1 Flores, D. (009) All you can drink: should we worry about quality? Journal of Regulatory Economics 35(1), Saggi, K., and Vettas, N. (00) On in

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2 1 Flores, D. (009) All you can drink: should we worry about quality? Journal of Regulatory Economics 35(1), Saggi, K., and Vettas, N. (00) On intrabrand and interbrand competition: The strategic role of fees and royalties. European Economic Review 46(1), Nguyen, X. (014) Monopolistic third-degree price discrimination under vertical product differentiation. Economics Letters 15(), Pazgal, A., and Soberman, D. (008) Behavior-based discrimination: Is it a winning play, and if so, when? Marketing Science 7(6), Chung, H.L., Lin, Y.S., and Hu, J.L. (013) Bundling strategy and product differentiation. Journal of Economics 108(3), 07 9.

3 3 16 3

4 fixed fee per unit royalty ad valorem royalty Heywood et al. (014, IJIO) 4

5 3 f r two-part tariff q y y = rq + f. y q = r + f q. q Flores (009, JRE) Saggi and Vettas (00, EER) 5

6 4 Flores (009, JRE) E p : E, : pq + E. Flores (009) 6

7 5 Flores (009, JRE) s p q q = s(1 p) p 0 E CS E E E = 1 s(1 p). CS = 1 p 0 p 0 q 0 1 x s 0 q 0 O q 0 dx p 0 q 0 E = 1 x s dx p 0 q 0 q = s(1 p) p = 1 q s 1 E s(1 p 0) 1 s q 7

8 6 Flores (009) s c 0 + s s max s (p c 0 s )q + E, s.t. q = s(1 p), p = 0, c 0 = 0, E = 1 s(1 p). 1 max s (1 s )s (= π B ). max p,s (p c 0 s )q + E, s.t. q = s(1 p), E = 1 s(1 p). max p,s 1 (1 p)(1 c 0 + p s )s (= π T ). 8

9 7 Flores (009) FOC π B s = 1 (1 6s ) = 0, s B = 1 6. π B = FOCs π T p = s(c 0 p + s ) = 0 and π T s = 1 (1 p)(1 c 0 + p 6s ) = 0, p T = 1 + 4c 0 5 and s T = 1 c0 5. π T = 8(1 c 0) c 0. 9

10 8 Flores (009) vs. Proposition 1. π B π T = (1 c 0) c 0 0 c Proposition. s B s T = c0 5 0 c < c 0 <

11 9 Saggi and Vettas (00, EER): Flores (009) Saggi and Vettas (00, EER) U 1 U U i n i U i D 1 i, D i,..., Dn i i U i r i f i D k i q k i D k i p i = a n i k=1 qk i s n j k=1 qk j 11

12 10 Saggi and Vettas (00): U 1 U D1 1 r 1, f 1 r, f n D 1 1 n 1 D D q1 1 q n 1 1 q 1 q n p i = a n i k=1 qk i s n j k=1 qk j 1

13 11 Saggi and Vettas (00): D m i max q m i n i a q k i s k=1 n j k=1 q k j qm i r i q m i f i (= π m Di ). U i max r i, f i r i n i k=1 q k i + n i f i (= π Ui ). 1 r i f i q m i 13

14 1 Saggi and Vettas (00): FOCs ( m {1,..., n 1 }, m {1,..., n }) π m D1 π m D = 0 and = 0, q m q m 1 = (1 + n )(r 1 a) + n (a r )s n 1 n s (1 + n 1 )(1 + n ) q m 1 and q m = (1 + n 1)(r a) + n 1 (a r 1 )s. n 1 n s (1 + n 1 )(1 + n ) [ ] [ ] (1 + π m D1 = n )(r 1 a) + n (a r )s (1 + f n 1 n s 1, π m D (1 + n 1 )(1 + n ) = n1 )(r a) + n 1 (a r 1 )s f n 1 n s. (1 + n 1 )(1 + n ) f i f i [ ] [ ] (1 + f1 = n )(r 1 a) + n (a r )s (1 +, f n 1 n s (1 + n 1 )(1 + n ) = n1 )(r a) + n 1 (a r 1 )s. n 1 n s (1 + n 1 )(1 + n ) 14

