^ 表示下標不是次方項喔
3. Consider the dynamics of an individual's personal (human) capital
stock as Ｓ is decribed as
Ｓ^(t+1) ＝ δＳ^t ＋ Ｉ^t ,
where δ＜１ represents the depreciation of accumulater capital ,
Ｉ is the level of investmaen in capital with a time cost of Ｃ（Ｉ）
, qnd Ｃ（Ｉ） is increasing and convex . The opportunity cost of
time is ｗ , repesenting the wage rate .
When an indivual has a lifespan of Ｔ periods , i.e. t=1,2,3...,T,
the maximization problem can described as :
T ^
Max β^t Σ [Ｓ^tＲ（Ｓ^t）－ｗＣ（Ｉ^t）] ,
t=0
^
s.t. Ｓ^(t+1) ＝ δψＳ^t ＋ Ｉ^t
where is the discount factor , Ｓ is the aggregate per-capita capital ,
^
ＳＲ（Ｓ） is the individual's market and non-market returns to capital ,
^
Ｒ'Ｓ（Ｓ）＞０ , ψ represents the decreication faciot arising from other
reasons such as job switching or cjager of career . Slove for the optimal
condition for Ｉ^t .
--
3. Consider the dynamics of an individual's personal (human) capital
stock as Ｓ is decribed as
Ｓ^(t+1) ＝ δＳ^t ＋ Ｉ^t ,
where δ＜１ represents the depreciation of accumulater capital ,
Ｉ is the level of investmaen in capital with a time cost of Ｃ（Ｉ）
, qnd Ｃ（Ｉ） is increasing and convex . The opportunity cost of
time is ｗ , repesenting the wage rate .
When an indivual has a lifespan of Ｔ periods , i.e. t=1,2,3...,T,
the maximization problem can described as :
T ^
Max β^t Σ [Ｓ^tＲ（Ｓ^t）－ｗＣ（Ｉ^t）] ,
t=0
^
s.t. Ｓ^(t+1) ＝ δψＳ^t ＋ Ｉ^t
where is the discount factor , Ｓ is the aggregate per-capita capital ,
^
ＳＲ（Ｓ） is the individual's market and non-market returns to capital ,
^
Ｒ'Ｓ（Ｓ）＞０ , ψ represents the decreication faciot arising from other
reasons such as job switching or cjager of career . Slove for the optimal
condition for Ｉ^t .
--
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