Lecture 6 1

Macroeconomic Analysis 2003

Endogenous Growth: Romer Model

Reference: Jones(2002:chapter 4& 5)

Lecture 6 2

a

b

c

AS0

AS1

AD0

AD1A better technology reduces production cost and AS shifts out

Technology creates more jobs and income and raises demand

Price

OutputY0 Y1

P0

P1

Technology and Growth in AS-AD

Lecture 6 3

Y

K

Y=AK End. Growth

Comparison of Production Technology in Endogenous and Solow Growth Models

kkay

y

kysag '

LAKY

Solow

In AK Model

1

1

Lecture 6 4

MPK

K

Marginal Product of Capital

AK Model

Solow Model

How is AK Technology possible?

There is an increasing return scale

to the knowledge. Many firms or

people can use the same designs

and formula at the same time or

duplicate them many times in the

production process.

1

LAKK

Y 1

AK

Y

1

Lecture 6 5

Does an Advancement in the Technology Increase the Real Wage Rate of Every one Equally?

• With mobility of labour across regions and sectors introduction of new technology should increase wages of all types of workers

– But

• Wage rates in the high tech and manufacturing sectors have grown at higher rate than in the service sectors.

• New technology replaces old technology and people with obsolete technology may become redundant and may spend a long time before finding a new job.

Lecture 6 6

Year

197919801981198219831984198519861987198819891990

                 

Earliest Patent No  (application) publishedGB 2,000,001GB 2,023,381GB 2,050,131GB 2,078,071GB 2,100,561GB 2,121,661GB 2,141,611GB 2,160,751GB 2,176,681GB 2.192,121GB 2,206,271GB 2,220,118                                 

Year

19911992199319941995199619971998199920002001

              

Earliest Patent No 

(application) published

GB 2,232,862GB 2,245,131GB 2,257,003GB 2,268,036GB 2,279,218GB 2,290,445GB 2,302,005GB 2,314,495GB 2,326,809GB 2,338,877GB 2,351,428

Growth of Idea: Number of Patent Rights in the UK

http://www.patent.gov.uk/patent/history/oldnumbers/after1979.htm

Lecture 6 7

Output: YALKY

A = Stock of knowledge

Labour use: Ay LLL Change in the stock of knowledge:

AA LALA

Growth rate of knowledge: A

LA

A

Ag AA

Capital Accumulation:

tItKtK 11

Market clearing: ttt ICY

Endogenous Growth Model

Lecture 6 8

nA gg

A

A

A

LsR '

A

LAAR g

A

Ls

A

LA

A

Ag AA

10

Assuming

Technological progress and Increase in R&D Share

Ay LLL ALAA

ss

nA gg

Lecture 6 9

Time

A

A

nA gg

t = 0

Technological Growth Rate Over Time

Lecture 6 10

Timet = 0

A

Level of Technology (Stock of Knowledge) Over Time

Level Effect

Lecture 6 11

Growth Rate of Knowledge and Population

A

LA

A

Ag AA

By log differentiation:

01 A

A

L

L

A

A

01 An gg

Knowledge grows at:

1

nA

gg

Higher the growth rate of population More people can work in the research sector Stock of knowledge increases and Output rises.

Lecture 6 12

Aky ggg

AL

Yy ; L

gAg

Yg

yg

Lg

Ag

Yg 0

Growth rate of per capita output:

Ag

Lg

Yg

Similarly from AL

Kk

Growth rate of per capita capital stock:

Ag

Lg

Kg

Link Between the Growth Rate of Per Capita Output and Capital Stock and the Knowledge

Lecture 6 13

Scientific Products of Research and Innovation(Economist, December 31, 1999)

• Algebra - Arabs, India (0) • Printing Press -Gutenberg

1440• Calculus - Newton (1684) • Steam Engine - James Watt

(1765)• Electricity - Edison (1879)• Computer- Babbage (1984)• Radium • Radio• TV

• Photography and Cinematography - Daguerre (1839)

• Telephone Bells (1876)• Wireless (1896)• Electro Magnetic

Telegraph (1833)• Powered flight (1903)• X-ray• Jet Engine• PC• Internet

Lecture 6 14http://www.bbc.co.uk/science/ http://www.bbc.co.uk/radio4/science/

Lecture 6 15

Endogenous Growth Model:Role of Human Capital

• Ideas come from skilled trained people• These ideas are translated into tools • Ideas are non-rivalrous; Many people can use it at the same

time can be found in books, journals, manuals and papers and reports

• Better tools allow production of more and high quality goods– Examples– Cars, computers, trains, planes, medicine, TV, Phone

Internet, Rockets; high yielding varieties of crops, cloning (?)

