, 2 goods, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
2 firms, 1 good, hierarchy 23 "
H1H2
Table: Summary of results on marginal e"ciency of taxation by market structure.
![Page 34: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/34.jpg)
Other Results
Market Structure Marginal E"ciency of Taxation1 firm, 1 good 2
3
2 firms, 1 good (Stackelberg leader) 23 "
2!2,1p!2 D2(p!1 ,p!2 )18!2,2p!1 D1(p!1 ,p!2 )+3!2,1p!2 D2(p!1 ,p!2 )
2 firms, 1 good (Stackelberg follower) 23 "
2!1,2[2p!1 !2,2D1(p!1 ,p!2 )"p!2 !2,1D2(p!1 ,p!2 )]p!2 D2(p!1 ,p!2 )[36!2,2!1,1"21!1,2!2,1]+6p!1 !2,2!1,2D1(p!1 ,p!2 )
2 firms, 1 good, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
1 firm, 2 goods, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
2 firms, 1 good, hierarchy 23 "
H1H2
Table: Summary of results on marginal e"ciency of taxation by market structure.
![Page 35: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/35.jpg)
Other Results
Market Structure Marginal E"ciency of Taxation1 firm, 1 good 2
3
2 firms, 1 good (Stackelberg leader) 23 "
2!2,1p!2 D2(p!1 ,p!2 )18!2,2p!1 D1(p!1 ,p!2 )+3!2,1p!2 D2(p!1 ,p!2 )
2 firms, 1 good (Stackelberg follower) 23 "
2!1,2[2p!1 !2,2D1(p!1 ,p!2 )"p!2 !2,1D2(p!1 ,p!2 )]p!2 D2(p!1 ,p!2 )[36!2,2!1,1"21!1,2!2,1]+6p!1 !2,2!1,2D1(p!1 ,p!2 )
2 firms, 1 good, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
1 firm, 2 goods, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
2 firms, 1 good, hierarchy 23 "
H1H2
Table: Summary of results on marginal e"ciency of taxation by market structure.
![Page 36: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/36.jpg)
Other Results
Market Structure Marginal E"ciency of Taxation1 firm, 1 good 2
3
2 firms, 1 good (Stackelberg leader) 23 "
2!2,1p!2 D2(p!1 ,p!2 )18!2,2p!1 D1(p!1 ,p!2 )+3!2,1p!2 D2(p!1 ,p!2 )
2 firms, 1 good (Stackelberg follower) 23 "
2!1,2[2p!1 !2,2D1(p!1 ,p!2 )"p!2 !2,1D2(p!1 ,p!2 )]p!2 D2(p!1 ,p!2 )[36!2,2!1,1"21!1,2!2,1]+6p!1 !2,2!1,2D1(p!1 ,p!2 )
2 firms, 1 good, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
1 firm, 2 goods, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
2 firms, 1 good, hierarchy 23 "
H1H2
Table: Summary of results on marginal e"ciency of taxation by market structure.
![Page 37: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/37.jpg)
Other Results
Market Structure Marginal E"ciency of Taxation1 firm, 1 good 2
3
2 firms, 1 good (Stackelberg leader) 23 "
2!2,1p!2 D2(p!1 ,p!2 )18!2,2p!1 D1(p!1 ,p!2 )+3!2,1p!2 D2(p!1 ,p!2 )
2 firms, 1 good (Stackelberg follower) 23 "
2!1,2[2p!1 !2,2D1(p!1 ,p!2 )"p!2 !2,1D2(p!1 ,p!2 )]p!2 D2(p!1 ,p!2 )[36!2,2!1,1"21!1,2!2,1]+6p!1 !2,2!1,2D1(p!1 ,p!2 )
2 firms, 1 good, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
1 firm, 2 goods, no hierarchy 23 "
!2,1[2p!2 !1,1D2(p!1 ,p!2 )"p!1 !1,2D1(p!1 ,p!2 )]p!1 D1(p!1 ,p!2 )[18!1,1!2,2"6!1,2!2,1]+3p!2 !1,1!2,1D2(p!1 ,p!2 )
2 firms, 1 good, hierarchy 23 "
H1H2
Table: Summary of results on marginal e"ciency of taxation by market structure.
![Page 38: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/38.jpg)
Further Work
Testing We’d like to test the magnitudes of theseine"ciencies econometrically and/or experimentally.
Comments? Any comments/questions are welcome
![Page 39: What is the Optimal Incidence of Taxation in Coupled Markets](https://reader036.vdocument.in/reader036/viewer/2022062419/5593fafd1a28ab694f8b45d8/html5/thumbnails/39.jpg)
References
Jean Tirole. The Theory of Industrial Organization. MIT Press,1993.