15 13 Saggi and Vettas (00): [1] q m 1 q m f 1 f π U1 π U r 1 r max r i r i n i k=1 q k i + n i f i (= π Ui (r i, r j )). FOCs π U1 (r 1, r ) r 1 = 0 and π U (r 1, r ) r = 0, r 1 = a[s n 1 (s + s )][1 + n + n 1 (n s n 1)] n 1 [4(1 + n 1 )(1 + n ) (1 + 3n + 3n 1 + 5n 1 n )s + n 1 n s 4 ], r = a[s + n (s + s )][1 + n 1 + n (n 1 s n 1 1)] n [4(1 + n 1 )(1 + n ) (1 + 3n 1 + 3n + 5n 1 n )s + n 1 n s 4 ]. 15

16 14 Saggi and Vettas (00): [] r i f i f 1 = a (1 + n ) [s + n 1 (s + s )] n 1 [4 s + n 1 (4 3s ) + n (4 3s ) + n 1 n (4 5s + s 4 )], f = a (1 + n 1 ) [s + n (s + s )] n 1 [4 s + n 1 (4 3s ) + n (4 3s ) + n 1 n (4 5s + s 4 )] 16

18 15 [1] 1 A B a b u a ( A) p A u a ( B) p B, u b ( B) p B u b ( A) p A, u a ( A) p A 0, u b ( B) p B 0. 1 self-selection constraints participation constraints 18

19 16 [] 3 Behavior-based discrimination: BBD) 1 3 Fudenberg and Tirole (000, RJE) Pazgal and Soberman (008, MS) 3 BBD 19

20 17 3 Nguyen (014, EL) Ikeda and Toshimitsu (010, EL) Ikeda and Toshimitsu (010) Nguyen (014) Nguyen (014) Ikeda and Toshimitsu (010) Nguyen (014) 3 0

21 18 Nguyen (014, EL): [1] 1 (p 1 p ) q θ i θ i [0, 1] θ 1 1 v 1 θ v v 1 (θ 1 ) = αθ 1 q p 1, v (θ ) = θ q p. ˆθ i v i ( ˆθ i ) = 0) ˆ θ 1 = p 1 αq, ˆ θ = p q ˆθ i 1 θ i

22 19 Nguyen (014): [] q q / ( π M = 1 p ) ) ( 1 (p 1 q + 1 p ) ) (p q. αq q } {{ }} {{ } =1 θˆ 1 1 θˆ CS = 1 p 1 /(αq) (αθ 1 q p 1 ) dθ p /q (θ q p ) dθ. S W = CS + π M p = p 1 = p p

23 0 Nguyen (014) q p 1 p q p 1 p Mathematica Nguyen (014) 3

24 1 max p 1,p ( 1 p ) ) 1 (p 1 q αq + ( 1 p ) ) (p q. q FOCs ( π M / p 1 = 0 π M / p = 0) p FPD 1 = q(q + α), p FPD = 4 q( + q), π FPD M 4 S W FPD = 3q[(1 + α)q 8αq + 4α(1 + α)]. 16α = q[(1 + α)q 8αq + 4α(1 + α)], 16α 4

25 ( max 1 p ) ) (p q + p αq ( 1 p ) ) (p q. q FOC ( π M / p = 0) p FU = q(q + 4α + qα), π FU M 4(1 + α) q(q 4α + qα) =, 16α(1 + α) S W FU = q[3(1 + α) q 4α(1 + α)q + 16α(1 + α + α )]. 3α(1 + α) π FPD M πfu M q(1 α) = 4(1 + α) (> 0), S W FPD S W FU q(1 α) = (< 0). 8(1 + α) q 5

26 3 max q ( ) 1 pfpd 1 p1 FPD q αq + ( ) 1 pfpd p FPD q. q FOC ( π FPD M / q = 0) q PD = (4α M) 3(1 + α), πpd M = (4α M)[M + 4Mα + α(9 14α + 9α )] 54α(1 + α), S W PD = (4α M)[M + 4Mα + α(9 14α + 9α )] 36α(1 + α). M = α( 3α + 10α 3) α [0.46, 1) M > 0 6

27 4 (1 pfu ) ) (p FU q (1 pfu ) ) (p FU q max q αq + q. FOC ( π FU M / q = 0) q U = 4α 3(1 + α), πu M = 16α 7(1 + α), S WU = α(3 α + 3α ) 9(1 + α). π PD M πu M = 4α (9 α + 9α ) 3Mα(3 10α + 3α ) M 3 54α(1 + α), S W PD S W U = 4α (3 10α + 3α ) 3Mα(3 10α + 3α ) M 3 36α(1 + α). 7

