romer model final

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Lecture 6 1

Endogenous GrowthModel: Romer Model



Lecture 6 3

Three Sectors in the Romer¶s Endogenous

Growth Model

Research Sector: Un vers t es/ research

labs produce deas

Intermediate sector: Takes those deas to

make tools and mach nes

Final Goods sector used those deas to

produce consumer goods.



Lecture 6 4

Research to Improve

the Economy:

The Big Market

Households

C u er

Firms ±

I e t r

Pr ucer

Banks ±

c I t tut

Ce tr B

C erc B

St c r et

Treasury ±

A c t

Pu c u

Revenue ± C ect r

Trade Unions er

Merchants and

Traders

± Wholesalers

± etailers

Rest of the World

(ROW) ±

Trading Partners

Multilateral

Organisation

S hools,Universities

Research Labs

ho Contributes More to Research in the Bigger Economy?



Lecture 6 5

a

b

c

0

1

D0

D1better technology

reduces product on costand sh fts out

Technology creates

more jobs and ncomeand ra ses demand

r ce

OutputY0 Y1

0

1

Technology and Growth n - D



Lecture 6 6

Does an Advancement in the Technology Increase the

Real Wage Rate of Every one Equally?

W th mob l ty of labour across reg ons and sectors

ntroduct on of new technology should ncrease

wages of all types of workersBut

Wage rates n the h gh tech and manufactur ng

sectors have grown at h gher rate than n the

serv ce sectors.

New technology replaces old technology and people w th obsolete technology may become

redundant and may spend a long t me before

f nd ng a new job.



Lecture 6 7

ut ut: FE

Y AL K Y !

A = St of knowl

L our use: A y L L L

Change in the stock of knowledge: PJ P

H H A A L A L A !!

Gr owth r ate of knowledge: A

L A

A

A g A

A

PJ H

Capital Accumulation:

t I t K t K ! H 11

Mar ket clear ing: t t t I C Y !

Endogenous Growth Model



Lecture 6 8

n A g g !

A

A

A

L s R '

A

L A

H

A R g

A

L s

A

L A

A

A g A

A

PJ H

1!P

0!J

ssuming

Technological progress and Increase in R&D Share

A y L L L !PJ

H A L A A !

ss

n A g g !



Lecture 6 9

Time

A

A

n A g g !

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 opulation

A

L A

A

A g A

A

PJ H !!

By log differentiation:

01 ! A

A

L

L

A

A

J P

P

P

0! An g g J P

Knowledge grows at: J

H

! n A

Higher the growth rate of population

More people can work in the research sector

Stock of knowledge increases and Output rises.



Lecture 6 12

Ak y g g g !!

AL

Y y ! ; L

g A

g Y

g y

g

L

g

A

g

Y

g !0

Gr owth r ate of per capita output:

A g

L g

Y g !

Simi ar fr om AL K k !

Gr owth r ate of per capita capital stock:

A g

L g

K g !

Link Between the Growth Rate of Per apita Output

and apital Stock and the Knowledge



Lecture 6 13

Scientif ic Products of Research and Innovation

(Economist, December 31, 1999)

lgebra - rabs, India (0)

Pr inting Press -Gutenberg1440

alculus - Newton (1684)

Steam Engine - James Watt(1765)

Electr icity - Edison (1879)

omputer- Babbage (1984)

Radium Radio

TV

Photography andinematography -

Daguerre (1839)

Telephone Bells (1876)

Wireless (1896) Electro Magnetic

Telegraph (1833)

Powered flight (1903)

X-ray

Jet Engine P

Internet



Lecture 6 14

Endogenous Growth Model:Role of Human apital

Ideas come from sk illed trained people

These ideas are translated into tools

Ideas are non-r ivalrous; 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

ars, computers, trains, planes, medicine, TV,Phone Internet, Rockets; high yielding var ieties

of crops, cloning (?)



Lecture 6 15

How Human apital ontr i butes to the

Economic Growth?

Think ing New Ideas Formula Design

Software

ction Better Tools Machines

onsultancy

pplication More and

High QualityProducts

ars

omputersPlanes

Medicine

Trains etc.



