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1 01M3065

2 A 34 1

3 Diamond

4 4 3 3

5 ) : 12 P.13 1) 4

6 % 18% % 16.5% %

7 % 20% 5% % 20% 6

8 2 20% 6% 26% 5% 20% % 20% 18% 7

9 2 2.1 Dynasty Model 1928 Ramsey Overlapping Generations Model) 2 Diamond(1965) Diamond Auerbach and Kotlikoff(1987) Auerbach and Kotlikoff cobb-dagulas Branchard and Fisher (1989) Azariadis(1993) Summers(1981) Chamely and Wright(1987) 8

10 2.2 Diamond(1965) 1) 2.1 t t +1 t +2 t +1 t +2 t +1 t t +1 t +2 t +3 1 C y,t C o,t+1 2 C y,t+1 C o,t+2 3 C y,t+2 C o,t+3 2.1: w t s t c y,t r t+1 c o,t+1 t c y,t = w t s t (2.1) c o,t+1 = (1+r t+1 )s t (2.2) 1) Diamond(1965) 9

11 (2.1) (2.2) c y,t + c o,t+1 1+r t+1 = w t (2.3) u t = u(c y,t,c o,t+1 ) (2.4) u t (2.4) (2.3) w t r t+1 u u =(1+r t+1 ) (2.5) c y,t c o,t+1 (2.5) (2.5) (2.1) s t = s(w t,r t+1 ) (2.6) K t L t Y t = F(K t,l t ) (2.7) Y t n L t =(1+n)L t 1 (2.8) (2.7) L t y t = f(k t ) (2.9) 10

12 y t k t = K t /L t f (k t+1 )=r t+1 (2.10) w t = f(k t ) f (k t )k t (2.11) (2.10) (2.11) (2.10) (2.11) w t r t w(r t ) 2) s t L t = K t+1 s t = 1 1+n k t+1 (2.12) 2 3) steady state (2.6) (2.10) (2.11) (2.12) k t+1 = 1 1+n s[f(k t) f (k t )k t,f (k t+1 )] = φ(k t ) (2.13) (2.13) uniqueness globally Ihori(1996) 4) 2) w(r t ) lim k 0 φ (k t ) > 0 lim f (k t )=0 k φ (k) 0 for all k > 0 3) (2.12) 4) k t+1 = φ(k t ) φ (k) 0 for all k > 0 ds 0 for all (w,r) 0 dr 11

13 0 <φ < 1 (2.14)

14 3 3.1 c yt+1 c o,t+1 U t (3.1) U t = ( 1 c 1 1/γ y,t + 1 ) 1 1/γ 1+δ c1 1/γ o,t+1 (3.1) (3.1) γ δ 0 <γ<1 δ >0 s t =(1 ω)w t + g (1 + θ t )c y,t (3.2) s t t w t t g ω θ t t (3.2) 13

15 s t = 1+θ t+1 1+(1 ρ)r t+1 c o,t+1 (3.3) r t+1 t +1 ρ θ t+1 t +1 (3.3) (3.2) (3.3) (1 ω)w t + g =(1+θ t )c y,t + (3.4) t 1+θ t+1 1+(1 ρ)r t+1 c o,t+1 (3.4) (3.4) (3.1) L = 1 1 1/γ +λ ( c 1 1/γ y,t + 1 ) 1+δ c1 1/γ o,t+1 { (1 ω)w t + g (1 + θ t )c y,t (3.5) } 1+θ t+1 c 1+(1 ρ)r o,t+1 t+1 (3.5) L = c 1/γ y,t λ (1 + θ t ) (3.6) c y,t L c o,t+1 = 1 1+δ c 1/γ o,t λ ( 1+θ t+1 1+(1 ρ)r t+1 L λ = (1 ω)w t + g (1 + θ t )c y,t ) (3.7) 1+θ t+1 1+(1 ρ)r t+1 c o,t+1 (3.8) (3.9) (3.6) (3.7) λ λ = c 1/γ y,t 1+θ t (3.10) λ = 1+(1 ρ)r t+1 (1 + θ t+1 )(1 + δ) c o,t+1 (3.11) 14

