,398 4% 017,

6 3 JEL Classification: D4; K39; L86,,., JSPS 34304, 47301..

1 01301 79 1 7,398 4% 017,390 01 013 1 1 01 011 514 8 1

Novos and Waldman (1984) Johnson (1985) Chen and Png (003) Arai (011) 3 1 4 3 4 5

0 1 0 1 [0, 1] x [0, 1] 0 p 0 u x = v p 0 tx v tx x 1 p 1 u x = v p 1 t(1 x) 0 0 1 x I x I = 1 + p 1 p 0 (1) t 0 x 0 1 x 1 x 0 = v p 0, x 1 = 1 v p 1 t t () (1) () x 1 x I x 0 v p 0 + p 1 + t (3) v (3) 3 3

.1 0 1 1 3 Stage 1 0 1 {r 0, r 1 } Stage Stage 3 0 ( 1 max π 0 = (p 0 r 0 ) p 0 + p ) 1 p 0 t subject to v p 1 + p 0 + t 1 ( 1 max π 1 = (p 1 r 1 ) p 1 p ) 1 p 0 t subject to v p 1 + p 0 + t 3 v (3t + r 0 + r 1 )/ p 0 = t + r 0 + r 1 3, p 1 = t + r 0 + r 1. 3 v r i / 3 4

0 1 1: ( 1 max π A = r 0 r 0,r 1 + r ) ( 1 r 0 1 + r 1 6t r ) 1 r 0 r 0 6t r 1 subject to v 3t + r 0 + r 1 v (3t + 1)/ r 0 = r 1 = 1 r0, r1 p 0, p 1 D 0, D1 π A π0, π1 CW SW 1 v (3t + 1)/ r 0 = r 1 = 1, p 0 = p 1 = t + 1, D 0 = D 1 = 1, π A = 1 4, π 0 = π 1 = t CS = v 1 5t 4, SW = v 1 4 t 4 5

0 ( ) v p0 max π 0 =(p 0 r 0 ) p 0 t subject to v < p 1 + p 0 + t ( ) v p1 max π 1 =(p 1 r 1 ) p 1 t subject to v < p 1 + p 0 + t v < (r 0 + r 1 + t)/ p 0 = v + r 0 p 1 = v + r 1 v max r 0,r 1 π A = r 0 ( ) v r0 t + r 1 ( v r1 t subject to v < r 0 + r 1 ) + t r 0 r 1 v < t(1 + t)/(t + 1) r 0 = r 1 = v (1 + t) v < t(1 + t)/(t + 1) D 0 = D 1 = r 0 = r 1 = (t + 1)v 4t(1 + t), π A = v (1 + t), p 0 = p 1 = (t + 3)v 4(1 + t), v 4t(1 + t), π 0 = π1 = (t + 1) v 16t(1 + t) CS = (t + 1) v 16t(1 + t), SW = (1t + 16t + 7) v 16t(1 + t) 6

. 1 0 0 F > 0 Stage 1 0 {r 0, r 1 } Stage 0 {p 0, p 1 } Stage 3 0 x 1 < x I < x 0 v x I v r 0 + t/ p 0 = p 1 = v t 0 max π A = r 0 r 0,r 1 + r 1 r 0 r 1 subject to v r 0 + t v (1 + t)/ r0 = r1 = 1 3 v (1 + t)/ r0 = r1 = 1, p 0 = p 1 = v t, D 0 = D 1 = 1, π A = 1 4, π 0 = v 1 t F CS = t 4, SW = v 1 4 t 4 F 7

0 : ( ) ( ) v p0 v p1 max π 0 = (p 0 r 0 ) + (p 1 r 1 ) p 0,p 1 t t subject to v < p 1 + p 0 + t v < (r 0 + r 1 + t)/ p 0 = v + r 0 p 1 = v + r 1 ( ) ( ) v r0 v r1 max π A = r 0 + r 1 r 0 r 0,r 1 t t r 1 subject to v < r 0 + r 1 v < t(1 + t)/(t + 1) r 0 = r 1 = v (1 + t) + t 8

