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7/27/2019 Lecture Outline PPTs Macro Ch 7 (1)
http://slidepdf.com/reader/full/lecture-outline-ppts-macro-ch-7-1 1/74
Modern Principles:
Macroeconomics
Tyler Cowen
and Alex Tabarrok
Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabarrok
Chapter 7
Growth, Capital Accumulation,
and the Economics of Ideas:Catching Up vs. the Cutting
Edge
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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?
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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.
12.3
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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.
12.4
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The Solow Model and Catch-Up Growth
• Robert Solow – Nobel Prize in Economics
• 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”:
12.5
eL)K,F(A,Y
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The Solow Model and Catch-Up Growth
• For now, ignore changes in ideas, education, and
labor so that A, e, and L are constant. The
production function becomes:
• 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:
)F(KY
KY
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• The “Iron Logic” of Diminishing Returns
12.7
Capital, K
Output, Y
0 1 2 3 4 5 6 7 8 9 10 11 12
Conclusion: as more
capital is added,
MP K declines.
K Y
2.0
910
0.32.3
K MP
101
01
K MP
The Solow Model and Catch-Up Growth
1
33.2
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The Solow Model and Catch-Up Growth
• Growth in China and the United States
The “iron logic of diminishing returns” largely explains why…
• The Chinese economy is able to grow so
rapidly.
It turned toward markets which increasedincentives.
The capital stock was low
The MPK was high.• China will not be able to achieve these high
growth rates indefinitely.
12.8
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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 destroyedduring WWII. Therefore the MPK was high.
Following the war, both Germany and Japanwere able to achieve much higher growthrates than the U.S. as they “caught up”.
• Check out the following table.
12.9
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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.
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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 isinvested in new capital.
• The next figure shows how output is divided
between consumption and investment wheng = 0.3.
12.11
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The Solow Model and Catch-Up Growth
12.12
Capital, K
Output, Y
0 100 200 300 400
20
15
10
5
3
2
0
Investment = 0.3∙Y
Consumption = (1- 0.3) x 10 = 7
Investment = (0.3) x 10 = 3
When K = 100, Output = 10 K Y
• Capital Growth Equals Investment Minus Depreciation
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The Solow Model and Catch-Up Growth• Capital Growth Equals Investment Minus
Depreciation (cont.).
Depreciat ion: amount of capital that wears outeach period
Let d be the fraction of capital that wears out
each period. This is called the depreciation rateso that:
The next diagram shows that the amount of depreciation depends on the capital stock.
12.13
K δ
ondepreciati
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• Capital Depreciation Depends on the Amount of Capital
12.14
Capital, K
0 100 200 300 400
DepreciationDepreciation = 0.02∙K 8
6
4
2
0
100200
24
Slope
The Solow Model and Catch-Up Growth
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The Solow Model and Catch-Up Growth
• Capital Alone Cannot be the Key to Economic
Growth
Again, the “iron logic of diminishing returns”
explains this insight. Let’s see how this works.
As capital increases,
• depreciation increases at a constant rate = d .
• output increases at a dimin ish ing rate.
• Because investment is a constant fraction of
output, at some point depreciation will equalinvestment.
The capital stock will stop growing.
Output will stop growing. 12.15
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• Capital Increases or Decreases Until Investment = Depreciation
12.16Capital, K 0 100 200 225 300 400
GDP, Y 8
6
4.54
3
2
0
Depreciation = 0.02∙K
Investment = 0.3∙Y
At K = 100,
Inv. > Dep.
→ ↑ K
At K = 400, Inv. < Dep. → ↓ K
Result:
equilibrium
at K = 225
Y = 4.5inv. = dep. =4.5
The Solow Model and Catch-Up Growth
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• Capital Increases or Decreases Until Investment = Depreciation
12.17
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.
Check the Math
• At K = 100, Y =√100 = 10
• Depreciation = 0.02x100 = 2
• Investment = 0.3x10 = 3
•Investment > DepreciationResult: K and Y grow.
The Solow Model and Catch-Up Growth
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The Solow Model and Catch-Up Growth
• Capital Alone Cannot be the Key to Economic
Growth (cont.)
