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- しまな まるこ
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3 CONTENTS The Actual State of Street Crimes Takashi KUSUMOTO Die Entwicklung der Beschäftigungspolitik für behinderte Menschen in Japan Hirofumi KONISHI The Aim of the Emergency Acts and the Responsibility of the Local Community Takato NARISAWA Can biocentrism consist with multiculturism? Arisato MINAMI Subjects of roadside landscape formation along the national route No.260 Shunji IWATA The state and political coping for people who doesn't pay national health insurance fee Masateru NAGATOMO An Industrial Location and Labour Supply-Demand Relations for Japanese=Brazilian Migrants Workers - Its Experiences of "Sharp" Location at Kameyama City, Mie Prefecture - Masatoshi OZAKI The Forecast and Wish for Gender Equality Society Ichiro TOFUKUJI Chuan-Zhong Li and Karl-Gustaf Lofgren, Renewable Resources and Sustainability : A Dynamic Analysis with Heterogeneous Time Preferences, Journal of Environmental Economics and Management, Vol.40, 2000, pp Hiroshi MORIOKA Tokai-Daiikki reported in the newspapers Youichi MOGI
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128 566(261) 743(287) 880(386) 1,084(458) 722(249) 541(188) 1,864(688) 1,531(520) 1,647(572) 2,559(869) 3,560(1,768) 2,936(1,328) 789(340) 755(318) 883(363) 1,007(359) 1,133(457) 1,026(409) 584(146) 723(177) 771(231) 897(298) 972(327) 1,158(265) *** *** *** *** 192(79) 204(95) ,258(3,718) 9,749(3,912) 9,119(3,512) 11,512(4,870) 12,524(5,339) 685(226) 678(332) 793(362) 1,117(577) 1,572(729) 4,078(1,975) 4,205(1,703) 2,996(1,104) 3,625(1,539) 3,381(1,399) 1,207(486) 1,591(758) 1,856(762) 2,447(1,201) 2,436(1,184) 1,121(255) 1,122(284) 1,434(399) 1,649(443) 2,196(712) *** 596(287) 413(212) 719(359) 1,134(535) , ,164 4,808 1,176 36,424 43,470 3,095 15,756 4,744 4, ,409 34,154 13,837 8,059 36, ,270 45,006 57,336 6,384 23,143 39,048 6,802 17,619 2,765 4, ,915, , ,654(985) ,248 1, ,595(1,435) ,280 3,111 1,392 4,503(3,359) ,
129 %
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132 22.3% 55.2% 3 80%
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134 62.5% 37.5% 57.1% 30%
135 47.6% 45.2% 50%
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147 1) 2 Chuan-Zhong Li and Karl-Gustaf Lfgren, Renewable Resources and Sustainability : A Dynamic Analysis with Heterogeneous Time Preferences, Journal of Environmental Economics and Management, Vol.40, 2000, pp Dasgupta and Heal14Solow30 Stiglitz31 (single-peaked) 3) Chichilnisky10,11 Ramsey (dictatorship) (utility stream) Chichilnisky (terms) 143
148 Heal17 Chichilnisky Chichilnisky Chichilnisky10,1117 Plato Heal17 (utilitarian)(conservationist) 0 = 0 u( c, x) c t x 144
149 t u > 0 u > 0 u < 0 < 0 c x x& = f ( x) c, x ( 0) = x0 (1) c fx 0 x x f ( x) 0 0 < x < xˆ f ( x) > 0 f ( xˆ) = 0 c x ˆ < x < x f ( x) < 0 (the growth function)xˆ (the golden rule resource stock) x c (the ecological carrying capacity) Clark12 1 t c 0 x 0 c x (2) U = 0 u( c, x)exp( θ t) dt (2) 1 3 c x cc u xx U 2 = lim 0 0 u( c, x)exp( δt) dt δ 3 θ > δ 0 δ ) U = α U 1 + βu 2 = u( c, x) p( t dt (4) +=1 p( t) = exp[ a( t) t] at = - lnexp-t+exp-t/t at t at a (0) = αθ, a ( t) < 0 lim a( t) = δ 0 t (5) 5,35= 0 pt limt p( t) = β 0 p( t) dt Courant13) p( t) = exp( θ t) lim p( t) = 0 t 145