16 (3.10) (3.11) ( ) γ ( ) 1+θt 1+(1 γ ρ)rt+1 c o,t+1 = c y,t (3.12) 1+θ t+1 1+δ (3.12) (3.4) c y,t (1 + θ t+1 ) γ 1 (1 + θ t ) 1 (1 + δ) γ {(1 ω)w t + g} c y,t = (1 + θ t+1 ) (γ 1) (1 + δ) γ +(1+θ t ) γ 1 (1 + (1 ρ)r t+1 ) γ 1 (3.13) (3.13) (3.2) s t = {(1 ω)w t + g}(1 + θ t ) γ 1 (1 + δ) γ (1 + θ t+1 ) γ 1 +(1+θ t ) γ 1 {1+(1 ρ)r t+1 } γ 1 (3.14) 3.2 K t L t cobb-douglas α 0 <α<1 Y t = K α t L1 α t (3.15) Π n Π=Y t w t L t r t K t (3.16) L t+1 =(1+n)L t (3.17) (3.15) (3.16) L t (3.15) L t Y t L t = Kα t L t L t L α t (3.18) 15

17 (3.18) y t = k α t (3.19) y t k t (3.15) f(0) = 0 f ( ) = 0 f (0) = L t (3.16) L t π = y t w t r t k t (3.20) π (3.20) y t w t r r k t (3.21) (3.20) (3.19) k α t w t r t k t = 0 (3.22) (3.22) k t r t = αk α 1 t (3.23) w t = (1 α)k α t (3.24) 16

18 (3.23) (3.24) 3.3 TR ω ρ c 1,t τ c L t c 2,t τ c L t 1 L t TR = ωw t L t + ρr t K t + θ t c y,t L t + θ t c o,t L t 1 gl t (3.25) (3.25) 1 L t tr = ωw t + ρr t k t + θ t c y,t + θ tc o,t 1+n g (3.26) 3.4 K t+1 = s t L t (3.27) (3.27) t +1 t (3.27) L t 17

19 k t+1 = 1 1+n s t (3.28) (3.14) (3.23) (3.24) s t = (1 + θ t ) γ 1 {(1 ω)(1 α)kt α + g} (1 + δ) γ (1 + θ γ 1 t+1 +(1+θ t) { γ 1 1+αkt+1 α 1(1 ρ)} γ 1 (3.29) (3.28) (3.29) k t+1 = 1 1+n (1 + θ t ) γ 1 {(1 ω)(1 α)k α t + g} (1 + δ) γ ( 1+θt+1 1+θ t ) γ 1 + { 1+αk α 1 t+1 (1 ρ)} γ 1 (3.30) (3.30) 3.5 (3.30) k t,k t+1 1) (3.30) k t+1 k t t t +1 dk t+1 dk t = (1 + n) 1 α(1 + θ t ) γ 1 (1 α)k α 1 (1 + δ) γ + X γ 1 +(γ 1)X γ 2 (1 ρ)α(α 1)k α 2 (3.31) X =1+(1 ρ)r dk t+1 /dk t 0 1 dk t+1 /dk t dk t+1 /dk t > 0 dk t+1 /dk t < 1 1) 18

20 4 k ρ dk dρ = (1 + θ t ) γ 1 X γ 1 αk α 1 (1 + δ) γ + X γ 1 +(γ 1)X γ 2 (1 ρ)(α 1)αk α 2 (1 ω)(1 α)αk α 1(3.32) (3.32) dk/dρ < 0 k ω dk dω = (1 + θ t ) γ 1 (1 α)k α (1 + δ) γ + X γ 1 +(γ 1)X γ 2 (1 ρ)(α 1)αk α 2 (1 ω)(1 α)αk α 1(3.33) 4 19

21 : α % δ % γ % g 0.03 n 0.01 α α =0.5 α =0.4 1) δ 1 40 δ =1.0 γ t t +1 1)

22 (2002) 9.0 % g0.03 2) 20.0 % 5.0 % (3.30) k t k t k t k t+1 4.1: 2) (2002)P.9 21

