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1 S 40 * IBM 2011 IBM 2017 nishihara@hiroshima-u.ac.jp *1 NHTSA Investigation: PE (Jan. 2017) 1

2 * *2 Russell et al. (2015) 2

3 6 8 Polinsky and Shavell (2010) Polinsky and Shavell (2010) Spier (2011) Chen and Hua (2012) Spier (2011) Chen and Hua (2012) Parchomovsky and Stein (2008) Dari-Mattiacci and Franzoni (2014) Parchomovsky and Stein (2008) Dari-Mattiacci and Franzoni (2014) 3

4 Endres and Bertram (2006) Jacob (2015) Baumann and Heine (2013) Baumann and Heine (2013) n i z i R + * 3 h z i *3 Loury (1979) 4

5 *4 h i = h(z i ) s i R + i π i r R ++ i V (z i, s i ) = 0 e (r+ j h j )t ( h i π i z i s i ) dt = h iπ i z i s i r + j h j 2.2 i q i R + p R + D γ f D γ f R + γ f = 1 γ f 1 * 5 c i R + π i π(q i, c i ; s i ) = (p c i γ f D)q i 2.3 p q γ c R γ c [0, 1] *4 h *5 γ f Daughety and Reinganum (1997) 5

6 u(q) = aq 1 2 bq2 pq γ c Dq * D(s i, c i ) *7 * 8 *9 * γ γ f + γ c [1, ) * 11 γ = 1 γ f > 1 *6 a b a *7 Ben-Shahar (1998) *8 *9 D lim si 0 D s i = lim ci 0 D c i = *10 Viscusi and Moore (1993) *11 γ c γ R ++ 6

7 * 12 γ 1 * 13 γ > 1 γ * 14 p = a bq γ c D c i π i = (a bq i c i γd)q i D c i = 1 γ (1) c (s i ) dc ds i = 2 D/ s i c i 2 D/ c 2 i D 1. D 1 (s i ), D 2 (c i ) 2 D/ s i c i = D 1D 2 > 0 2. q i q i = 1 2b (a c i γd) (2) *12 Spence (1977) Daughety and Reinganum (1995) Oi (1973) Polinsky and Rogerson (1983) Polinsky and Rogerson (1983) *13 γ 1 D *14 γ > 1 7

8 c (s i ) q (s i ) c i + D q c i + γd c i γ π i = bq 2 s i q 3. π π(q (s i ), c (s i )) s i 3.2 z s V s i h i π i = 1 (3) * 15 π i < 0 s i π i z i 1 s i z i * 16 2 π 6 7 z i h iπ i = 1 + h iv (4) h iπ i = 1 h iv 4 *15 h i π i > (h i π i )2 π i < 0 *16 (Nussim and Tabbach, 2009) 8

9 2 c w(q, c) = u(q) + π(q, c) = (a 1 bq c γd)q 2 D c = 1 γ (1) q q = 1 (a c γd) b s 2q (2) w(2q, c ) = 2π(q, c ) 1 W (z, s) = e (r+nh)t n ( hw(2q, c ) z s ) dt 0 = n( 2hπ(q, c ) z s ) r + nh s (3) W s (z, s ) = n r + nh (2hπ 1) > 0 z (4) sgn W z (z, s rπ ) = sgn (n 1)V r + nh 1 2 (n 1) D c i + γd q i 5. 9

10 5 r n (3) (4) (4) F (h iπ i 1)(r + nh i ) (h i π i z i s i )h i = 0 h π 1 > 0 F r F n F z dz + F s ds + F γ (3) h π dz + hπ ds + h dπ = 0 z s = 0 F z h π hπ F s = (n 1)(h π 1)h + (h π 1)(r + nh) } {{ } } {{ } >0 >0 ( + h π }{{} <0 (h π ) 2 hπ } {{ } >0 ) (r + nh) } {{ } >0 (5) h h h h 0 h r n h z h * 17 h h *17 10

11 6. (i) (ii) γ * 18 dπ = D sq 0 dz/ q 0 a c 2b (> q ) F r F n sgn F γ + h dπ ( hπ F s sgn dπ + D ) sq 0 π r + nh π r + (n 1)h dπ = Dq (6) η(s) D s/d q 0 π /π q r + nh r + (n 1)h (7) η η (7) η (6) (5) ds/ F γ + h dπ h π F z = F γ + D sq 0 F π s η q 0 q r + nh r + (n 1)h F z h π hπ F s F z h π hπ F s. (7) (5) (5) (7) η * 19 *18 Baumann and Heine (2013) s *19 η h h η h η h η 8 11