150 0 p( t) dt (the objective functional)4 ct,xt 6feasible programmec*t,x*t { p( t) dt} 0 T * * T inf u[ c ( t), x ( t)] p( t) dt u[ c( t), x( t) ] lim 0 0 T c*t,x*t(the catching up criterion) 28,29 14(the current value Hamiltonian)Ht=uc,x+ qfx- c q x (a co-state variable) 5) q = uc( c, x) q& = [ h( t) f ( x)] q ux( c, x) 7 [ ~ x( t) x( )] 0 lim inf q( t) t t = 0 h( t) = d[ a( t) t]/ dt = αθ /[ α + β exp( θt)] ~ x ( t ) 7 u c c x c = cx, qx q c 7 x 1 x& = f ( x) c( x, q) q& = [ h( t) f ( x)] q u ( c, x) (8) x = 0 ht= 146
151 Clark12c = fx f (x) + u x c,x/u c c, x=(the modified golden rule path) = 0 ht= 0 89 x& = f ( x) c( x, q) q& = qf ( x) ux( c, x) (9) 13 8 t (non-autonomus) 9(the autonomus system) lim h( t) 0 89 ) 9 ( x, q) x& = 0 q& = 0 10 c = f (x) ( c, x) = qf ( x) 10 c = c( x, q) q = uc ( c, x) 1011 ux ( c, x) / uc( c, x) = f ( x) 11 ux u x u c f (x) fxheal17 (the green golden rule) x Phelps26 f ( xˆ) = 0 xˆ t 8 t 147
152 (9) ht 8 ht 1/ t lim h ( t) = exp( θ ) 12 t h( t) = αθ /( α + β exp( θt )) 1/ t = h( t) 1 R ln( R) = (ln( αθ ) ln( α + β exp( θt))) R t L'Hospital lim t ln( R) = θ limt R = exp( θ ) Benam and Hirsh48 9 θ > 0 8 z*t=x*t,q*t9 z 0 t=x 0 t,q 0 t exp( θ ) 13 * 0 1/ t lim z ( t) z ( t) exp( θ ) 13 t the Euclid norm Benam and irsh4 12 ht 7) z*t z 0 t * 0 lim z ( t) z ( t) = 0 13 t convergent utility streams 148
153 x( 0) = x0 > 0 the augmented curvature matrix positive B = 1 2 H * qq 1 h(1 + η ) h(1 + η ) * H xx definite 8) t 8 z = ( x, q) GAS η = dq / dh ( h / q) q h 9) H V ( t, x) = q& x& V > 0 q = W x x q & = Wxx x & Wxa strictly concave value function7,19 W W < 0 2 > ( t, x) = W x& 0 V the time derivative V xx V & ( t, x) < 0 8(14) V &( t, x) = qx &&& qx &&& * * = ( hqx && + hqx & & + qh & q& xh & x& ) qq xx xx T = ( q &, x& ) B( q&, x& ) < 0 14 B GAS ( x, q) t q x an internally implicit demand system3,9 H* q x (the rate of time dis- 149
154 count)b (the green golden rule steady state) h variation 9 z = ( x, q) GAS t h = 0 8 c x x H* q x B 7 10) (dominance) 28 t 0 z*t z 0 t89 u [ v( z ( t)) v( z ( t))] dt < 15 = 0 * 0 z ( t) = ( x( t), q( t)) ν ( z ( t)) = u( c( x, q), x) 15 u (the compromise solution)z*t z t z 0 t u z*t * * u θ ( z ( t)) = exp( θt )[ v( z θ ( t)) v( z ( t))] dt 0 150
155 0 * u ( z ( t)) [ v( z ( t)) v( z ( t))] dt = 0 0 * vz 0 t vz*t vz θ t- vz*t duality result (8)z*t (16) θ * 0 * θ 0 α u ( z ( t)) + β u ( z ( t)) = min α u ( z( t)) + β u ( z( t)) 16 { z( t)} 0 α u θ ( z( t)) β u ( z( t)) t zt (16) max{ z ( t)} limt 0[ α exp( θt ) + β ] v( z( t)) dt T θ [ α exp( θt ) v( z ( t)) + βv( z T 0 0 ( t))] dt zt pt = exp- att CU max{ z( t)} 0 p( t) v( z( t)) dt z*t c θ t,x θ tc 0 t,x 0 t c*t,x*t u xc ( c, x) > 0 ( c, x) / c > 0 ( c, x) > 0 u xc x( 0) = x0 > 0 u x c0 0 c0 * c0 θ 151
156 0 * θ c 0 < c0 < c 0 17 ( 2) exp- (4(time consistent)5,17,33 t 0 x*t,q*t T t T t T T T T T T pt= exp- attt t T 152
157 (time inconsistency) T T t T pt = exp- at - Tt (18) c * = f ( x * ) * * * ux ( c, x ) αθ = f '( x ) + 18 * * uc ( c, x ) a0 t 0 a(0) = αθ 8 h(t) = αθ (8)αθ < θ K z (a compact neighborhood)t 0 z*t K T K T 0 - T t = 0 T T 0 T n ( T n > T0 ) T n - T T K Pollak27 153
158 (long run maximum sustainable utility) (8) at (the maximum long-run sustainable utility) f ( x) c = 0 max ( c, x) u( c, x) c x (19) ux ( c, x) / uc ( c, x) = f ( x) 19 maxx u( f ( x), x) x uc ( c, x) f ( x) + ux ( c, x) = 0 89 x*t8 * * * min lim q ( t) x( t) = lim q ( t) x ( t) 20 x( t) t t 297 * * liminf q ( t) ( x( t) x ( t)) 0 21 t 19 Weitzman34 t (a static equivalent) Weitzman 154