Lecture 6 16

How Human Capital Contributes to the Economic Growth?

Thinking New Ideas FormulaDesignSoftware

Action Better Tools MachinesConsultancy

Application More andHigh QualityProducts

CarsComputersPlanesMedicineTrains etc.

Lecture 6 17

Vast areas of Economically Meaningful of Researchhttp://www.hull.ac.uk/home/research_and_innovation/index.html

Core Scientific research

Sound, heat, radio, light, sound waves, radioactivity; forces, motion, power

Energy, Electricity,

Chemical formulas: elements, bonds compounds

Genetics, medicine

Electormagnetism,

Outer space

Deep Sea, Ocean and environment

Mathematical and statistical theories

Economic research (ESRC)

Information about prices, income

Estimation of elasticities of demand, supply behaviour of firms, labour supply behaviour of households,

Substitution elasticities

Revenue and spending decision of central and local government, trade and investment, inflow-outflow of capital

Impacts of policies living standards

Improved management practices

Applied science (STRC)

Use of scientific knowledge in building tools and in production process; laser, radar, automation, cenematograpy

Diagnosis and Treatment of diseases

Engineering of sophisticated machines, Buildings

Social research

Social engineering, Causes of Crimes

Personal and communal disorders

Rights and responsibilities of each individuals in a society,

Wars and conflict resolution

Lecture 6 18

Economically Important Innovations: Product of Genius, Active and Risk-loving People (Forbes Dec 2002)

year Innovation year Innovation year Innovation1917 Sneakers (Bowerman) 1940 Radar (Watson-Watt)1918 Spectometer, Uranium 235 1942 Electronic digital computer 1964 Mainframe (IBM)1921 Tetrathyle lead (Midgley) 1945 Nuclear power Mouse 1923 Business Management (Sloan) 1948 LP (Goldmark) 1971 Microprocessor (Noyce)1923 Multiple camera (Disney) 1949 Magnetic core memory (Wang) Answering machine (Poulsen)1924 Mutual funds 1947 Cellular phone (Ring) 1972 3-D images of body (MRI)1924 Frozen food (Birdseye) Microwave (Spencer) Ethernet -LAN (Metcalf)1925 Transistor, digital signal processor (Bell) Instant Photos (Land) Unix/C programming (Ritchie &Thompsen)1926 Rocket science (Goddard) Transistors (Shockley) E-entertainment (Bushnell)1927 TV (Farnsworth) Tupperware (Tupper) 1976 DNA (Swansen)1928 Penicillin (Fleming) 1951 Pill (Mccormick and Singer) Personal computer chips (Job and Wozniak)1929 Synthetic rubber (Newland) 1952 FORTRAN (Backus) 1979 Spreadsheets (Bricklin and Frankston)1930 Jet engine (Whittle) 1955 Fast food Krock) 1984 Dell PC (Dell)1933 Radio frequency modulation (Armstrong) 1956 Containerised Shipping 1991 WWW (Bernerslee)1937 Pulse code modulation Disk drives (Johnson) 1995 Internet business (Bezos)

Blood bank Fiber optics (Kapung) 1998 Viagra (Ellis and Terrett)1938 Xerography (Carlson) 1958 Laser (Patel) 2000 Automated sequencing machine (Venter)1939 Automatic transmission (Thompson) 1959 Integrated circuit 2001 ?

Helicopter (Sikorsky) 1961 diapers (Pampers) ?1962 Modem (AT&T) 2002 ?

