chapter 7 经济增长 economic growth i macro © 2002 worth publishers, all rights reserved

CHAPTER 7

经济增长 Economic Growth I

mac

ro

© 2002 Worth Publishers, all rights reserved

CHAPTER 7CHAPTER 7 Economic Growth I Economic Growth I slide 2

A typical family with all their possessions in the U.K., an advanced economy

GDP per capita: $35,580Life expectancy: 79 yearsAdult literacy: 99%


A typical family with all their possessions in Mexico, a middle income country



A typical family with all their possessions in Mali, a poor country



Estimated effects of economic growthEstimated effects of economic growth

A 10% increase in income is associated with a 6% decrease in infant mortality （婴儿死亡率）

Income growth also reduces poverty. Example:

+65%-12%1997-99

-25%+76%

Growth and Poverty in Indonesia

1984-96

change in # of persons living below poverty line

change in income per capita


Income and poverty in the world Income and poverty in the world selected countries, 2000selected countries, 2000

0

10

20

30

40

50

60

70

80

90

100

$0 $5,000 $10,000 $15,000 $20,000

Income per capita in dollars

% o

f p

op

ula

tio

n

livi

ng

on

$2

per

day

or

less

Madagascar

India

BangladeshNepal

Botswana

Mexico

ChileS. Korea

Brazil Russian Federation

Thailand

Peru

China

Kenya


Huge effects from tiny differencesHuge effects from tiny differences

In rich countries like the U.S., if government policies or “shocks” have even a small impact on the

long-run growth rate, they will have a huge impact

on our standard of living in the long run…


Huge effects from tiny differencesHuge effects from tiny differences

1,081.4%243.7%85.4%

624.5%169.2%64.0%

2.5%

2.0%

…100 years…50 years…25 years

percentage increase in standard of living after…

annual growth rate of income per capita


问题思考问题思考 why our national income grows?

why some economies grow faster than others?– 东亚国家年均 7% 的增长– 部分非洲国家多年来的人均收入停滞

Poor countries are always poor?

What kind of policies can help economies grow?


Outline Outline 内容提要内容提要

Learn the closed economy Solow growth model

学习封闭经济下的索洛模型

See how a country’s standard of living depends on its saving and population growth rates

了解储蓄率和人口增长率如何影响一国的生活水平


Analysis Steps Analysis Steps 分析步骤分析步骤 first step is to examine how the supply

and demand for goods determine the accumulation of capital. – 产品供求如何决定资本积累

Second step is to examine which factors effect the change in capital stock– 哪些因素引起资本存量的变化

Third step is to build Solow model– 建立索洛模型


生产函数生产函数The production functionThe production function

Y = F (K, L )

Assume constant returns to scale( 规模收益不变 ):

zY = F (zK, zL ) for any z > 0



Define:– y = Y/L = output per worker 人均产出– k = K/L = capital per worker 人均资本量

Pick z = 1/L. Then ( , )

( ,1)

zY F zK zL

Y K KF F

L L L

( )y f k


Output per worker, y

Capital per worker, k

f(k)

Note: diminishing MPK

资本边际产量递减

Note: diminishing MPK

资本边际产量递减

1

MPK =f(k +1) – f(k)



国民收入核算恒等式国民收入核算恒等式The national income accounts identityThe national income accounts identity

Y = C + I

In “per worker” terms:

y = c + i

where c = C/L and i = I/L


消费函数消费函数The consumption functionThe consumption function

Define: s = the saving rate( 储蓄率 )

Consumption function: c = (1–s)y


储蓄和投资储蓄和投资Saving and investmentSaving and investment

saving (per worker)

s = y – c = y – (1–s)y = sy

National income identity is y = c + i

Rearrange to get: i = y – c = sy

Using the results above,

i = sy = sf(k)


产出，消费和投资产出，消费和投资Output, consumption, and investmentOutput, consumption, and investmentOutput per worker, y


f(k)

sf(k)

k1

y1

i1

c1


资本存量的变化资本存量的变化 change in capital stockchange in capital stock

two forces– investment 投资

– depreciation 折旧

The basic idea:The basic idea:

Investment makes Investment makes the capital stock bigger,the capital stock bigger,

depreciation makes it smaller.depreciation makes it smaller.