159 1,16,23,25 4 t (22) t dh ( t) / dt = h( t) q( t) x& ( t) 22 cx q (23) dh ( t) / dt = H ( t) / c( t) c& ( t) + H ( t) / x( t) x& ( t) + H ( t) / q( t) q& ( t) (23) H ( t) / c( t) = 0 H ( t) / q( t) = x& ( t) q& ( t) = h( t) q( t) H ( t) / x( t) 2322 h( t) > 0 q( t) > 0 the stable saddle point path t x& ( t) > 0 x& ( t) < 0 x = x u( c, x) 11) steady technical progress t t the current utility2,15,22,25,34 H (t) 24 * * t ( H ( t) u( c ( s), x ( s)))exp( a( s) s) ds = 0 (24) 25 * * t u( c ( s), x ( s))exp( a( s) s) ds H ( t) = exp( a( s) s) ds t 155 (25) a( t) = θ > 0 a( t) = δ = 0 H (t) 2627 t * * H ( t) = θ u( c ( s), x ( s)) exp( θs) ds (26) * * H ( t) = lim δ t u( c ( s), x ( s))exp( δs) ds δ 0 1 T * * = lim t u( c ( s), x ( s))exp( δ s) ds T T t
160 < 27 (the standard utility based net national income)34 Chichilnisky10,11 Heal17 Plato Heal17Heal (the catching up criterion) 28 (the utility sequences) the exact boundgasgas 156
161 K z( s) K s 15 s 0 * u = [ v( z ( t)) v( z ( t))] dt + [ v( z ( t)) v( z 0 s * 0 ( t))] dt s * 0 [ v ( z ( t)) v( z ( t))] dt v( z ( t)) v( z ( t)) dt x v q v * 0 v z t v z t dt Dv ~ * * 0 ( ( )) ( ( )) ( z ( t)) ( z ( t) z ( t)) dt s s s * 0 M s * 0 z ( t) z ( t) dt * * ~ * v( z ( t)) / x ( t) Dv ( z ( t)) = 0 0 * * v( z ( t)) / q ( t) = sup ~ ( z * * 0 M t s Dv ( t)) < z ( t) z ( t) m > 1 t m high order exp- s * 0 z ( t) z ( t) dt 13 * θ θ c 0 < c 0 c 0 > c 0 * qc = ucc( c, x) < 0 q = uc ( c, x) * θ q 0 < q 0 x ( 0) = x0 x& * θ = f ( x) c x & (0) < x& (0) * θ * θ qtinfinitesimal τ > 0 q ( τ ) < q ( τ ) x ( τ ) < x ( τ ) q& / q = h f ( x) ux ( c, x) / q h < θ f ( x * ) < f ( x θ ) u xc c,x) 0 157
162 u ( c *, x * θ ) u ( c θ, x * * θ θ x < x ) q & ( τ ) / q ( τ ) < q& ( τ ) / q ( τ ) t > 0 * * t > 0 c& θ ( t) / c ( t) > c& θ ( t) / c ( t) * θ * θ t > 0 x ( t) < x ( t) c ( t) > c ( t) * * θ θ θ limt x ( t) = x < limt x ( t) = x x ˆ < x * < x * * θ * θ c > c u ( c, x ) u ( c θ, x * x > x ) f θ θ ( x ) > f ( x ) lim t q& ( t) = 0 (the asymptotic shadow value) qt * * θ θ * ux( c, x ) θ ux( c, x ) lim q ( t) = > lim q ( t) = t * θ f '( x ) t θ f '( x ) * θ * * q 0 < q 0 q& θ ( t) / q ( t) < q& θ ( t) / q ( t) 1) SJFR William A. Brock Peter Berck Larry Karp 2)Chuan-Zhong Li, Department of Economics,T&S, University of Dalarna, S Borlänge, Sweden. 3)Krautkraemer20 4) δ Brock and Gale6 (the critical discount rate)δ 5 6 (asymptotically autonomous equations) Markus[24] Benam and Hirsch[4] Thieme[32] 7 8H * q x Brock and Malliaris7 158
163 9 h x q dq/dh a chain rule 10Carlson and Haurie8 (a catching-up optimal programme) T. Aronsson and K. G. Lfgren, Welfare consequences of technological and environmental externalities in the Ramsey growth model, Natur. Resour. Modelling 7,1-14 (1993). 2. T. Aronsson and K. G. Lfgren, National product related welfare measures in the presence of technological change, externalities and uncertainty, Environ. Resour. Econom. 5, (1995). 3. K. J. Arrow and M. Kurz, Public Investment, the Rate of Return, and the Optimal Fiscal Policy, Johns Hopkins Press, Baltimore (1970). 4. M. Benam and M. W. Hirsch, Asymptotic pseudotrajectories and chain recurrent flows with applications, J. Dynam. Differential Equations 8, (1996). 5. O. J. Blanchard and S. Fischer, Lectures in Macroeconomics, MIT Press, Cambridge, MA (1989). 6. W. A. Brock and D. Gale, Optimal growth under factor augmenting progress, J. Econom. Theory l, (1969). 7. W. A. Brock and A. G. Malliaris, Differential Equations, Stability and Chaos in Dynamic Economics, North-Holland, Amsterdam(1989). 