幾題個體題目 - 經濟

^ 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 .






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