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1 CIRJE-J-30 CIRJE 000 8
2 5 9 3 Estmaton of Fatgue Cost of Commutng Congeston and Optmal Congeston Fare Ths paper has three ams. Frst, we estmate a hedonc housng rent functon along the Chuo Lne n Tokyo wth ( commutng tme dstance and ( congeston degree as explanatory varables. Second, from the hedonc rent functon thus estmated, we measure tme cost and fatgue cost of commutng n terms of Equvalent Varaton. We show that the fatgue cost of commutng s 5-9% of total commutng cost. Thrd, from the fatgue cost thus estmated, we measure margnal external congeston cost of an addtonal passenger at the peak rush hour. Ths margnal external congeston cost s nterpreted as optmal congeston toll. The result ndcates that the optmal congeston toll for the most congested tme s -3 tmes the current commuter-pass fare dependng upon the tran lne segment.
3 5 9 3 (976 (988, E-mal yamaga@ser.osaka-u.ac.jp E-mal hatta@css.u-tokyo.ac.jp 89% 00% 0
4 (995 (999 (995 Hatta and Ohkawara(994 (995 (999 (995 (995 (995 (999 (999
5 u h,z,l = h z l ( β β α ( h z l l δ x 3 x l = δ x ( δ ( l ( u U h,z,x = h z δ x ( β β ( α (3 ( l δ ( x + a = (4 a a a a x + a x k m(x k 4 3 x δ 3
6 (x x + a = m k (5 m( k ( m( k x m( k m( k m( k m k m 0 m 0 k 0 m( k (4 (5 ( ( β U h,z,x,k = h z β ( δ m( k x α (x k (6 m( k m 0 0 k 0 k ~ k m( k 3 m( k x r ( x h + z = Y (7 4 m( k k 4
7 r( x x Y Y x r( x z h (7 (6 ( ( Y max U h,z,x,k h,z s.t. r x h + z = v( r( x,y,x,k v v r( x Y x k v ( r( x,y,x,k = v (8 (8 r( x * r( x r ( Y,x,k,v = (9 r * 5, 6 (6 (9 β α β β r * ( Y,x,k,v = β( β β Y v [ δ m( k x] β Y v α r * ( x,k = C[ δ m( k x] β (0 β β β ( β C β β Y v m( k k = m( k ( σ m k = λ k ( 7 λ k σ ( m( k (0 r * = C δ λ k σ x [ ] β α ( 5 v 6 (999 max u( h,z,k s.t. r( x h + z = Y tx tx x v( r( x,y tx,k v r( x r( x = R( Y tx,k,v k 7 (989 5
8 ( δ 80 ( * α σ log r = p + p s + p + p3 y + log[ 80 ( γ x + λ k x ] + e 0 W (3 s β p0 log C, s y e..d. ( 70 U 8 x W x 9 δ NHK( (3 JR JR JR Y JR k ( x JR x W k 0 I 0,, L, I =,, L, I k 8 s h s (996 9 W x γ 0 6
9 k N = (4 K N ( K N 0 k = ω k =,, L, I (5 ω (5 (5 k I I 0 5 (3 log r * = s y s (. (.8 (5.9 ( log[ x k x] 0 (6 (.44 (3.50 (3.96 (4.0 W R = (3 (6 α β = (6 β β = 0. α =0.76 (5 m( k (5 9,043 43,350 7
10 . m( k = k m 0 k 0 m( k x m(x k x m( k [ ]x m(k 3.5. ( k 0. 8 k m = m k 0. k m( k 6 m( k x m( k Y 3 3 Y ,350 43, ,86 8
11 x = 0 c (9 * * r ( Y,x,k,v r ( Y c,x,k,v = (7 c Y x c = c( x c x x Y c( x m( k ~ = k ~ k ~ x Y Y c * * r ( Y,x,k,v r ( Y c,x,k,v = (8 f Y k = k ~ k c = c ( f f x c f ( x c f ( x x x m( k k ~ Y (8 c f ( x c t x ( x c x c t ( c ( x 5 9 f f 9
12 x m(k x [m(k-]x , , , , ,33.0, ,343.3, m( k k z MRS F MRS ( h,z,x,k 4 U ( h,z,x,k ( h,z,x,k U k F = (9 U z k z U U( h,z,x,k z k (9 (9 - h z h Y z = z Y (9 Y h = ( ( k x f ( k,x f ( k,x MRS ( h( Y,z( Y,x,k (0 F Y f ( (6 z k = ( β h β z β ( δ m( k x α α β β U k = α( δ m( k x h z m ( kx U z ( ( 0
13 m ( k = dm( k f ( k,x (0 m ( k x ( δ m( k x = αy (3 (3 (6 ( k,x % 5 f 8 (9 k k ( k N x (3 f ( k( k,x N k 0 k ( k k (4 4 5 k (3 (3
14 = (4 K k k ( k (5 (4 (5 k k k = (6 ( ( ( = K f ( k ( k,x N E (6 ( k E = N f ( k ( k,x (7 f ( 3 x f k,x ( , , ,07 44, ,83 44, ,38 487,
15 ( ( ( k k n N n N k k 0 k k (4 f ( k,x k (4 = =, (8 K ( k,k ( k =, (9 3
16 (5 (8 (9 k,k k,k k,k = =, (30 ( ( ( = K k k k = (3 ( ( ( = K n x, x f k, x ( =, n ( ( k ( k,k, x ( k ( k, f x E (30 (3 E n f ( k ( k,k,x f n n ( k,k ( k ( k,x = + n f (3 E ( k n N n N k k k ( k, k k ( k 0 k ( k, f x n E (30 4
17 E n f ( k ( k,k,x ( k,k = (33 n ( k, x ( k, f x E (30 (3 E n f ( k ( k,k,x ( k,k f n n ( k ( k,x = + n f (34 (7 (33 (34 E E = E + E = n f ( k ( k,k,x + n f ( k ( k,k,x ( k,k ( k,k + n f ( k ( k,x ( k ( k (35 E E 0 I 0 E j ( (,x I E = E n j f k j k, L +,k j= E = 0 =,, L,I 0 ( j j j ( k, L,k (36JR, (36 n N n N k k k( k, k k( k, k k ( k 0 k k 5
18 ,(988,, 6,(989,, (995,,, (996, (976, 7 (999,,,VOL.34. (999, ISIZE ( (997 7 ( (999 0 NHK 995,NHK 999 Hatta, T. and Ohkawara, T. (994, Housng and the Journey to Work n the Tokyo Metropoltan Area, n Yuko Noguch and James M. Poterb ed. Housng Markets n the Unted States and Japan, Unversty of Chcago Press, pp
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