8. D. A. Carlson and A. Haurie, Infinite Horizon Optimal Control:Theory and Applications, Lecture Notes in Economics and Mathematical Systems, Series 290, Springer-Verlag, Berlin/ New York (1987). 9. D. Cass and K. Shell, The structure of stability of competitive dynamic systems, J. Econom. Theory 12, 1-10 (1976). 10. G. Chichilnisky, An axiomatic approach to sustainable development, Soc. Choice Welf. 13, (1996). 11. G. Chichilnisky, What is sustainable development? Land Econom. 73, (1997). 12. C.W.Clark, Mathematical Bioeconomics.The Optimal Management of Renewable Resources, 2nd ed., Wiley, New York (1990). 13. R. Courant, Differential and Integral Calculus, 2nd ed., Blackie, Glasgow/London (1965). 159
164 14. P. S. Dasgupta and G. M. Heal, The optimal depletion of exhaustible resources, Rev. Econom. Stud. (Sympos.), 3-28 (1974). 15. I. Fisher, The Nature of Capital and Income, Macmillan Co., New York (1906). 16. J.M.Hartwick,Degradation of environmental capital and national accounting procedures,europ. Econom. Rev. 35, (1990). 17. G. M. Heal, Lecture Notes on Sustainabilty, Memorandum 16,Department of Economics, University of Oslo, Norway (1995). 18. M. W. Hirsch, Asymptotic phases, shadow and reaction-diffusion systems,in Cnontrol Theory, Dynamic Systems and Geometry Dynamics (D. Elworthy, W. N. Everitte, and E. B. Lee,Eds.), Dekker, New York (1993). 19. M. W. Hirsch and S. Smale, Differential Equation, Dynamic Systems, and Linear Algebra, Academic Press, San Diego (1974). 20. J. A. Krautkraemer, Optimal growth, Resource amenities and the preservation of natural environments, Rev. Econom. Stud. 52, (1985). 21. J. P. LaSalle and S. Lefschetz, Stability by Liapunov s Direct Method with Applications, Academic Press, New York (1961). 22. K. G. Lfgren, Comment on C. R. Hulten Accounting for the wealth of nations: The net versus gross output controversy and its ramifications, Scand. J. Econom. 94, 25-28(1992) 23. K. G. Mler, National accounts and environmental resources, Environ. Resour. Econom. 1,1-15 (1991) 24. L. Markus, Asymptotic autonomous differential systems, Ann. Math. Stud. 36, (1956). 25. W. D. Nordhaus, How Should We Measure Sustainable Income, Department of Economics, Yale University (1995). 26. E. Phelps, Golden rule of economic growth, Amer. Econom. Rev. 51, (1961). 27. R. A. Pollak, Consistent planning, Rev. Econom. Stud. 35 (1968). 28. R. Radner, Efficiency prices for infinite horizon production programmes, Rev. Econom. Stud. 34, (1967). 29. A. Seierstad and K. Sydsaeter, Optimal Control Theory with Economic Applications, North- Holland, New York (1987). 30. R. M. Solow, Intergenerational equity and exhaustible resources, Rev. Econom. Stud. (Sympos.), (1974). 31. J. E. Stiglitz, Growth with exhaustible resources: Efficient and optimal growth paths, Rev. Econom. Stud. (Sympos.), l (1974). 32. H. R. Thieme, Convergent results and a Poincaré-Bendixson trichotomy for asymptotic autonomous equations, J. Math. Biol. 30, (1992). 160
165 33. H. Uzawa,Time preference, the consumption function and optimum asset holdings, in, Capital and Growth: Papers in Honour of Sir John Hicks (J. N. Wolfe, ed.), Univ. of Edinburgh Press, Edinburgh (1968). 34. M. L. Weitzman, On the welfare significance of national product in a dynamic economy, Quart. J. Econom. 90, (1976). 35. M. L. Weitzman, Why the far-distant future should be discounted at its lowest possible rate, J. Environ. Econom. Management 36, (1998). 161
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