The basic idea:The basic idea:

Investment makes Investment makes the capital stock bigger,the capital stock bigger,

depreciation makes it smaller.depreciation makes it smaller.


折旧折旧DepreciationDepreciation

Depreciation per worker, k


k

= 折旧率 =the rate of

depreciation

= 折旧率 =the rate of

depreciation

1


资本积累资本积累Capital accumulationCapital accumulation

Change in capital stock= investment – depreciationk = i – k

Since i = sf(k) , this becomes:

k = s f(k) – k


The steady stateThe steady state

Investment and

depreciation


sf(k)

k

k*


稳态稳态The steady stateThe steady state

If investment is just enough to cover depreciation [sf(k) = k ],

then capital per worker will remain constant: k = 0.

This constant value, denoted k*, is called the steady state capital stock （稳态资本存量）

k = s f(k) – k


稳态的意义稳态的意义Signification of steady stateSignification of steady state

an economy at the steady state will stay there– 处于稳定状态的经济会停在那里

an economy not at the steady state will go there– 非稳定状态会趋向于稳定状态

the steady state represents the long-run equilibrium of the economy– 稳态代表了长期均衡


向稳态的调整向稳态的调整Moving toward the steady stateMoving toward the steady state

Investment and

depreciation


sf(k)

k

k*

k = sf(k) k

depreciation

k

k1

investment



Investment and

depreciation


sf(k)

k

k*

k = sf(k) k

k2

investment depreciati

on

k



Investment and

depreciation


sf(k)

k

k*

k = sf(k) k

k

k2


A numerical exampleA numerical example

Production function (aggregate):

1/ 2 1/ 2( , )Y F K L K L K L

1/ 21/ 2 1/ 2Y K L KL L L

1/ 2( )y f k k

To derive the per-worker production function, divide through by L:

Then substitute y = Y/L and k = K/L to get


A numerical example, A numerical example, cont.cont.

Assume:

s = 0.3

= 0.1

initial value of k = 4.0


Approaching the Steady State: Approaching the Steady State: A Numerical ExampleA Numerical Example

Year k y c i k k

1 4.000 2.000 1.400 0.600 0.4000.200

2 4.200 2.049 1.435 0.615 0.4200.195

3 4.395 2.096 1.467 0.629 0.4400.189

Year k y c i k k

1 4.000 2.000 1.400 0.600 0.4000.200

2 4.200 2.049 1.435 0.615 0.4200.195

3 4.395 2.096 1.467 0.629 0.4400.189

Assumptions: ; 0.3; 0.1; initial 4.0y k s k


Approaching the Steady State: Approaching the Steady State: A Numerical ExampleA Numerical Example

Year k y c i k 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

4 4.584 2.141 1.499 0.642 0.458 0.184 … 10 5.602 2.367 1.657 0.710 0.560 0.150 … 25 7.351 2.706 1.894 0.812 0.732 0.080 … 100 8.962 2.994 2.096 0.898 0.896 0.002 … 9.000 3.000 2.100 0.900 0.900 0.000

Year k y c i k 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

4 4.584 2.141 1.499 0.642 0.458 0.184 … 10 5.602 2.367 1.657 0.710 0.560 0.150 … 25 7.351 2.706 1.894 0.812 0.732 0.080 … 100 8.962 2.994 2.096 0.898 0.896 0.002 … 9.000 3.000 2.100 0.900 0.900 0.000

Assumptions: ; 0.3; 0.1; initial 4.0y k s k

chapter 7 经济增长 economic growth i macro © 2002 worth publishers, all rights reserved

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