曼昆宏观经济学第七版英文课件第八章
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( + n + g)k = break-even investment: the amount of investment necessary to keep k constant.
Consists of: k to replace depreciating capital
n k to provide capital for new workers g k to provide capital for the new “effective”
CHAPTER 8
Economic Growth II
14
Growth empirics: Convergence
What the Solow model really predicts is
conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education.
11
= f (k* )
c* is maximized when MPK = + n + g or equivalently, MPK = n + g
CHAPTER 8
Economic Growth II
Growth empirics: Balanced growth
Solow model’s steady state exhibits
workers created by technological progress
CHAPTER 8
Economic Growth II
8
Technological progress in the Solow model
Investment, break-even investment
k = s f(k) ( +n +g)k
similar savings & pop. growth rates, income gaps shrink about 2% per year.
In larger samples, after controlling for differences
in saving, pop. growth, and human capital, incomes converge by about 2% per year.
faster than rich ones. Does this mean the Solow model fails?
CHAPTER 8
Economic Growth II
13
Growth empirics: Convergence
Solow model predicts that, other things equal,
Economic Growth II
4
CHAPTER 8
Technological progress in the Solow model A new variable: E = labor efficiency Assume:
Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g:
can be due to differences in: 1. capital – physical or human – per worker
This prediction comes true in the real world.
CHAPTER 8
Economic Growth II
15
Growth empirics: Factor accumulation vs. production efficiency
Differences in income per capita among countries
k = K/(L×E )
y = Y/(L×E )
0
0
Output per worker
Total output
CHAPTER 8
(Y/ L) = y×E
Y = y×E×L
g
n+g
10
Economic Growth II
The Golden Rule with technological progress
about policies to promote growth about growth empirics: confronting the
theory with facts
two simple models in which the rate of
technological progress is endogenous
wk.baidu.com
Introduction
In the Solow model of Chapter 7, the production technology is held constant. income per capita is constant in the steady state. Neither point is true in the real world: 1908-2008: U.S. real GDP per person grew by a factor of 7.8, or 2.05% per year. examples of technological progress abound (see next slide).
To find the Golden Rule capital stock, express c* in terms of k*: c* = y* i* ( + n + g) k* In the Golden Rule steady state, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress.
CHAPTER 8
Economic Growth II
3
Examples of technological progress
From 1950 to 2000, U.S. farm sector productivity
nearly tripled. The real price of computer power has fallen an average of 30% per year over the past three decades. Percentage of U.S. households with ≥ 1 computers: 8% in 1984, 62% in 2003 1981: 213 computers connected to the Internet 2000: 60 million computers connected to the Internet 2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of True Blood. 2009: iPod capacity = 120gb, 30,000 songs. Can play episodes of True Blood.
balanced growth - many variables grow at the same rate.
Solow model predicts Y/L and K/L grow at the
same rate (g), so K/Y should be constant.
This is true in the real world.
“poor” countries (with lower Y/L and K/L) should grow faster than “rich” ones.
No, because “other things” aren’t equal. In samples of countries with
same effect on output as increases in the labor force.
CHAPTER 8
Economic Growth II
6
Technological progress in the Solow model
Notation:
y = Y/LE = output per effective worker k = K/LE = capital per effective worker
12
Growth empirics: Convergence
Solow model predicts that, other things equal,
“poor” countries (with lower Y/L and K/L) should grow faster than “rich” ones.
Solow model predicts real wage grows at same
rate as Y/L, while real rental price is constant.
Also true in the real world.
CHAPTER 8
Economic Growth II
( +n +g ) k
sf(k)
k*
CHAPTER 8
Economic Growth II
Capital per worker, k
9
Steady-state growth rates in the Solow model with tech. progress
Capital per effective worker Output per effective worker
MACROECONOMICS
N. Gregory Mankiw
PowerPoint® Slides by Ron Cronovich
CHAPTER
8
Economic Growth II: Technology, Empirics, and Policy
Modified for EC 204 by Bob Murphy
© 2010 Worth Publishers, all rights reserved
SEVENTH EDITION
In this chapter, you will learn:
how to incorporate technological progress in
the Solow model
If true, then the income gap between rich & poor
countries would shrink over time, causing living standards to “converge.”
In real world, many poor countries do NOT grow
Production function per effective worker:
y = f(k)
Saving and investment per effective worker:
s y = s f(k )
CHAPTER 8
Economic Growth II
7
Technological progress in the Solow model
CHAPTER 8
Economic Growth II
5
Technological progress in the Solow model
We now write the production function as:
where L × E = the number of effective workers. Increases in labor efficiency have the
Consists of: k to replace depreciating capital
n k to provide capital for new workers g k to provide capital for the new “effective”
CHAPTER 8
Economic Growth II
14
Growth empirics: Convergence
What the Solow model really predicts is
conditional convergence - countries converge to their own steady states, which are determined by saving, population growth, and education.
