Lecture Outline PPTs Macro Ch 7 (1)

7/27/2019 Lecture Outline PPTs Macro Ch 7 (1)

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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



Slide 2 of 73

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?



Slide 3 of 73

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



Slide 4 of 73

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



Slide 5 of 73

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



Slide 6 of 73


• 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


http://slidepdf.com/reader/full/lecture-outline-ppts-macro-ch-7-1 7/74Slide 7 of 73

• 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


1

33.2




• 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



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




Conclusions:1. Catch-up growth (Germany, Japan) is much greater

than cutting-edge growth (U.S.)

2. Eventually the catch-up growth slows down.




• 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




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



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



• 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





• 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



• 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


At K = 100,

Inv. > Dep.

→ ↑ K

At K = 400, Inv. < Dep. → ↓ K

Result:

equilibrium

at K = 225

Y = 4.5inv. = dep. =4.5




• 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.





• 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



12.19


Th S l M d l d C h U G h




• 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



Slide 21 of 73

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




Slide 22 of 7312.22





Slide 23 of 73


• 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



Slide 24 of 73

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



Slide 25 of 73

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




Slide 26 of 73


12.26

Capital, K

0 100 200 225 300 400

Output, Y 8

6

4.54

3

2

0



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




Slide 27 of 73

• When K is in steady state equilibrium, Y is in steady state equilibrium.

12.270 100 200 300 400

Capital, K

Output,Y


5

10

15

Steady state capital stock

20

Steady state output

225


K Y

K 0.3Investment

CHECK YOURSELF



Slide 28 of 73

CHECK YOURSELF

12.28

What happens when the capital

stock is 400?What is investment?

What is depreciation?

What happens to output?




Slide 29 of 73


• 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




Slide 30 of 73

• 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 Solo Model Details and F rther Lessons



Slide 31 of 73


• 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



Slide 32 of 73





Slide 33 of 73


• 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




Slide 34 of 73


•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




Slide 35 of 73


•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




Slide 36 of 73


•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.




Slide 37 of 7312.37





Slide 38 of 73


• 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




Slide 39 of 73

• 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





Slide 40 of 73

Capital, K

Output, Y

Depreciation = 0.02∙ K

225

15

33.7

506

a

b

c

Better

Ideas


• 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



Slide 41 of 73

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



Slide 42 of 73


•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




Slide 43 of 73


• 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




Slide 44 of 73


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.




Slide 45 of 73

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





Slide 46 of 73


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.




Slide 47 of 73


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.




Slide 48 of 73


• 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




Slide 49 of 73


• 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




Slide 50 of 73


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.




Slide 51 of 73


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.

12.51

Optimal SocialInvestment in R&D

Optimal PrivateInvestment in R&D <




Slide 52 of 73

• 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




Slide 53 of 73

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.

12.53




Slide 54 of 73

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.

12.54




Slide 55 of 73

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.

12.55

CHECK YOURSELF



Slide 56 of 7312.56

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



Slide 57 of 73

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%

12.57




Slide 58 of 73

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




Slide 59 of 73

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




Slide 60 of 73

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.

12.60




Slide 61 of 73

• 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.

12.61

Takeaway



Slide 62 of 73

• 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.

12.62

y

Takeaway



Slide 63 of 73

• 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.

12.63

y

Takeaway



Slide 64 of 73

• 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.

12.64

y



Modern Principles:

MacroeconomicsTyler Cowen

and Alex Tabarrok

Copyright © 2010 Worth Publishers • Modern Principles: Macroeconomics • Cowen/Tabbarrok

Chapter 7 Appendix:

Excellent Growth

Appendix



Slide 66 of 73

pp• Excellent Growth

Using a spreadsheet, you can easily explore

the Solow model and duplicate all the graphs.

12.66

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.

Appendix



Slide 67 of 73

pp• Excellent Growth (cont.)

12.67

Second, calculate output,Y, using the formula:

KY

Appendix



Slide 68 of 73


12.68

Third, graphs can be created using the data generated

In the steps one through three.

Appendix



Slide 69 of 73


12.69

Lastly, you can experiment with different investment

shares in E2 or the depreciation rates in F2.

Appendix



Slide 70 of 73

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.

12.70

Appendix



Slide 71 of 73

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.

Appendix



Slide 72 of 73

pp• The Mathematics

12.72

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.

Appendix



Slide 73 of 73

pp• The Spreadsheet

12.73

Plotting Y against time shows the transition to steady

state

Appendix



• 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.

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Lecture Outline PPTs Macro Ch 7 (1)