文档介绍：The Solow growth model
Assumptions
z The production function: Y(t) = F(K(t), A(t)L(t))
AL is effective labor. Labor-augmenting Harrod-neutral
Y(t) = F(A(t)K(t), L(t)) Capital-augmenting
Y(t) = A(t)F(K(t), L(t)) Hicks-neutral
z Constant returns to scale. F(cK(t), cA(t)L(t)) = cF(K(t), A(t)L(t)) ∀c ≥ 0
No specialization: the economy is big enough.
No other important factors, . Land and other natural resources
⎛ K ⎞ 1
⇒ F⎜,1⎟= F(K, AL)
⎝ AL ⎠ AL
⇔ y = f (k)
k is the amount of capital per unit of effective labor.
z f (0) = 0, f '(k) > 0, f "(k) < 0
z Inada (1964) conditions: lim f '(k) = ∞, lim f '(k) = 0
k→0 k→∞
To ensure that the path of the economy does not diverge
z Example: Cobb-Douglas production function F(K, AL) = K α(AL)1−α 0 < α< 1
to verify its constant return
to find the intensive form
to check all conditions
to see that all technical progresses are same
z The evolution of the inputs into production
dL(t)
L&(t) ≡= nL(t)
dt
A&(t) = gA(t)
K& (t) = sY (t) −δK(t)
1
We assume n + g +δ> 0
z What can we expect in such a simple model?
The dynamics of the model
z k&(t) = sf ()(k()t − n + g +δ)k(t)
Investment per per Investment
unit of effective labor labor of effective unit
k
Actual and break-even investment
Inada condition ensures that the two line