23 4.2 E k t k t+1 E k E :

24 4.3 ω ρ (3.33) (3.32) 4.2: 4.2 5%

25 : 4.3 5%

26 α α α 4.4: (α ) 4.5: (α ) 25

27 α 4.6: (α ) 4.7: (α ) α cobb-douglas 26

28 δ δ 4.8: (δ ) 4.9: (δ ) 27

29 4.10: (δ ) 4.11: (δ ) δ δ 28

30 γ γ 4.12: (γ ) 4.13: (γ ) γ 29

31 4.14: (γ ) 4.15: (γ ) γ α δ γ

32 CaseA 20% 25% CaseB 20% 15% CaseC 20% 25% CaseD 20% 15% 4.3: CaseA CaseB CaseC CaseD CaseA CaseB CaseA 9.0% 5.5% 39.2% 3.83% 2.23% 1.51% 3.29% 7.69% 31

33 CaseB 9.0% 12.4% 37.9% 3.69% 2.28% 1.49% 3.18% 8.37% CaseC CaseD CaseC 5.0% 2.9% 42.3% 1.2% 0.76% 0.5% 2.3% 5.5% CaseD 5.0% 7.3% 46.0% 1.23% 0.73% 0.49% 2.67% 6.85% 4.6 Lucas(1990) Lucas 30% (2001) Lucas(1990) 10% 32

34 Lucas 36%

35 A (3.30) ( (1 + δ) γ + { 1+αk α 1 t+1 (1 ρ)} γ 1 ) k t+1 =(1+θ t ) γ 1 {(1 ω)(1 α)k α t + g} { (1 + δ) γ + X γ 1 +(γ 1)X γ 2 (1 ρ)(α 1)αk α 2 t+1 } dk t+1 =(1+θ t ) γ 1 (1 ω)(1 α)αkt α 1 dk t dk t dk t+1 dk t = (1 + θ t ) γ 1 (1 ω)(1 α)αk α 1 (1 + δ) γ + X γ 1 +(γ 1)X γ 2 (1 ρ)(α 1)αk α 2 k 0 <dk t+1 /dk t <

36 [1] A.J.Auerbach and L.J.Kotlikoff(1987), Dynamic fiscal policy, Cambridge University Press. [2] C.Azariadis(1993), Intertemporal Macroeconomics, Blackwell. [3] G.T.McCandless,Jr.,and N.Wallace(1991), Introduction to dynamic macroeconomic theory, Harvard University Press. [4] Ch.Chamley and B.Wright(1987), Fiscal Incidence in Overlapping Generations Model with a Fixed Asset, Journal of Public Economics, Vol.32 [5] J.B.Shoven and J.Whalley(1992), Applying General Equilibrium, Cambridge University Press. [6] L.H.Summers(1981), Capital Taxation and Accumulation in a Life Cycle Growth Model, The American Economic Review, Vol. 71(4) [7] O.J.Branchard and S.Fischer(1989),Lectures on Macroeconomics, MIT Press. [8] P.A.Diamond(1965), National dept in a neoclassical growth model, The American Economic Reviwe, Vol. 55(5) [9] R.Lucas,Jr(1990), Supply-side economics: An analytical review,oxford Economic papers,vol.42,no.2. [10] T.Ihori(1996), Public Finance in an Overlapping Generation Economy, Macmillan Press. [11] (1991),,. 35

37 [12] (2002), 14,. [13] (1996),,. [14] (1989),,. [15] (2001),,, Vol.52,No.1. [16] (2002), 14,. [17] (2001), 11,. [18] (1994), - -. [19] (1998),,. [20] (2002), [21] (1987,,. 36

Auerbach and Kotlikoff(1987) (1987) (1988) 4 (2004) 5 Diamond(1965) Auerbach and Kotlikoff(1987) 1 ( ) ,

,, 2010 8 24 2010 9 14 A B C A (B Negishi(1960) (C) ( 22 3 27 ) E-mail:[email protected] E-mail:[email protected] E-mail:[email protected] 1 1 1 2 3 Auerbach and Kotlikoff(1987) (1987)