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Chapter 8
Growth, Capital Accumulation,
and the Economics of Ideas:
Catching Up vs. the Cutting
Edge
1
Chapter Outline
 The Solow Model and Catch-Up Growth
 The Solow Model – Details and Further
Lessons (Optional Section)
 Growing on the Cutting Edge: The
Economics of Ideas
 The Future of Economic Growth
 Appendix: Excellent Growth
2
Introduction
 In 2006:
• China: GDP per capita grew by 10%
• United States: GDP per capita grew by 2.3%
 United States has never grown as fast as the
Chinese economy is growing today.
 Why is China growing more rapidly than the
U.S.?
• Is there something wrong with the U.S. economy?
• Do the Chinese have a magical potion for
growth?
3
Introduction
 There are two types of growth
• Catch-up growth
 Takes advantage of ideas, technologies, or
methods of management already in existence
• Cutting-edge growth
 Primarily about developing new ideas
 China is growing much faster than the
U.S. because:
• The U.S. economy is on the cutting edge.
• The Chinese economy is catching up.
4
Introduction
 What do we learn in this chapter?
• A model based on capital accumulation.
 Explains catch-up growth.
 Allows us to answer the following questions:
•
•
Why China is growing faster than the U.S.
Why the losers of WWII grew much faster than the winner.
 How poor and rich countries can converge in
income over time.
• About cutting-edge growth and the economics
of ideas.
5
The Solow Model and Catch-Up Growth
 Total Output, Y, of an economy depends
on:
• Physical capital: K
• Human capital: education x Labor = eL
• Ideas: A
 This can be expressed as the following
“production function”:
Y  F(A,K, eL)
6
The Solow Model and Catch-Up Growth
 For now, let A, e, and L be constant so that:
Y  FK 
 MPK: marginal product of capital
• The additional output resulting from using an
additional unit of capital.
• As more capital is accumulated, the MPK gets
smaller and smaller.
 We draw a particular production function in
the next slide where:
Y K
7
Capital, Production, and Diminishing
Returns
Output, Y
Y K
3.2
3
3 .2  3 .0
MPK 
 0 .2
10  9
MPK 
1
1 0
1
1 0
Conclusion: as
more capital is
added, MPK
declines.
Capital, K
0 1 2 3 4 5 6 7 8 9 10 11 12
8
Growth in China and the United States
 The “iron logic of diminishing returns”
explains why…
• The Chinese economy is able to grow so
rapidly.
 It turned toward markets which increased
incentives.
 The capital stock was low
 The MPK was high.
• China will not be able to achieve these high
growth rates indefinitely.
9
The Solow Model and Catch-Up Growth
 Why Bombing a Country Can Raise Its
Growth Rate.
 Also explained by the “iron law”…
• Much of the capital stock was destroyed
during WWII. Therefore the MPK was high.
• Following the war, both Germany and Japan
were able to achieve much higher growth
rates than the U.S. as they “caught up”.
 Check out the following table.
10
The Solow Model and Catch-Up Growth
Conclusions:
1. Catch-up growth (Germany, Japan) is much greater
than cutting-edge growth (U.S.)
2. Eventually the catch-up growth slows down.
11
The Solow Model and Catch-Up Growth
 Capital Growth Equals Investment Minus
Depreciation
• Capital is output that is saved and
invested.
• Let g be the fraction of output that is
invested in new capital.
 The next figure shows how output is
divided between consumption and
investment when g = 0.3.
12
Output = Consumption + Investment
Output, Y
20
When K = 100, Output = 10
Y K
15
10
Consumption = (1- 0.3) x 10 = 7
5
Investment = 0.3∙Y
3
2
Investment = (0.3) x 10 = 3
Capital, K
0
0
100
200
300
400
13
Depreciation
 Depreciation – amount of capital that
wears out each period.
 Depreciation Rate (d) – fraction of capital
that wears out each year.
depreciation
d
K
…Or…
depreciation = d K
12.14
Depreciation
Depreciation
8
Depreciation = 0.02K
6
4
42
Slope 
d
200  100
2
0
Capital, K
0
100
200
300
400
15
Why Capital Alone Cannot be the Key to
Economic Growth
 As capital increases:
• Depreciation increases at a constant rate = d.