12 η (5) 7. (i) η (ii) η (iii) η (ii) (ii ) h h h h η h W (z, s ; γ) = n(v + Ω), Ω(z, s) hu r + nh γ V z, s dw ( V = n γ + Ω γ + Ω }{{} z >0 dz + Ω }{{} s >0 ds } {{ } 7 ) (8) dw V γ + Ω γ = = w γ = Dq h dw r + nh = hdq r + nh < 0 7 (8) 8. η 12

13 6 (5) (6) (5) (5) F z h π hπ F s = (n 1)(h π 1)h + (h π 1)(r + nh) + (h π (h π ) 2 ) hπ (r + nh) (3) F s = h π (r + nh) h π hπ F s = (h π ) 2 hπ (r + nh) F z = h π(r + nh) + (h π 1)nh (h π 1)h (hπ z s)h 2 3 (n 1)(h π 1)h > 0 4 F = 0 (h π 1)(r + nh) > 0 (6) π = γd s q 2 q c s γ (2) q dπ = D sq γd s ( D 2b ) = D sq 0, q 0 a c 2b > q F γ = dπ ( r + (n 1)h ) h (6) (r + (n 1)h)h 13

14 Baumann, F. and K. Heine (2013). Innovation, tort law, and competition. Journal of Institutional and Theoretical Economics 169 (4), Ben-Shahar, O. (1998). Should products liability be based on hindsight? Journal of Law, Economics, and Organization 14 (2), Chen, Y. and X. Hua (2012). Ex ante investment, ex post remedies, and product liability. International Economic Review 53 (3), Dari-Mattiacci, G. and L. A. Franzoni (2014). Innovative negligence rules. American Law and Economics Review 16 (2), Daughety, A. F. and J. F. Reinganum (1995). Product safety: Liability, R&D, and signaling. American Economic Review 85 (5), Daughety, A. F. and J. F. Reinganum (1997). Everybody out of the pool: Products liability, punitive damages, and competition. Journal of Law, Economics, and Organization 13 (2), Endres, A. and R. Bertram (2006). The development of care technology under liability law. International Review of Law and Economics 26 (4), Jacob, J. (2015). Innovation in risky industries under liability law: the case of double-impact innovations. Journal of Institutional and Theoretical Economics 171 (3), Loury, G. C. (1979). Market structure and innovation. Quarterly Journal of Economics 93 (3), Nussim, J. and A. D. Tabbach (2009). A revised model of unilateral accidents. International Review of Law and Economics 29 (2), Oi, W. Y. (1973). The economics of product safety. Bell Journal of Economics and Management Science 4 (1), Parchomovsky, G. and A. Stein (2008). Torts and innovation. Michigan Law Review 107 (2), Polinsky, A. M. and W. P. Rogerson (1983). Products liability, consumer misperceptions, and market power. Bell Journal of Economics 14 (2), Polinsky, A. M. and S. Shavell (2010). The uneasy case for product liability. Harvard Law Review 123 (6), Russell, S., D. Dewey, and M. Tegmark (2015). Research priorities for robust and beneficial artificial intelligence. AI Magazine 36 (4), Spence, M. (1977). Consumer misperceptions, product failure and producer liability. Review of Economic Studies 44 (3), Spier, K. E. (2011). Product safety, buybacks, and the post-sale duty to warn. 14

15 Journal of Law, Economics, and Organization 27 (3), Viscusi, W. K. and M. J. Moore (1993). Product liability, research and development, and innovation. Journal of Political Economy 101 (1),

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2)

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2) (1) I 44 II 45 III 47 IV 52 44 4 I (1) ( ) 1945 8 9 (10 15 ) ( 17 ) ( 3 1 ) (2) 45 II 1 (3) 511 ( 451 1 ) ( ) 365 1 2 512 1 2 365 1 2 363 2 ( ) 3 ( ) ( 451 2 ( 314 1 ) ( 339 1 4 ) 337 2 3 ) 363 (4) 46