4 v < t(1 + t)/(t + 1) D 0 = D 1 = r 0 = r 1 = (t + 1)v 4t(1 + t), π A = v (1 + t), p 0 = p 1 = (t + 3)v 4(1 + t), v 4t(1 + t), π 0 = (t + 1) v 8t(1 + t) F CS = (t + 1) v 16t(1 + t), SW = (1t + 16t + 7) v 16t(1 + t) F.3 0 1 0 re / 3 Stage 1 0 {r 0, r 1 } Stage 0 1 {r E } Stage 3 0 {p 0, p 1 } Stage 4 0 ( 1 max Π 0 = (p 0 r 0 ) p 0 + p ) 1 p 0 + (r E r 1 ) t subject to v p 1 + p 0 + t 1 ( 1 maxπ 1 = (p 1 r E ) p 1 p ) 1 p 0 t subject to v p 1 + p 0 + t ( 1 p ) 1 p 0 r E t v r E + (r 0 r 1 + 3t)/ p 0 = t + r E + (r 0 r 1 ) 3 p 1 = t + r E + r 0 r 1 3 9

0 1 3: 0 r E 0 ( max Π 0 = t + r E r ) ( 0 + r 1 1 r E 3 + r ) ( 1 r 0 1 + (r E r 1 ) 6t r ) 1 r 0 r E 5t subject to v r E + r 0 r 1 + 3t 0 r E = 1 ( 1 max π A = r 0 r 0,r 1 + r ) ( 1 r 0 1 + r 1 6t r ) 1 r 0 r 0 6t r 1 subject to v 3t + r 0 + r 1 v 3t/ + 1 + 1 r 0 = r 1 = 1 10

5 v 3t/ + 1 r 0 = r 1 = 1, r E = 1, p 0 = p 1 = t + 1, D 0 = D 1 = 1, π A = 1 4, π 0 = π 1 = t CS = v 1 5t 4, SW = v 3 4 t 4 ( ) ( ) v p0 v p1 max Π 0 = (p 0 r 0 ) + (r E r 1 ) p 0 t t subject to v < p 1 + p 0 + t 1 ( ) v p1 max Π 0 = (p 1 r E ) p 1 t subject to v < p 1 + p 0 + t r E v < t + (r 0 + r E )/ p 0 = v + r 0 p 1 = v + r E 0 0 ( ) ( ) ( ) v r0 v r0 v re max Π 0 = + (r E r 1 ) r E r E t t subject to v < t + r 0 + r E 0 r E = v + r 1 (1 + t) ( ) ( ) v r0 v + tv r1 max π A =r 0 + r 1 r 0 r 0,r 1 t 4t(1 + t) r 1 subject to v < (1 + t)(t + r 0) + r 1 4t + 3 11

v < 8t(1 + t)(t + t + 1)/(t + 1)(8t 8 + 8t + 3) r0 v = (1 + t), v(t + 1) r 1 = (t + t + 1) 6 v < 8t(1 + t)(t + t + 1)/(t + 1)(8t 8 + 8t + 3) r0 v = (1 + t), v r 1 = (1 + t) vt (1 + t)(t + t + 1), v(4t + 6t + 3) r E = 4(1 + t)(t + t + 1), p v(t + 3) 0 = 4(1 + t), v(t + 3) p 1 = 4(1 + t) + v(t + 1) 8(1 + t)(t + t + 1), D 0 = v(t + 1) 4(1 + t), D 1 = π A = v(t + 1) 4(1 + t) v(t + 1) 8(1 + t)(t + t + 1), v 4t(1 + t) v 16t(1 + t)(t + t + 1), π 0 = v (t + 1) 16t(1 + t) v (16t 4 + 3t 3 + 0t + 4t 1) 3t(1 + t)(t + t + 1), π 1 = CS = v (t + 1) 16t(1 + t) v (t + 1) (8t + 8t + 3) 18t(1 + t) (t + t + 1), v (t + 1) 6 64t(1 + t) (t + t + 1) SW = v (1t + 16t + 7) v (t + 1) (16t 3 + 56t + 44t + 13) 16t(1 + t) 18t(1 + t) (t + t + 1).4 4 Stage 1 0 1 {r 0, r 1 } Stage 0 1 {r E } Stage 3 Stage 4 1

