4.消费 .由 d[ae (r n ) t
]/ dt = a eT 0
.
(r n ) t
a(r n)eT 0
(r n )t
,将 a t (r n)atT 0
.
= wt ct 两边同乘
e (r n ) t 得： ∫ (d[ate (rt n ) t ]/ dt)dt = ∫ wte (rt n ) t dt ∫ cte (rt n ) t dt ,也即：aTe∞ (rt n )T
+ ∫ cte0
T
(rt n ) t
dt = ∫
wte (rt n ) t dt a(0) …………………...2-170
T
当 T → ∞ ,由 2-16,可得
∫
0
cte
(rt n ) t
dt = ∫ wte0
∞
(rt n )t
dt + a(0) = w(0) + a(0) = W ……………….2-18
~
由 2-14 可得
ct = c0e(1/ θ)[rt ρ ]t将 2-19 代入到 2-18 得；∞
……………………………………………………………2-19
c(0) = W /( ∫ e[rt (1 θ) / θ ρ / θ+ n ]t dt) ………………………………………….2-200