The logic of diminishing returns means that
eventually capital and output will cease
growing.
Therefore, other factors must be responsiblefor long-run economic growth.
Consider:
• Human capita l: knowledge, skills,experience
• Techno logical know ledge: better ideas
12.18
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12.19
The Solow Model and Catch-Up Growth
Th S l M d l d C h U G h
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The Solow Model and Catch-Up Growth
• Better Ideas Drive Long-Run Economic Growth
Human Capital• Like capital, it is subject to diminishing
returns and it depreciates.
• Logic of diminishing returns also applies tohuman capital.
• Conclusion: Human capital also cannot
drive long-run economic growth.
What about technological knowledge?
12.20
Th S l M d l d C t h U G th
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The Solow Model and Catch-Up Growth• Better Ideas Drive Long-Run Economic Growth
(cont.)
Technological knowledge
• A way of getting more output from the sameinput (an increase in productivity).
• We can include technological knowledge inour model by letting A stand for ideas thatincrease productivity. Therefore, let theproduction function be:
12.21
K AY
Th S l M d l d C t h U G th
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The Solow Model and Catch-Up Growth
Th S l M d l d C t h U G th
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The Solow Model and Catch-Up Growth
• An Increase in A Increases Output Holding
K Constant (cont.)
Conclusion:
• Technological knowledge or more generally
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.
12.23
CHECK YOURSELF
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CHECK YOURSELF
12.24
What happens to the marginal
product of capital as more capital isadded?
Why does capital depreciate? What
happens to the total amount of capitaldepreciation as the capital stock
increases?
Th S l M d l D t il d F th L
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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 conclusions
Steady state equilibrium occurs when
investment equals depreciation.
When K is in steady state equilibrium, Y is insteady state equilibrium.
These results are illustrated in the next two
diagrams. 12.25
Th S l M d l D t il d F th L
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The Solow Model – Details and Further Lessons
12.26
Capital, K
0 100 200 225 300 400
Output, Y 8
6
4.54
3
2
0
Depreciation = 0.02∙K
Investment = 0.3∙Y
When K is in steady state equilibrium, Y
is in steady state equilibrium.• When K is in steady state equilibrium, Y is in steady state equilibrium.
The Steady State K is found
where investment = Depreciation
Th S l M d l D t il d F th L
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• When K is in steady state equilibrium, Y is in steady state equilibrium.
12.270 100 200 300 400
Capital, K
Output,Y
Depreciation = 0.02∙K
5
10
15
Steady state capital stock
20
Steady state output
225
The Solow Model – Details and Further Lessons
K Y
K 0.3Investment
CHECK YOURSELF
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CHECK YOURSELF
12.28
What happens when the capital
stock is 400?What is investment?
What is depreciation?
What happens to output?
Th S l M d l D t il d F th L
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The Solow Model – Details and Further Lessons
• Solow Model and an 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.
12.29
Th S l M d l D t il d F th L
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• An Increase in the Investment Rate Increases Steady State Output
Capital, K
0 100 200 225 300
Output, Y
5
10
15
20
400
K Y
K 0.3Inv.
K 0.4 Inv.
The Solow Model – Details and Further Lessons
Depreciation = 0.02∙K
The Solo Model Details and F rther Lessons
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The Solow Model – Details and Further Lessons
• An Increase in the Investment RateIncreases Steady State Output (cont.)
The results presented in the previous diagrampredict that:
• An increase in investment rate, g , causesoutput to increase.
• Because labor is held constant, output per capi ta also increases.
An important test of our model:
• Are its predictions consistent with real worlddata?
• The next figure suggests that they are.
12.31
The Solow Model Details and Further Lessons
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The Solow Model – Details and Further Lessons
The Solow Model Details and Further Lessons
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The Solow Model – Details and Further Lessons
• An Increase in the Investment RateIncreases Steady State Output (cont.)
An Important Idea
• An increase in the investment rate = ↑ steadystate level of output.
• As the economy moves from the lower to thehigher steady state output = ↑ growth rate of output
• This higher growth rate is temporary.