0 1 4: 0 ( 1 max π 0 = (p 0 r 0 ) p 0 + p ) ( 1 p 0 1 + r E t p 1 p 0 t subject to v p 1 + p 0 + t 1 ( 1 max π 1 = (p 1 r 1 r E ) p 1 p ) 1 p 0 t subject to v p 1 + p 0 + t ) r E v r E + (3t + r 0 + r 1 )/ p 0 = t + r E + r 1 + r 0 3 p 1 = t + r E + r 1 + r 0 3 0 1 0 ( max π 0 = t + r E + r ) ( 1 r 0 1 r E 3 + r ) ( 1 r 0 1 + r E 6t r ) 1 r 0 r E 6t subject to v r E + 3t + r 0 + r 1 v 1 + (3t + r 0 + r 1 )/ 0 r E = 1. 13

( 1 max π A = r 0 r 0,r 1 + r ) ( 1 r 0 1 + r 1 6t r ) 1 r 0 r 0 6t r 1 subject to v 1 + 3t + r 0 + r 1 v 3(1 + t)/ r 0 = r 1 = 1. 7 v 3(1 + t)/ r 0 = r 1 = 1, r E = 1, p 0 = p 1 = t + 3, D 0 = D 1 = 1, π A = 1 4, π 0 = t + 1, π 1 = t CS = v 3 5t 4, SW = v 1 4 t 4 ( ) ( v p0 v p1 max Π 0 =(p 0 r 0 ) + r E p 0 t t subject to v < p 1 + p 0 + t ) r E ( ) v p1 max Π 1 =(p 1 r 1 r E ) p 1 t subject to v < p 1 + p 0 + t v < (r 0 + r 1 + t + r E )/ p 0 = v + r 0 p 1 = v + r 1 + r E. 14

0 1 0 max π 0 = v r ( ) ( ) 0 v r0 v r1 r E + r E r E r E t t subject to v < r 0 + r 1 + t + r E v < {(1 + t)(r 0 + r 1 + t) r 1 }/(4t + 3) r E = v r 1 (1 + t). ( ) v r0 max π A =r 0 r 0,r 1 t + r 1(t + 1)(v r 1 ) 4t(1 + t) subject to v < (1 + t)(r 0 + r 1 + t) r 1 4t + 3 r 0 r 1 v < 8t(1 + t)(t + 4t + 1)/(4t + 1)(t + 1)(t + 3) r0 v v(t + 1) = (1 + t) r 1 = (t + 4t + 1). 8 v < 8t(1 + t)(t + 4t + 1)/(4t + 1)(t + 1)(t + 3) r0 v = (1 + t), v r 1 = (1 + t) vt (1 + t)(t + 4t + 1), v(4t + 6t + 1) r E = 4(1 + t)(t + 4t + 1) p v(t + 3) 0 = 4(1 + t), v(t + 3) p 1 = 4(1 + t) + v(t + 1) 8(1 + t)(t + 4t + 1), D0 v(t + 1) = 4t(1 + t), v(t + 1) D 1 = 4t(1 + t) v(t + 1) 8t(1 + t)(t + 4t + 1), πa v = 4t(1 + t) v (4t + 1) 16t(1 + t)(t + 4t + 1), π 0 = (1 + t) v 16t(1 + t) + v (4t + 6t + 1) 3t(1 + t)(t + 4t + 1), π1 = v (4t + 6t + 1) (t + 1) 64t(1 + t)(t + 4t + 1), CS = (t + 1) v 16t(1 + t) v (t + 1) 3 (4t + 1)(t + 3) 18t(1 + t) (t + 4t + 1) SW = v (t + 1) 16t(t + 1) v (t + 1) (16t 3 + 56t + 44t + 13) 18t(1 + t) (t + 4t + 1) 15