• Output increases at a diminishing rate.
• Investment is a constant fraction of output.
 At some point depreciation will equal
investment.
 The capital stock will stop growing (steady
state).
 Output will stop growing.
16
Capital Increases or Decreases Until
Investment = Depreciation
GDP, Y
8
Depreciation = 0.02∙K
At K = 400, Inv. < Dep. → ↓ K
6
Investment = 0.3∙Y
4.5
4
At K = 100,
Inv. > Dep.
→↑K
3
2
0
0
100
200 225
300
Result:
equilibrium
at K = 225
Y = 4.5
inv. = dep. =4.5
400 Capital, K
17
Capital Increases or Decreases Until
Investment = Depreciation
Check the Math
• At K = 100, Y =√100 = 10
• Depreciation = 0.02x100 = 2
• Investment = 0.3x10 = 3
•Investment > Depreciation
Result: K and Y grow.
Check the Math
• At K = 400, Y =√400 = 20
• Depreciation = 0.02x400 = 8
• Investment = 0.3x20 = 6
•Investment < Depreciation
Result: K and Y decrease.
Check the Math
• At K = 225, Y =√225 =15
• Depreciation = 0.02x225 =
4.5
• Investment = 0.3x15 = 4.5
• Investment = Depreciation
Result:
1. Investment = Depreciation
2. K and Y are constant.
This is a steady state.
18
Capital Alone Cannot be the Key to
Economic Growth
 The logic of diminishing returns means
that eventually capital and output will
cease growing.
 Other factors must be responsible for longrun economic growth.
• Human capital: knowledge, skills, experience?
• Technological knowledge: better ideas?
19
Increasing Human Capital
20
Better Ideas Drive Long-Run Economic
Growth
 What about Human Capital?
• Like capital, it is subject to diminishing returns
and it depreciates.
• Logic of diminishing returns also applies to
human capital.
• Conclusion: Human capital also cannot drive
long-run economic growth.
 What about technological knowledge?
21
Better Ideas Drive Long-Run Economic
Growth
 Technological knowledge
• A way of getting more output from the same
input (increase in productivity).
• We can include technological knowledge in
our model by letting A stand for ideas that
increase productivity. Therefore, let the
production function be:
YA K
22
Better Ideas Drive Long-Run Economic
Growth
Output, Y
20
Y  ( 2) K
15
↑Output due to
technical change
10
Y  (1) K
5
3
2
Capital, K
0
0
100
200 225
300
400
12.23
Better Ideas Drive Long-Run Economic
Growth
 Conclusion:
• Technological knowledge (better ideas) are
the key to long-run economic growth.
 Solow estimated that better ideas are
responsible for ¾ of our increased
standard of living.
24
Check Yourself
 What happens to the marginal product of
capital as more capital is added?
 Why does capital depreciate? What
happens to the total amount of capital
depreciation as the capital stock
increases?
25
The Solow Model – Details and Further
Lessons
 Let’s review what we know now:
• If Investment > Depreciation → K and Y grow.
• If Investment < Depreciation → K and Y fall.
• If Investment = Depreciation → K and Y are
constant.
 Two important results:
• Steady state equilibrium occurs when investment
equals depreciation.
• When K is in steady state equilibrium, Y is also in
steady state equilibrium.
 These results are illustrated in the next two
diagrams.
26
When K Is In Steady State Equilibrium, Y,
Is In Steady State Equilibrium
Output, Y
8
Depreciation = 0.02∙K
6
Investment = 0.3∙Y
4.5
4
3
The Steady State K is found
where investment = Depreciation
2
0
Capital, K
0
100
200 225
300
400
27
When K Is In Steady State Equilibrium, Y,
Is In Steady State Equilibrium
Output, Y
20
Steady state output
Y K
15
Depreciation = 0.02∙K
10
Investment  0.3 K
5
Steady state capital stock
0
100
200 225 300
400
Capital, K
28
Check Yourself
In the previous figure:
 What happens when the capital stock is
400?
 What is investment?
 What is depreciation?
 What happens to output?
29
Increase In the Investment Rate
 What happens when g, the fraction of
output that is saved and invested
increases?
• ↑g↑K↑Y
 Conclusion: an increase in the investment
rate increases a country’s steady state
level of GDP.