28 5 M = α( 3α + 10α 3) π PD M S W PD S W U α πu M α [0.46, 1) π PD M πu M > 0 S W PD S W U < 0 (p.155, Proposition 1.) 8

29 6 Nguyen (014) Ikeda and Toshimitsu (010) Ikeda and Toshimitsu (010, EL) (p.55, Proposition 1.) Nguyen (014) ( π M = 1 p ) ) ( 1 (p 1 q + 1 p ) ) (p q. αq q } {{ }} {{ } =1 θˆ 1 1 θˆ Ikeda and Toshimitsu (010) ( π M = 1 p ) ( 1 p p ) p q αq q. } {{ }} {{ } =1 θˆ 1 1 θˆ Nguyen (014) Ikeda and Toshimitsu (010) 9

30 7 Amazon.com Web Fudenberg and Tirole (000, RJE) Pazgal and Soberman (008, MS) (Behavior-Based Discrimination: BBD) 30

31 8 Pazgal and Soberman (008, MS): [1] 1 1 (BBD) BBD 1 x [0, 1] Hotelling s linear city v B x 1 x 1 x 31

32 9 Pazgal and Soberman (008): [] x u(x) = { v x p1 + ECS (1) if 1 1, v (1 x) p + ECS () if 1. p i 1 i ECS (1) 1 1 ECS () q v q p 1 + ECS (1) = v (1 q) p + ECS () q = 1 p 1 + p + ECS (1) ECS (). 3

33 30 Pazgal and Soberman (008): [3] 0 q 1 x 1 x x 33

34 31 Pazgal and Soberman (008): [4] BBD [0, q] [q, 1] [0, q] 1 [q, 1] 1 q ECS (1) ECS () 1 ECS (1) = v (1 q) p 1, ECS () = v q p 1. p i j 1 i j 34

35 3 Pazgal and Soberman (008): [5] q 1 i j p i j [0, q] 1 1 x u(x) = { v x p1 + [B + v x p 1 1 ] if 1, v x p 1 + [v (1 x) p 1 ] if. x 1 [v x 1 p 1 ] + [B + v x 1 p 1 1 ] = [v x 1 p 1 ] + [v (1 x 1 ) p 1 ] x 1 = 1 + B p1 1 + p1. 35

36 33 Pazgal and Soberman (008): [6] [q, 1] 1 x u(x) = { v (1 x) p + [v x p 1 ] if 1, v (1 x) p + [B + v (1 x) p ] if. x v (1 x ) p + [v x p 1 ] = v (1 x ) p + [B + v (1 x ) p ] x = 1 B p 1 + p. 36

37 34 Pazgal and Soberman (008): c π 1 = (p 1 c)q + ( p 1 } {{ } 1 c) x 1 + ( p 1 c) (x q), } {{ } 1 π = (p c)(1 q) + ( p 1 } {{ } c) (q x 1 ) + ( p c) (1 x ). } {{ } p 1 p q 1 p 1 1 p 1 p1 p 37

38 35 [1] max p 1 1, p 1 max p 1, p (p 1 c)q + ( p 1 1 c) x 1 + ( p 1 c) (x q), s.t. x 1 = 1 + B p1 1 + p1 and x = 1 B p 1 + p. (p c)(1 q) + ( p 1 c) (q x 1 ) + ( p c) (1 x ), s.t. x 1 = 1 + B p1 1 + p1 and x = 1 B p 1 + p. FOCs p 1 1 p b + 3c + q =, p 1 3 3c + 4q 1 B =, p 3 3 B + 3c 4q =, B + 3c q =. 3 38

39 36 [] q = [1 p 1 + p + ECS (1) ECS ()]/ ECS (1) = v (1 q) p 1 ECS () = v q p 1 p1 1, p 1, p1, p q q = 4 3p 1 + 3p 8 q p 1 1, p 1, p1, p. p 1 1 = 8 + 4B + 1c 3p 1 + 3p, p 1 1 = B + 6c + 3p 1 3p, 6 p 1 = B + 6c 3p 1 + 3p, p 6 = 8 + 4B + 1c + 3p 1 3p. 1 x 1 x p 1 1, p 1, p1, p x 1 = 8 + 4B 3p 1 + 3p 4, x = 16 4B 3p 1 + 3p 4. 39