3 3 3.1 3. v 3(1 + t)/ v < t(1 + t)/(t + 1) 3.1 3 1 1 v 3(1 + t)/ F re / v < t(1 + t)/(t + 1) r E r 1 p 1 9 1 3 5 9 v 3(1 + t)/ 1. F < v t 1. F v t 1 F F F 16

r E p 1 p 0 p 0 4 6 10 v < t(1 + t)/(t + 1) 1. 4t(1 + t)(t + 1) > 1 t F < α F α. 4t(1 + t)(t + 1) 1 t F < β F β α v (t+1), β v (t+1) v (1 16t 4 3t 3 0t 4t) 16t(1+t) 16t(1+t) 3t(1+t)(t +t+1) F 9 v < t(1+t)/(t+ 1) v 3(1 + t)/ t r 1 r E 0 1 r E t F t 9 10 3. 17

11 v 3(1 + t)/ 1. F < v t 1. F v t 1 0 1 r 1 r E r E r 1 0 11 1 v < t(1 + t)/(t + 1) 1. F < γ. F γ γ v (t+1) 16t(1+t) v (4t +6t+1) 3t(1+t)(t +4t+1) r E r 1 r 1 11 1 v 3(1 + t)/ 1. 18

. 3. F > v t 1 v t 1 F v t 1 v t 1 > F 4. F > v t 1 v t 1 F v t 1 v t 1 > F v 3(1 + t)/ 9 F v t 1/ r 1 r E p 1 p 1 0 1 v r E v t 1/ > F v t 1 0 F v t 1/ > F v t 1 v t 1 > F 3 v < t(1 + t)/(t + 1) 1. 19

. F γ F < γ 3. 4t(1 + t)(t + 1) 1 F β r 1 r E 4t(1 + t)(t + 1) > 1 γ < F 4t(1 + t)(t + 1) < 1 γ < F < β r 1 4. F γ F < γ 5. 4t(1 + t)(t + 1) > 1 F α 4t(1 + t)(t + 1) > 1 > 4t(1 + t) α > F γ 4t(1 + t)(t + 1) 1 β > F γ 4t(1 + t)(t + 1) 1 F β 4t(1 + t) > 1 α > F γ v 3(1 + t)/ 10 4t(1 + t)(t + 1) > 1 F α r 1 r E r E r 1 r 1 4t(1 + t)(t + 1) 1 F β 0

r E r 1 r E r 1 r E r 1 r E r 1 r 1 r 1 r E r 1 1 r E r 1 r E 4t(1 + t)(t + 1) > 1 α > F γ 4t(1 + t)(t + 1) 1 β > F γ r E r 1 r 1 r 1 1 4t(1 + t)(1 + t) 1 F β t r 1 r E r E 1 v < t(1 + t)/(t + 1) t 4t(1 + t) > 1 F 4 1 9 10 1

3 Arai, 011; Novos and Waldman, 1984; Yoon, 00 v 4

5 3. 3.1 3.4 1 v < t(1 + t)/(t + 1) SW 4 SW 3 16t 6 + 1t 5 78t 4 148t 3 106t 35t 4 10 4t(1 + t)(t + 1) < 1 t 16t 6 + 1t 5 78t 4 148t 3 106t 35t < 4 SW4 > SW3 SW SW 4 F v (1 + t) 16t(1 + t) v (1 + t)(16t 3 + 40t + 30t + 5)(4t + 4t 1) 18t(t + 4t + 1) (1 + t) (4) 4t(1 + t)(t + 1) < 1 (4) α F < α SW > SW4 4t(1 + t)(t + 1) < 1 t 4t(1 + t)(t + 1) 4t(1 + t) > 1 (4) γ F SW < SW4. (013) 013 R&D. (01) 01 R&D Arai, Y. (011) Civil and Criminal Penalties for Copyright Infringement. Information Economics & Policy, Vol.3, pp.70-80. Chen, Y. and Png, I. (003) Information Goods Pricing and Copyright Enforcement: Welfare Analysis. Information Systems Research, Vol. 14, No.1, pp.107-13. Johnson, W. (1985) The Economics of Copying. Journal of Political Economy, Vol.93, No.1, pp.158-174. 3

Novos, I. and Waldman, M. (1984) The Effect of Increased Copyright Protections: An Analytic Approach. Journal of Political Economy, Vol.9, No., pp.36-46. Yoon, K. (00) The Optimal Level of Copyright Protection. Information Economics and Policy, Vol.14, pp.37-348. 4