11
= f (k* )
c* is maximized when MPK = + n + g or equivalently, MPK = n + g
CHAPTER 8
Economic Growth II
Growth empirics: Balanced growth
Solow model’s steady state exhibits
workers created by technological progress
CHAPTER 8
Economic Growth II
8
Technological progress in the Solow model
Investment, break-even investment
k = s f(k) ( +n +g)k
similar savings & pop. growth rates, income gaps shrink about 2% per year.
In larger samples, after controlling for differences
in saving, pop. growth, and human capital, incomes converge by about 2% per year.
faster than rich ones. Does this mean the Solow model fails?
CHAPTER 8
Economic Growth II
13
Growth empirics: Convergence
Solow model predicts that, other things equal,
Economic Growth II
4
CHAPTER 8
Technological progress in the Solow model A new variable: E = labor efficiency Assume:
Technological progress is labor-augmenting: it increases labor efficiency at the exogenous rate g:
can be due to differences in: 1. capital – physical or human – per worker
This prediction comes true in the real world.
CHAPTER 8
Economic Growth II
15
Growth empirics: Factor accumulation vs. production efficiency
Differences in income per capita among countries
k = K/(L×E )
y = Y/(L×E )
0
0
Output per worker
Total output
CHAPTER 8
(Y/ L) = y×E
Y = y×E×L
g
n+g
10
Economic Growth II
The Golden Rule with technological progress
about policies to promote growth about growth empirics: confronting the
theory with facts
two simple models in which the rate of
technological progress is endogenous
wk.baidu.com
Introduction
In the Solow model of Chapter 7, the production technology is held constant. income per capita is constant in the steady state. Neither point is true in the real world: 1908-2008: U.S. real GDP per person grew by a factor of 7.8, or 2.05% per year. examples of technological progress abound (see next slide).
To find the Golden Rule capital stock, express c* in terms of k*: c* = y* i* ( + n + g) k* In the Golden Rule steady state, the marginal product of capital net of depreciation equals the pop. growth rate plus the rate of tech progress.
CHAPTER 8
Economic Growth II
3
Examples of technological progress
From 1950 to 2000, U.S. farm sector productivity
nearly tripled. The real price of computer power has fallen an average of 30% per year over the past three decades. Percentage of U.S. households with ≥ 1 computers: 8% in 1984, 62% in 2003 1981: 213 computers connected to the Internet 2000: 60 million computers connected to the Internet 2001: iPod capacity = 5gb, 1000 songs. Not capable of playing episodes of True Blood. 2009: iPod capacity = 120gb, 30,000 songs. Can play episodes of True Blood.
balanced growth - many variables grow at the same rate.
Solow model predicts Y/L and K/L grow at the
same rate (g), so K/Y should be constant.
This is true in the real world.
“poor” countries (with lower Y/L and K/L) should grow faster than “rich” ones.
No, because “other things” aren’t equal. In samples of countries with
same effect on output as increases in the labor force.
CHAPTER 8
Economic Growth II
6
Technological progress in the Solow model
Notation:
y = Y/LE = output per effective worker k = K/LE = capital per effective worker
12
Growth empirics: Convergence
Solow model predicts that, other things equal,
“poor” countries (with lower Y/L and K/L) should grow faster than “rich” ones.
Solow model predicts real wage grows at same
rate as Y/L, while real rental price is constant.
Also true in the real world.
CHAPTER 8
Economic Growth II
( +n +g ) k
sf(k)
k*
CHAPTER 8
Economic Growth II
Capital per worker, k
9
Steady-state growth rates in the Solow model with tech. progress
Capital per effective worker Output per effective worker
MACROECONOMICS
N. Gregory Mankiw
PowerPoint® Slides by Ron Cronovich
CHAPTER
8
Economic Growth II: Technology, Empirics, and Policy
Modified for EC 204 by Bob Murphy
© 2010 Worth Publishers, all rights reserved
SEVENTH EDITION
In this chapter, you will learn:
how to incorporate technological progress in
the Solow model
If true, then the income gap between rich & poor
countries would shrink over time, causing living standards to “converge.”
In real world, many poor countries do NOT grow
Production function per effective worker:
y = f(k)
Saving and investment per effective worker:
s y = s f(k )
CHAPTER 8
Economic Growth II
7
Technological progress in the Solow model
CHAPTER 8
Economic Growth II
5
Technological progress in the Solow model
We now write the production function as:
where L × E = the number of effective workers. Increases in labor efficiency have the