LECTURE 7 Economic Growth I
slide 7
消费函数The consumption function
s = 储蓄率the saving rate, 我们假设s 是一个外生变量is an
exogenous parameter
Note: s 是唯一的一个不等于它的大写形 除以L 的小写字母the only lowercase variable that is not equal to its uppercase version divided by L
k = 0.
这一不变的值 k* 就是 稳态资本存量。This constant value, denoted k*, is called the steady state capital stock.
LECTURE 7 Economic Growth I
slide 15
The steady state
k sf(k)
k
k1
k*
LECTURE 7 Economic Growth I
Capital per worker, k
slide 18
向稳态的移动Moving toward the steady state
Investment and
depreciation
k = sf(k) k
k sf(k)
Year
k
y
c
i
δk
k
1
4.000
2.000 1.400 0.600 0.400 0.200
2
4.200
2.049 1.435 0.615 0.420 0.195
3
4.395
2.096 1.467 0.629 0.440 0.189
slide 26
Approaching the Steady State: A Numerical Example
LECTURE 7 Economic Growth I
人均资本, k
slide 6
国民收入恒等式The national income identity
Y = C + I (记住我们假设没有G )
以 “人均per worker” 形式就是:
y=c+i
其中 c = C/L 且 i = I/L
加总形式In aggregate terms: Y = F (K, L )
定义Define: y = Y/L =人均产出
k = K/L =人均资本
假设规模收益不变 constant returns to scale: zY = F (zK, zL ) for any z > 0
提出L, 有：
在水平轴上，找出一个比k* 大的经济初始 资本存量，记为k1. 用刚才的方法看看 k 会随时间怎么变化。 k 会向稳态移动还是其它方向移动呢？
LECTURE 7 Economic Growth I
slide 23
例子A numerical example
生产函数
Y F (K ,L) K × L K 1/2 L1/2
in chap. 3!)
于是有： i = sy = sf(k)
LECTURE 7 Economic Growth I
slide 9
产出，消费和投资Output, consumption, and investment
人均产出, y
f(k)
c1 y1i1k1LECTURE 7 Economic Growth I
存量减少Investment makes the capital stock bigger,
depreciation makes it smaller.
LECTURE 7 Economic Growth I
slide 12
Capital accumulation
Change in capital stock = investment – depreciation
集约形式:
Y L
K L 1/2 1 / 2 L


K L
1 / 2
将 y = Y/L and k = K/L 代入得到：
y f (k ) k 1/2
LECTURE 7 Economic Growth I
slide 24
A numerical example, cont.
消费函数Consumption function:
c = (1–s)y (per worker)
LECTURE 7 Economic Growth I
slide 8
储蓄和投资Saving and investment
储蓄（人均） = sy 国民收入恒等式 y = c + i
就是: i = y – c = sy (投资 = 储蓄, like
Assumptions: y k ; s 0.3; 0.1; initial k 4.0
(only to simplify presentation; we can still do fiscal policy experiments)
5. 外表不同Cosmetic differences.
LECTURE 7 Economic Growth I
slide 4
生产函数The production function
sf(k)
人均资本, k
slide 10
折旧Depreciation
人均折旧, k
= 折旧率 = 每期磨损掉的资本比率
k
1
LECTURE 7 Economic Growth I
人均资本, k
slide 11
资本积累Capital accumulation
The basic idea基本思想: 投资使 资本存量增大，折旧使 资本
假设: s = 0.3 = 0.1 初始资本存量 k = 4.0
LECTURE 7 Economic Growth I
slide 25
向稳态靠拢Approaching the Steady State
Assumptions: y k ; s 0.3; 0.1; initial k 4.0
Y/L = F (K/L , 1)
y = F (k, 1)
y = f(k)
其中 f(k)
= F (k, 1)
LECTURE 7 Economic Growth I
slide 5
The production function
人均产出, y
f(k)
MPK =f(k +1) – f(k) 1
注意：这一生产函数的资本边 际产量是递减的。Note: this production function exhibits diminishing MPK.
已经成为增长理论的一个范式paradigm: – widely used in policy making – benchmark against which most recent growth theories are compared
寻找经济在长期内增长的决定因素
LECTURE 7 Economic Growth I
k
折旧 depreciation
k1
k*
LECTURE 7 Economic Growth I
Capital per worker, k
slide 17
Moving toward the steady state
Investment and
depreciation
k = sf(k) k
8 CHAPTER
Economic Growth I: Capital Accumulation and Population Growth
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learning objectives
学习封闭经济的Solow 模型。Learn the
3. 消费函数更简单The consumption function is simpler.
LECTURE 7 Economic Growth I
slide 3
How Solow model is different from Chapter 3’s model
4. 没有G 和T No G or T
Rule” to find the optimal savings rate and capital stock
LECTURE 7 Economic Growth I
slide 1
索罗模型The Solow Model
Robert Solow, MIT won Nobel Prize for contributions to the study of economic growth
k
=i
– k
由 i = sf(k) , 这就是:
k = sf(k) – k
LECTURE 7 Economic Growth I
slide 13
K 的变动方程式
k = sf(k) – k
Solow 模型的核心方程式 决定了资本随时间变化的行为 …这样，它也就决定了所有其它 内生变量的行
投资 investment
k
折旧 depreciation
k2
k*
LECTURE 7 Economic Growth I
Capital per worker, k
slide 20
向稳态的移动Moving toward the steady state