#6 : ( 8-13) RL : http://chaosweb.complex.eng.hokudai.ac.jp/ j inoue/index.html 23 5 31 9 5 9.1 :...................... 51 9.2 Neugart..................................... 53 9.2.1................................ 53 9.2.2........................ 56 9.2.3................ 57 9.2.4................... 58 5. /* */ #include <stdio.h> #include <math.h> double func(x,a) /* f(x)=. f(x) */ double x; double a; { return (pow(a*x,2)-a*(a+1)*x+a+1); } double Dfunc(x,a) /* f(x) 1.. */ double x; double a; { return (2*a*a*x-a*(a+1)); } main() { 49
FILE *fpr; int i,imax=1; double x,y,a; if((fpr = fopen("lower.dat", "wt"))!=nll){ for(a=3.; a<=1.+sqrt(6.); a=a+.1){ /* a */ for(i =, x=.1; i <= imax; i++){ x = x - func(x,a)/dfunc(x,a); if(fabs(y-x)<1.e-5){ fprintf(fpr,"%lf %lf\n",a,x); break; }else{ y = x; } }} } fclose(fpr); }, a 2, 2 x,, x., a, a x, a x a a x,,. a x. for(a=3.,x=.1; a<=1.+sqrt(6.); a=a+.1){ /* a */ for(i = ; i <= imax; i++){ 27. 9, : x n+1 = ax n (1 x n ) (123),., ( 1 ), ( ). ( 5 ), 2, ( x ), ( a ),. 5
.85.8.75 x.7.65.6 upper branch lower branch (a+1+sqrt((a+1)*(a-3)))/(2*a) (a+1-sqrt((a+1)*(a-3)))/(2*a).55.5.45.4 2.95 3 3.5 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 a 27: 2., ( ), ( ).,,,,. ( ),,, 1., 6,,, ( ).,. 9.1 :, ( ),., /,,., ( ),,,.,,,,,. (, ),, ( / ), 1, ( ). 51
,,.,, ( ).,, ( ), ( ),,,,.,,,. 1958 Alban William Housego Phillips.,,.,,,,,,. 28 197 2 1.,. 25 2 197 198 199 2 15 inflation (%) 1 5-5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 unemployment (%) 28:.,, Neugart (24), 2.,. 52
.25 197s in Japan **(-.12163)-1.55.1 198s in Japan **(-.117667)-1.52.2.8.6.15.4.1.2.5.1.12.14.16.18.2.22.24.5.4.3 199s in Japan **(-.35119)-1.12 -.2.18.2.22.24.26.28.3.32.25.2.15.1 2s in Japan **(-.47525)-1.16.2.5.1 -.5 -.1 -.15 -.1 -.2 -.2.2.25.3.35.4.45.5 -.25.35.4.45.5.55.6 29:. 9.2 Neugart Neugart.,,.,. 9.2.1, t 2 t, i.,, o t., t., t + 1 t+1 ( 1) t t t+1 = t + i(1 t ) o t t (124)., t + 1 t+1, t t : o t t, : i(1 t ). 2 t. 53
Neugart i,. : x t+1 = ax t (1 x t ) (125) a., i,., t o t. t. o t = J s + J c,t t + d(1 t ) (126) J c,t = γ(m t ) (127), (126) J s + J c,t. 2 1 J s,., 2 J c,t J s,, Neugart (127) m t. γ < γ < 1.,, J s + J c,t,,. ( t ), 2 d(1 t ),, 1 t t + d(1 t )., d On the job searching., (126) t,., e,t, w b,t, ( ) w p.,. Neugart, t + 1, t t, a ( a 1),. e,t+1 = a t + (1 a) e,t (128), t,, w p, t w b,t.. w p = (1 µ)y (129), y, µ.,, ( 3 ).,,.,,, (y),,.., y = 1., 3, 3, ( ),, ( ). 54
1 1.9.9.8.8.7.7 1/µ.6.5 1/µ.6.5.4.4.3.3.2.2.1.2.4.6.8 1 demand.1.2.4.6.8 1 demand 3: 1/µ (demand).,..., t w b,t = 1 (1 b) t (13)., b < b < 1, 4,,,,,, y = 1 5., t. t = 1 δ ( e,t + w ) b,t w p = 1 ( e,t + µ (1 b) ) t w p δ 1 µ,, t (131) w t w b,t w p w p (132)., w t w p, t w b,t w p., (131), t ( w t > ), t, e,t,, ( w t < ),,.,,,,,,., (131) δ, (131) w p = w b,t, ( )., t t., (124) (126),(127) (131) (128) t+1 = t + i(1 t ) t J s + γ(m t ) t + d(1 t ) (133) 4,. 5,,. 55
t+1 = 1 ( µ δ 1 µ + a t + (1 a) 1 ( 1 b δ 1 µ ( δ t µ (1 b) )) t 1 µ )) ( t + i(1 t ) t J s + γ(m t ) t + d(1 t ) (134)., t t,., (133)(134) = t+1 = t, = t+1 = t µ m(δ 1)(1 µ) = (135) 1 b = m (136).,, m,, = m (, (136) ), (133), = t+1 = t, = t+1 = t = m J s + i(1 ) + d(1 ) = (137) J s = i(1 )( + d(1 )) (138) J s., (138) (133)(134). 9.2.2 (133)(134) i,. 31 i =.18 t t.12.35.1.3.8.25 t.6 t.2.15.4.1.2.5 2 4 6 8 1 12 14 16 18 2 t 2 4 6 8 1 12 14 16 18 2 t 31: i =.18 ( ) ( )., d =.1, b =.5, µ =.4, γ =.5, δ = 2, a =.5, m =.3. t = 2.,,,., 56
i =.1 i =.185 t, t,. 32., i, d =.1, b =.5, µ =.4, γ =.5, δ = 2, a =.5, m =.3., i.13199, i,., m d,.14.35.12.3.1.25.2.8.15.6.1.4.5.2.1.11.12.13.14.15.16.17.18 i -.5.1.11.12.13.14.15.16.17.18 i 32: i ( ) ( ). i =.18., d =.1, b =.5, µ =.4, γ =.5, δ = 2, a =.5, m =.3.,,. 9.2.3 i( ) 33. 33,.35.3.25.2.15.1.5.2.4.6.8.1.12 33: ( )., d =.1, b =.5, µ =.4, γ =.5, δ = 2, a =.5, i =.18, m =.3. 57
., 34,,, t, t + 1.,., Neugart,..12.35.1.3 t+1.8.6 t+1.25.2.15.4.1.2.5.2.4.6.8.1.12 t t.5.1.15.2.25.3.35 34: i =.18 ( ) ( ) t, t+1., d =.1, b =.5, µ =.4, γ =.5, δ = 2, a =.5, m =.3. 9.2.4 t, t,,, ( ) P (), P (). 35., Neugart.6.14.5.12 P().4.3 P().1.8.6.2.4.1.2.2.4.6.8.1.12 -.5.5.1.15.2.25 35:, P ()( ), P ()( ). d =.1, b =.5, µ =.4, γ =.5, δ = 2, a =.5, m =.3.,,,.,,, 58
. ( ):,., Neugart,. HSCAP. http://eprints.lib.hokudai.ac.jp/dspace/handle/2115/43998, ( ) (, ),., HP: http://chaosweb.complex.eng.hokudai.ac.jp/~chen/. ( ): (6/7) ( ).,,.. 59