 We show this result in the next diagram.
30
An Increase in the Investment Rate
Increases Steady State Output
Output, Y
20
Y K
15
Depreciation = 0.02∙K
10
Inv.  0.4 K
Inv.  0.3 K
5
Capital, K
0
100
200 225
300
400
31
An Increase in the Investment Rate
Increases Steady State Output
 The results presented in the previous
diagram predict that:
• An increase in investment rate, g, causes
output to increase.
• Because labor is held constant, output per
capita also increases.
 Testing the model:
• Are its predictions consistent with real world
data?
• The next figure suggests that they are.
32
An Increase in the Investment Rate
Increases Steady State Output
33
An Increase in the Investment Rate
Increases Steady State Output
 Conclusions:
• ↑g = ↑ steady state level of output.
• As the economy moves from the lower to the
higher steady state output → ↑ growth rate of
output
• This higher growth rate is temporary.
• ↑investment rate → ↑ steady state level of
output but not its long-run growth rate.
• These points are illustrated in following case
study of South Korea.
34
An Increase in the Investment Rate
Increases Steady State Output
 The Case of South Korea
• In 1950, South Korea was poorer than
Nigeria.
• 1950s: the investment rate was < 10%.
• 1970s: Investment rate more than doubled.
• 1990s: Investment rate increased to over
35%.
• South Korea’s GDP increased rapidly.
• As GDP reached Western levels, the growth
rate has slowed.
35
An Increase in the Investment Rate
Increases Steady State Output
 Favorable Incentives and institutions
 Savings must be efficiently collected and
used.
• Soviet Union had a high saving rate, but
savings were not invested well.
• This made the “effective” investment rate very
low.
 A country can have a low saving rate but a
high investment rate by importing savings.
36
The Solow Model and Conditional
Convergence
 Conditional Convergence – Among
countries with similar steady state levels of
output, poorer countries grow faster than
richer countries.
 A country will grow faster the farther its
capital stock is below its steady state
value.
 The next figure presents evidence of
convergence.
37
Conditional Convergence
38
From Catching Up to Cutting Edge
 Several predictions of Solow model are
consistent with the evidence.
• Countries with higher investment rates have
higher GDP per capita.
• Countries grow faster the farther their capital
stock is from the steady state level.
 One prediction is not consistent with the
evidence:
• Steady state: Long-run growth = 0
39
From Catching Up to Cutting Edge
 What explains the observed long-run
growth?
• Generation of ideas results in long-run
economic growth.
 Let’s see how this works:
• New ideas → ↑A → ↑Output at every level of K
• ↑ Output → ↑Investment → Investment >
Depreciation →↑ K→ ↑ Output (movement
along new production function).
• As ideas continue to grow, output continues to
grow.
Let’s use the model to see this.
40
Solow and the Economics of Ideas in One
Diagram
Output, Y
Effect of ↑A from 1 to 1.5
c
33.7
Output ↑
b
Better
Ideas
15
Y  (1.5) K
a
Y  (1) K
Dep. = 0.02∙K
Inv .  0.3(1.5) K
Inv .  0.3(1) K
225
506 Capital, K
41
Check Yourself
 What happens to investment and
depreciation at the steady state level of
output?
 In the previous figure, how much is
consumed in the old steady state? How
much is consumed in the new steady
state?
42
Check Yourself
 Do countries grow faster if they are far
below their steady state or if they are
close?
 Do countries with higher investment rates
have lower or higher GDP per capita?
43
Growing on the Cutting Edge: The
Economics of Ideas
 The United States, Japan, and Western
Europe are on the cutting edge of
economic growth.
 To keep this growth up these countries
must continue to develop new ideas.
 Conclusion: The economics of ideas
becomes the key to understanding growth
on the cutting edge.
44
Growing On The Cutting Edge:
The Economics of Ideas
 Research and Development Is Investment
For Profit
 Spillovers mean that ideas are
underprovided.
 Government has a role in improving the
production of ideas.
 The larger the market, the greater the
incentive to research and develop new
ideas.
Let’s look at each of these in turn.
45
Research and Development Is
Investment For Profit
 Keys to increasing technological
knowledge:
• Incentives
• Institutions that encourage investment in
physical and human capital and R&D.