Conclusion: ↑investment rate = ↑ steady statelevel of output but not i ts long-run g row th
rate .
These points are illustrated in following case
study of South Korea. 12.33
The Solow Model Details and Further Lessons
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The Solow Model – Details and Further Lessons
•The Case of South Korea
In 1950, South Korea was poorer thanNigeria.
1950s: the investment rate was < 10%.
1970s: Investment rate more thandoubled.
1990s: Investment rate increased to over
35%. South Korea’s GDP increased rapidly.
As GDP reached Western levels, the
growth rate has slowed. 12.34
The Solow Model Details and Further Lessons
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The Solow Model – Details and Further Lessons
•What Determines High Investment Rates?
Incentives which include
• Low real interest rates
• Low marginal tax rates
Institutions which include
• Honest government• Secure property rights
One of the reasons that the investmentrate increased in South Korea is that
capitalists believed that their investmentswould be protected.
• Effective financial intermediaries
12.35
The Solow Model Details and Further Lessons
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The Solow Model – Details and Further Lessons
•The Solow Model and Conditional
Convergence
Cond i t ional Convergence: Among countries
with similar steady state levels of output, poorer
countries grow faster than richer countries.
The Solow model predicts that a country willgrow faster the farther its capital stock is below
its steady state value.
• Conclusion: Conditional convergence is a
prediction of the Solow model.
The next figure presents evidence of
convergence.
The Solow Model Details and Further Lessons
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Slide 37 of 7312.37
The Solow Model – Details and Further Lessons
The Solow Model Details and Further Lessons
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The Solow Model – Details and Further Lessons
• 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 theevidence:
Steady state: Long-run growth = 0• What explains the observed long-run growth?
Answer: Better ideas
12.38
The Solow Model Details and Further Lessons
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• Solow and the Economics of Ideas inOne diagram Generation of ideas results in long-run economic
growth.
Let’s see how this works:
• We begin at steady state equilibrium.• 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.
12.39
The Solow Model – Details and Further Lessons
The Solow Model Details and Further Lessons
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Capital, K
Output, Y
Depreciation = 0.02∙ K
225
15
33.7
506
a
b
c
Better
Ideas
The Solow Model – Details and Further Lessons
• Solow and the Economics of Ideas in One diagram(cont.)
K Y )5.1(
K 0.3(1)Investment
Effect of ↑A from 1 to 1.5
Output ↑
K Y )1(
K 0.3(1.5)Investment
CHECK YOURSELF
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CHECK YOURSELF
12.41
What happens to investment and
depreciation at the steady state level of capital?
In Figure 7.9, how much is consumed in
the old steady state? How much isconsumed in the new steady state?
Do countries grow faster if they are far
below their steady state or if they are close?Do countries with higher investment rates
have a lower or higher GDP per capita?
Growing on the Cutting Edge: The Economics of Ideas
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Growing on the Cutting Edge: The Economics of Ideas
•The United States and other developed
regions such as Japan and Western Europe
are on the cutting edge of economic growth.
• In order to keep on growing these countries
must develop new ideas to increase the
productivity of capital and labor.
•Conclusion: The economics of ideas
becomes the key to growth on the cutting
edge.
12.42
Growing on the Cutting Edge: The Economics of Ideas
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Growing on the Cutting Edge: The Economics of Ideas
• The Economics of Ideas
1. Ideas for increasing output are primarilyresearched, developed, and
implemented by profit-seeking firms.
2. Spillovers mean that ideas are
underprovided.
3. Government has a role in improving the
production of ideas.
4. The larger the market, the greater the
incentive to research and develop new
ideas.12.43
Growing on the Cutting Edge: The Economics of Ideas
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Growing on the Cutting Edge: The Economics of Ideas
1. Research and Development Is Investmentfor Profit.
keys to increasing technological knowledge:• Incentives
• Institutions that encourage investment inphysical and human capital and R&D.
70% of scientists and engineers in the U.S. workfor private firms.
Profits provide incentive to invest in R&D
• Implication: Property rights, honestgovernment, political stability, a dependablelegal system, and competitive open marketshelp drive the generation of technologicalknowledge.