40 max p 1 max p (p 1 c)q + ( p 1 1 c) x 1 + ( p 1 c) (x q ), (p c)(1 q ) + ( p 1 c) (q x 1 ) + ( p c) (1 x ). FOCs 1 p 1 = p 4 B + 3c =. 3 π 1 = π = 17 4B + B

42 38 A B 1 (a, b) = (1, ), (, 4), (3, 6), (i) Hotelling unit square (ii) (ii) (i) Belleflamme and Peitz (010, pp.60 65) Brito an Vasconcelos (015, SEJ), Nalebuff (004, QJE) 4

43 39 Chung et al. (013, JE): [1] Chung et al. (013, JE) A B 3 A1 A B A B θ, α, γ q A1, q A, q B p A1, p A, p B 43

44 40 Chung et al. (013, JE): [] max q A1,q A,q B,m q A1 + q A + q B 1 ( q A1 + q A + q B ) θqa1 q A αq A1 q B γq A q B + m, s.t. p A1 q A1 + p A q A + p B q B + m I. m q A1, q A, q B FOCs p A1, p A, p B A p A1 = 1 q A1 θq A αq B, p A = 1 q A θq A1 γq B, p B = 1 q B αq A1 γq A. θ A1 α = f(θ,γ) A γ B 44

45 41 Chung et al. (013, JE): [3] max q A1,q A (1 q A1 θq A αq B ) q A1 + (1 q A θq A1 γq B ) q A, max q B (1 q B αq A1 γq A ) q B. FOCs q A1, q A, q B 45

46 4 Chung et al. (013, JE): [4] A1 A 1 A1 1 A b A B b B p A B p B b A = q A1 = q A b B = q B max b A,b B,m b A + b A + b B 1 ( b A + b A + b B ) θba b A αb A b B γb A b B + m, s.t. p A b A + p A b A + p B b B + m I. 46

47 43 Chung et al. (013, JE): [5] m b A, b B FOCs p A, p B A p A = (1 b A θb A αb B ) + (1 b A θb A γb B ), p B = 1 b B αb A γb A. max b A [ (1 ba θb A αb B ) + (1 b A θb A γb B ) ] b A, max b B (1 b B αb A γb A ) b B. b A = q A1 = q A b B = q B Hinloopen et al., 014, EER FOCs b A b B 47

49 44 [1] Belleflamme, P. and Peitz, M. (010) Industrial Organization: Markets and Strategies, 1st ed., Cambridge University Press, New York. Brito, D. and Vasconcelos, H. (015) Interfirm bundling and vertical product differentiation. Scandinavian Journal of Economics 117(1), 1 7. Chung, H.L., Lin, Y.S., and Hu, J.L. (013) Bundling strategy and product differentiation. Journal of Economics 108(3), Flores, D. (009) All you can drink: should we worry about quality? Journal of Regulatory Economics 35(1), Fudenberg, D. and Tirole, J. (000) Customer poaching and brand switching. RAND Journal of Economics 31(4), Heywood, J.S., Li, J., and Ye, G. (014) Per unit vs. ad valorem royalties under asymmetric information. International Journal of Industrial Organization 37,

50 45 [] Hinloopen, J., Müller, W., and Normann, H.T. (014) Output commitment through product bundling: Experimental evidence. European Economic Review 65, Ikeda, T. and Toshimitsu, T. (010) Third-degree price discrimination, quality choice, and welfare. Economics Letters 106(1), Nalebuff, B. (004) Bundling as an entry barrier. Quarterly Journal of Economics 119(1), Nguyen, X. (014) Monopolistic third-degree price discrimination under vertical product differentiation. Economics Letters 15(), Pazgal, A. and Soberman, D. (008) Behavior-based discrimination: Is it a winning play, and if so, when? Marketing Science 7(6), Saggi, K. and Vettas, N. (00) On intrabrand and interbrand competition: The strategic role of fees and royalties. European Economic Review 46(1),

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bottleneckjapanese.dvi 1 M&A Keywords:,. Address: 742-1, Higashinakano, Hachioji-shi, Tokyo 192-09,Japan fax:+81 426 74 425 E-mail: yangc@tamacc.chuo-u.ac.jp ; yasuokaw@tamacc.chuo-u.ac.jp 1 Yang and Kawashima(2008) 1 2 ( MVI