 Property rights
 honest government
 political stability
 a dependable legal system
 competitive open markets
46
Research and Development Is
Investment For Profit
 Not just the number of scientists and
engineers that is important
 All kinds of people come up with new ideas.
 Business culture and institutions
 Institutions that are especially important:
• Commercial settings that help innovators to
connect with capitalists
• Intellectual property rights
• A high-quality education system
Let’s look at each of these in turn.
47
Research and Development Is
Investment For Profit
 A commercial setting that helps innovators
connect with capitalists.
• Ideas without financial backers are sterile.
• The U.S. is good at connecting innovators
with businessmen and venture capitalists.
• American culture supports entrepreneurs:
 People like Apple CEO Steve Jobs are lauded in
the popular media.
 Contrast this to the treatment of 18th century
British entrepreneur John Kay.
48
Research and Development Is
Investment For Profit
John Kay (1704-1780) invented the
“flying shuttle” used in cotton
weaving, the single most important
invention launching the industrial
revolution. Kay, however, was not
rewarded for his efforts. His house
was destroyed by “machine breakers,” who
were afraid that his invention would put them
out of a job. Kay was forced to flee to France
where he died a poor man.
49
Research and Development Is
Investment For Profit
 Patents
• New processes, products, and methods can
be copied by competitors.
 World’s first MP3 player was the Eiger Labs
MPMan introduced in 1998.
 Copied by other firms and Eiger Labs lost out
• Patents
 Can slow down spread of technology.
 Trade-off between creating incentives to research
and develop new products and avoiding too much
monopoly
50
Spillovers, and Why There Aren’t Enough
Good Ideas
 Non-rivalrous – A good that two or people
can consume at the same time.
 Ideas are non-rivalrous.
• The spillover or diffusion of new ideas
generates widespread economic growth.
• Implication: Too few ideas are generated.
Let’s see why.
51
Spillovers, and Why There Aren’t Enough
Good Ideas
 Optimal social investment in R&D occurs
where: MSB = MSC
 Optimal private investment occurs where
MPB = MPC
 With spillover benefits: MSB = MPB +
spillovers so that MSB > MPB
 Result:
Optimal Private
Investment in R&D
<
Optimal Social
Investment in R&D
52
Spillovers Mean Too Little Investment in
Research and Development
$
Spillover benefits
IP = optimal private investment in R&D
IS =optimal social investment in R&D
MPC = MSC
MPB = MPC
MSB = MSC
Assumes there
MSB are no spillover
costs
MPB
IP
IS
Quantity of R&D
53
Government’s Role in the Production of
Ideas
 Ideas in mathematics, physics, and
molecular biology have many applications
so spillovers can be large.
• Problem: Even if the social benefits are large,
the private benefits can be small.
• Solution: Subsidize the production of new
ideas or give tax breaks for R&D.
 Both shift the MC of R&D curve down → ↑ R&D
investment.
Let’s see this.
54
Spillovers Mean Too Little Investment in
Research and Development
$
MPC = MSC
MPB = MPC
MSB = MSC
MSB
MPB
IP
IS
Quantity of R&D
55
Spillovers, and Why There Aren’t Enough
Good Ideas
 Large spillovers to basic science suggest
a role for government subsidies to
universities.
• Especially those parts of the universities that
produce innovations and the basic science
behind those innovations.
• Universities produce scientists
 Most of the 1.3 million scientists were trained in
government subsidized universities.
56
Market Size and Research and
Development
 Innovations like pharmaceuticals, new
computer chips, software, and chemicals
require large R&D expenditures.
 Companies will avoid investing in
innovations with small potential markets.
 Larger markets mean increased rewards
(thus incentives) for R&D.
 As the world market grows, companies will
increase their R&D investments.
57
Check Yourself
 What would happen to the incentive to
produce new ideas if all countries imposed
high tax rates on imports?
 What are spillovers, and how do they
affect the production of ideas?
58
Check Yourself
 Some economists have proposed that the
government offer large cash prizes for the
discovery of cures for diseases like
malaria that affect people in developing
countries. What economic reasons might
there be to support a prize for malaria
research rather than, say, cancer
research?
59
The Future of Economic Growth
 Over the last 10,000 years per capita
world GDP has been growing.