2003 Cloning?

Lecture 6 19

Research Intermediate and Final Goods Sectors

Final goods

Intermediate sector

Research

A

jjy xLY

1

1

jjjj rxxp X

X set of new and

Innovative ideas

models

ConsultancyApply knowledgein production

Research SectorUniversities: scientific and technical knowledgeResearch centres such as ESRC,STRC, Bell Lab, microsoftSoftware companies

Appliers:BT/BAEFinancial institutions (LSE)Government organisationsFactories: Rolls Royce

New knowledgederive from existing stock of knowledge

Lecture 6 20

Three Sectors in the Romer’s Endogenous Growth Model

• Research Sector: Universities/ research labs produce ideas

• Intermediate sector: Takes those ideas to make tools and machines

• Final Goods sector used those ideas to produce consumer goods.

Lecture 6 21

Research to Improve the Economy:

The Big Market

Households Consumers

Firms – Investors Producers

Banks – Central Bank

Commercial Banks Stock Market

Financial Institutions

Treasury – Allocation of Public Funds

Revenue – Tax Collector

Trade Unions Employer

Unions

Merchants and Traders

– Wholesalers – Retailers

Rest of the World (ROW) –

Trading Partners Multilateral Organisation

Schools, Universities Research Labs

Who Contributes More to Research in the Bigger Economy?

Lecture 6 22

Final goods sectorProduction

A

jjy xLY

1

1

where j=1….A index of ideas

Ayyy xLxLxLY 12

11

1 ...

Input Prices = marginal product

L

Yw 1

and

11jyj xLp

Lecture 6 23

Intermediate good sector:

Profit: jjjj rxxp

MR = MC principle implies that

rxpxxp jjj ' or

rr

p

xxpp

1

)('1

1

Research sector

ALdA

average productivity in the research sector

ALA

Intermediate and Research Sectors

X = ideasr = price of ideas

A = stock of knowledgeLA= number of peopleworking in the knowledgesector

Lecture 6 24

Growth Rate of knowledge

1A

L

A

dAg AA

In Steady State stock of knowledge grows by the growth rate of researchers:

1

ng A

Total labour resource can either be used in the knowledge sector or in the production of final goods sector:

Ay LLL

Growth Rate of Knowledge

Lecture 6 25

1. Constant return to K and L but increasing return to scale relative to all inputs

2. Imperfect competition in the intermediate goods sector

3. Inventors can extract profits by selling patent rights to producers of intermediate goods

4. Increase in stock of knowledge relates to number of people working in the research

5. Research drives up productivity in the whole economy by the arbitrage condition

L

Ywpw yAr 1 but L

Yr

2

Main Features of the Romer Model

Lecture 6 26

MC

CS

DWL

Pm

MC

R m R opt

Why Market Under Provides Research?

o

Outcome of research is uncertain at the outset.

Patents provide Monopoly rights for research firms.Profit of a

Research firm

Intellectual Property right:PatentsDesignsTrademarkCopyright

http://www.intellectual-property.gov.uk/

Lecture 6 27

Output: FLY 100 F = fixed labour

Cost: wLC

Cost function:

FY

wC100

Constant marginal cost pricing: Pw

Y

C

100

Declining average cost:

Y

Fw

Y

C

100

Negative profit: 0100100

FY

wYw

CR

Thus marginal cost pricing is not profitable for a research firm. Government need to subsidise to produce optimal amount of research.

Economic reason for granting a patent right or subsidy to a research firm

Lecture 6 28

Growth is prevented by lack of optimal research for the following reasons

1. Market values research according to the stream of profit that are earned from the new design but market does not see how the current research raises productivity in the future.

2. There is a missing market for research. Also there is positive externality

or “spill over” of current research and “standing on the shoulder” effect. 3. There is a danger of “stepping on toes” –there may be too many

researcher either duplicating the same research work, which may provide negative externality.

4. There is “too little” research because of monopoly power due to patent

rights though profit incentives are vital for innovation of new ideas.

Lecture 6 29

Exercises• Unbounded growth with AK Technology• Link between research, intermediate and final goods

sectors in Romer’s Endogenous Growth Model• Production function in the final goods sector• Production function in the Research sector• Why is not larger size of population necessarily an

obstacle for economic growth?• Intermediate markets for research products: how do

research firms determine price of research products?