Growing on the Cutting Edge: The Economics of Ideas
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1. Research and Development Is Investment
for Profit (cont.). Not just the number of scientists and engineers
that are important
• All kinds of people come up with new ideas.
• Business culture and institutions are alsoimportant.
Institutions that are especially important:
• Commercial settings that help innovators to
connect with capitalists
• Intellectual property rights
• A high-quality education system
12.45
Growing on the Cutting Edge: The Economics of Ideas
Growing on the Cutting Edge: The Economics of Ideas
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Growing on the Cutting Edge: The Economics of Ideas
1.Research and Development is Investmentfor Profit (cont.).
A commercial setting that helps innovatorsconnect with capitalists.
• Ideas without financial backers are sterile.
• The U.S. is good at connecting innovatorswith 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.
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Growing on the Cutting Edge: The Economics of Ideas
12.47
John Kay (1704-1780) invented the
“flying shuttle” used in cottonweaving, the single most important
invention launching the industrial
revolution. Kay, however, was notrewarded for his efforts. His housewas destroyed by “machine breakers,” who
were afraid that his invention would put them
out of a job. Kay was forced to flee to Francewhere he died a poor man.
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Growing on the Cutting Edge: The Economics of Ideas
• Institutions that are especially important
Intellectual property rights
• New processes, products, and methods can becopied by competitors.
World’s first MP3 player was the Eiger LabsMPMan introduced in 1998.
Copied by other firms and Eiger Labs lost outin the competition.
Patents
• Grant temporary monopoly.
• Can slow down spread of technology.• Trade-off between creating incentives to
research and develop new products and
avoiding too much monopoly power = one of
trickiest in economic policy 12.48
Growing on the Cutting Edge: The Economics of Ideas
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Growing on the Cutting Edge: The Economics of Ideas
• Institutions that are especially important(cont.)
A high-quality education system• Important at all levels of education.
• Creates necessary talent.
• Universities generate basic andapplied research.
12.49
Growing on the Cutting Edge: The Economics of Ideas
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Growing on the Cutting Edge: The Economics of Ideas
2.Spillovers, and Why There Aren’t Enough
Good Ideas
Ideas are non-r ivalrous.
Ideas can be used simultaneously.
• Use of an idea by one individual does not mean
less of the idea available to someone else. The spillover or diffusion of new ideas generates
widespread economic growth.
Implication: Spillovers mean that the generator of
the idea doesn’t get all of the benefits.
• Result: Too few ideas are produced.
• Let’s see why.
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Growing on the Cutting Edge: The Economics of Ideas
2. Spillovers, and Why There Aren’t Enough
Good Ideas (cont.) Optimal social investment in R&D occurs where:
MSB = MSC
Optimal private investment occurs where:
MPB = MPC
With spillover benefits: MSB = MPB + spillovers
and MSC = MSB
Conclusion:
Implication: Spillovers result in too littleinvestment in research and development.
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Optimal SocialInvestment in R&D
Optimal PrivateInvestment in R&D <
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• Spillovers Mean Too Little Investment in Research and Development
Quantity of R&D
$
MSB
MPB
MPC = MSC
IP IS
Spillover benefits
IP = optimal private investment in R&D
IS =optimal social investment in R&D
Assumes there
are no spillover costs
MPB = MPC MSB = MSC
g g g
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g g g
3. Government’s Role in the Production of New
Ideas
Ideas in mathematics, physics, and molecular biology have many applications so spi l lovers
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
expenditures.
Both shift the MC of R&D curve down → ↑
R&D investment.
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g g g
3. Government’s Role in the Production of New
Ideas (cont.)
Large spillovers to basic science suggest a rolefor government subsidies to universities.
• Especially those parts of the universities that
produce innovations and the basic sciencebehind those innovations.
• Universities produce scientists
Most of the 1.3 million scientists were
trained in government subsidized
universities.
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g g g
4. Market Size and Research andDevelopment
Innovations like pharmaceuticals, newcomputer chips, software, and chemicalsrequire large R&D expenditures.