• Dawn of civilization to about 1500: growth =
0%
• AD 1500 – 1760: growth = 0.08%
• Growth doubled in next 100 years.
• Increased even further during the 19th and
20th centuries.
• Today: world wide growth of per capita GDP =
2.2%
60
The Future of Economic Growth
 Economic growth can be even faster
• A (ideas) = Population x Incentives x
Ideas/Hour
• Population
 ↑population → ↑ number of people with new ideas
 Much of the world is poor; thousands of potentially
great scientists are laboring in menial jobs.
• As the world gets richer → ↑ production of
ideas → everyone benefits
61
The Future of Economic Growth
 Incentives appear to be increasing
• Consumers are richer
• Markets are expanding due to trade
• World-wide improvement in institutions
 Property rights
 Honest government
 Political stability
 Dependable legal system
62
The Future of Economic Growth
 Ideas per Hour
• New ideas do not experience diminishing
returns.
• Two reasons why this is so.
 Many ideas make creating new ideas easier.
 The field of ideas that can be explored is so large
that diminishing returns may not set in for a very
long time.
63
Takeaway
 As K accumulates, the MPK declines until
investment = depreciation, and growth
stops.
 The Solow model tells us three things:
• Countries that have higher investment rates
will be wealthier.
• Growth will be faster the further away a
country’s capital stock is from its steady state
value.
• Capital accumulation cannot explain long-run
economic growth.
64
Takeaway
 New ideas are the driving force behind
long-run economic growth.
• Ideas create spillover benefits.
• Spillover benefits means that the originator of
the new idea will not receive all of the
benefits.
• In order to achieve the optimal number of
ideas, government can support production of
new ideas…
 By protecting intellectual property.
 By subsidizing production of new ideas.
65
Takeaway
 There is a trade-off between providing
appropriate incentives to produce new
ideas and providing appropriate incentives
to share new ideas.
 The larger the size of the market, the
greater the incentive to invest in R&D.
66
Takeaway
 More people and wealthier countries
increase the number of people devoted to
the production of new ideas.
 The increased wealth of many developing
nations, the move to freer trade, and the
spread of better institutions all encourage
the future of economic growth.
67
End of Chapter 8
Second Edition
68
Appendix
Excellent Growth
69
Excellent Growth
 Using a spreadsheet, you can easily explore the
Solow model and duplicate all the graphs.
First, calculate the
increasing capital stock
using the formula in A3
and let the spreadsheet
do the rest.
Note: Clicking on the lower
right corner of a cell and
dragging it down will
duplicate the formula in the
70
lower cells.
12.70
Excellent Growth
Second, calculate output, Y,
using the formula:
Y K
Investment and depreciation
can be calculated using:
I  gY
depreciation  dK
You may use any values for g
and d you wish.
71
12.71
Excellent Growth
72
Excellent Growth
Third, graphs can be created using the data generated
73
In the steps one through three.
12.73
Excellent Growth
Lastly, you can experiment with different investment
shares in E2 or the depreciation rates in F2.
74
12.74
The Mathematics of Economic Growth
 Objective: To see how economic growth
varies along the transition path to a new
steady state equilibrium.
 We will do two things:
• Outline the mathematics.
• Use a spreadsheet to visualize our
results.
75
12.75
The Mathematics of Economic Growth
Recall
1
2
Investment  gY  γ K  γK ( e.g., 0.3  K )
Depreciation  dK( e.g., 0.02  K )
By
thus
1
2
ΔK  Investment - Depreci ation  gK  dK
The growth rate of the capital stock is given by
1
2
ΔK
gK
dK
g
 Growth rate of K 

 1 d
K
K
K
K2
Implicatio n :
g
If
 d  Growth rate of K is positive
1
K2
g
 d  Growth rate of K is negative
1
K2
plotting these two
expressions
separately on a
graph,
we can see how the
steady state changes
with the values of the
investment rate and
depreciation rate.
76
12.76
The Mathematics
d, g/K1/2
0.08
0.07
0.06
Difference is the growth rate of the
capital stock. The bigger the difference
the faster K grows.
0.05
0.04
0.03
d = 0.02
0.02
0.01
0.4/K1/2
400
Capital, K
77
77