* *2 Russell et al. (2015) 2

2017 6 1 1 2016 S 40 *1 1997 IBM 2011 IBM 2017 nishihara@hiroshima-u.ac.jp *1 NHTSA Investigation: PE 16-007 (Jan. 2017) 1

*2 1 2 3 4 *2 Russell et al. (2015) 2

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

Endres and Bertram (2006) Jacob (2015) Baumann and Heine (2013) Baumann and Heine (2013) 2 3 4 5 6 2 2.1 n i z i R + * 3 h z i *3 Loury (1979) 4

*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

u(q) = aq 1 2 bq2 pq γ c Dq *6 1 2 3 2.4 D(s i, c i ) *7 * 8 *9 * 10 3 3.1 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

* 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

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

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) 4. 1 2 D c i + γd q i 5. 9

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) 1 2 3 h h h h 0 h r n h z h * 17 h h *17 10

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

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

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

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