Companies will avoid investing in innovationswith small potential markets.
Larger markets mean increased rewards (thusincentives) for R&D.
As the world market grows companies willincrease their R&D investments.
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CHECK YOURSELF
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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?
Some economists have proposed that the
government offer large cash prizes for thediscovery 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?
The Future of Economic Growth
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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%
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The Future of Economic Growth• Economic growth can be even faster. How?
The following framework helps us think about
this.
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 12.58
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The Future of Economic Growth• Economic growth can be even faster. How?
(cont.)
• A (ideas) = Population x Incentives x Ideas/Hour
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 12.59
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e utu e o co o c G o t• Economic growth can be even faster. How?
(cont.)
• A (ideas) = Population x Incentives x Ideas/Hour
Ideas per Hour
• New ideas do not experience diminishing
returns.
• Two reasons why this is so.
1. Many ideas make creating new ideas
easier.2. The field of ideas that can be explored is
so large that diminishing returns may not
set in for a very long time.
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• Recap: Economic growth might be evenfaster in the future than it has been in the
past. There are more scientists and engineers in the
world than ever before, and their numbers arealso increasing as a percentage of the
population. Incentives are increasing due to growing
markets resulting from
• Increasing trade
• Increasing wealth in developing countries
Better institutions and more secure propertyrights are spreading throughout the world.
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Takeaway
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• As K accumulates, the MPK declines until
investment = depreciation, and growth stops.
• The Solow model tells us three things abouteconomic growth:
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-runeconomic growth.
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y
Takeaway
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• New ideas are the driving force behind
long-run economic growth.
Ideas are non-rivalrous which means there
are spillover benefits.
Spillover benefits means that the originator of
the new idea will not receive all of thebenefits.
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.
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Takeaway
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• There is a trade-off between providingappropriate incentives to produce new ideas
and providing appropriate incentives to sharenew ideas.
• The larger the size of the market, the greater the incentive to invest in R&D.
• More people and wealthier countries increasethe number of people devoted to theproduction of new ideas.
• The increased wealth of many developing
nations, the move to freer trade, and thespread of better institutions all encourage thefuture of economic growth.
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Modern Principles:
MacroeconomicsTyler Cowen
and Alex Tabarrok
Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabbarrok
Chapter 7 Appendix:
Excellent Growth
Appendix
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pp• Excellent Growth
Using a spreadsheet, you can easily explore
the Solow model and duplicate all the graphs.
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First, calculate theincreasing 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 lower cells.
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pp• Excellent Growth (cont.)
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Second, calculate output,Y, using the formula:
KY
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pp• Excellent Growth (cont.)
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Third, graphs can be created using the data generated
In the steps one through three.
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pp• Excellent Growth (cont.)
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Lastly, you can experiment with different investment
shares in E2 or the depreciation rates in F2.
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pp
• The Mathematics of Economic Growth
along the Transition Path
• 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.
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pp• The Mathematics
12.71
negativeisK of rateGrowth
positiveisK of rateGrowthIf
:nImplicatio
K of rateGrowth
bygivenisstock capitaltheof rategrowthThe
thus
)K 0.02e.g.,(
)K 0.3e.g.,
Recall
2
1
2
1
2
1
2
1
2
1
2
1
d g
d g
d g d g
d g
d
g
K
K
K K
K
K
K
K
ΔK
K K ation- Depreci Inv estment ΔK
K on Depreciati
( γK K γY Inv estment
By plotting these two
expressions
separately on a graph,we can see how the
steady state changes
with the values of the
investment rate anddepreciation rate.
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pp• The Mathematics
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d, g/K1/2
Capital, K
d = 0.020.4/K1/2
400
0.07
0.06
0.050.04
0.03
0.01
0.02
0.08 Difference is the growth rate of the
capital stock. The bigger the difference
the faster K grows.
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pp• The Spreadsheet
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Plotting Y against time shows the transition to steady
state
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• The Spreadsheet
Output, Y
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
0 100 200 300 400 500 600
Time
Output, Y
Result: The transition to steady state proceeds at a
decreasing rate. As K approaches 400 growth slows down.