Lecture 6 16

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

ore Scientif ic research

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

Energy, Electr icity,

hemical formulas: elements, bonds

compounds

Genetics, medicine

Electromagnetism,

Outer space

Deep Sea, Ocean and environment

Mathematical and statistical theor ies

Economic research (ESR )

Information about pr ices, incomeEstimation of elasticities of demand,

supply behaviour of f irms, 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

pplied science (STR )

Use of scientif ic knowledge in building

tools and in production process; laser,

radar, automation, cenematograpy

Diagnosis and Treatment of diseases

Engineer ing of sophisticated machines,

Buildings

Social research

Social engineer ing, auses of r imes

Personal and communal disorders

R ights and responsi bilities of each

individuals in a society,

Wars and conflict resolution



Lecture 6 17

Economically Important Innovations: Product of Genius,

ctive and R isk-loving People (Forbes Dec 2002)year Innovation year Innovation year Innovati

1917 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 (Ritchi

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 (Jo

1929 Synthetic rubber (Newland) 1952 FORTRAN (Backus) 1979 Spreadsheets (Bricklin and F

1930 Jet engine (Whittle) 1955 Fast food Krock) 1984 Dell PC (Dell)

1933 Radio frequency modulation (Armstron 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 mac1939 Automatic transmission (Thompson) 1959 Integrated circuit 2001 ?

Helicopter (Sikorsky) 1961 diapers (Pampers) ?

1962 Modem (AT&T) 2002 ?

2003 Cloning?



Lecture 6 18

Research Intermediate and Final Goods Sectors

Final goods

Intermediate sector

Research

§

A

j

j y x LY 1

1 E

j j j jrx x p4 X

onsultancy

pply knowledge

in production

Research Sector Universities: scientif ic

and technical knowledge

Research centres such as ESR ,

STR , Bell Lab, microsoft

Software companies

ppliers:BT/BAE

Financial institutions (LSE)

Government organisations

Factor ies: Rolls Royce

New knowledgeder ive from existing

stock of knowledge



Lecture 6 19

Final goods sector Production

§ A

j

j y x LY 1

1 E

whe e j=1«.A index o ideas

A y y y x L x L x LY EEE

1

2

1

1

1...

nput Prices = mar ginal pr oduct

L

Y w E! 1

and

EEE 11

j y j x L p



Lecture 6 20

ntermediate good sector:

ro it: j j j j r !

4

MR = MC princi ple implies that

r x p x x p j j j

!'or

r r

p

x x p p

E

1)('

1

1 !

!

y Resear ch sector

P

H A LdA !

H aver age pr oductivity in the r esear ch sector

PJ H H A

L A!

Intermediate and Research Sectors

X = ideas

r = pr ice of ideas

A = stock of knowledge

LA= number of people

work ing in the knowledgesector



Lecture 6 21

Gr owth ate of knowledge

J

PH

!!1 A

L

A

dA A A

In Steady State stock of knowledge gr ows y the gr owth r ate of r esear chers:

J !1

n g

otal labour r esour ce can either be used in the knowledge sector or in the

pr oduction of f inal goods sector:

y L L L !

Growth Rate of Knowledge



Lecture 6 22

M

S

DWL

Pm

M

R m R opt

Why Market Under Provides Research?

o

Outcome of research

is uncertain at the outset.

Patents provideMonopoly r ights

for research f irms.Prof it of a

Research f irm

Intellectual Property r ight:Patents

Designs

Trademark

opyr ight

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



Lecture 6 23

ut put: F LY !100

F = f i ed labour

Cost: wLC !

Cost function: ¹ º

¸©ª

¨! F

Y wC

100

Constant margi al cost pr ici g: P w

Y

C !!xx

100

Decli i g average cost: ¹ º

¸©ª

¨!Y

F w

Y

C

100

Negative prof it: 0100100

¹ º ¸©

ª¨ !! F Y

wY w

C RT

Thus margi al cost pr ici g is not prof itable for a research

f irm. Government need to subsidise to produce optimal

amount of research.

Economic reason for granti g a patent r ight or subsidy

to a research f irm



Lecture 6 24

Growth is prevented by lack of optimal research for

the following reasons

y Market values research according to the stream of prof it that are earned

from the new design but market does not see how the current research

raises productivity in the future.

y There is a missing market for research. Also there is positive externalityor ³spill over´ of current research and ³standing on the shoulder´ effect.

y There is a danger of ³stepping on toes´ there may be too many

researcher either dupli ating the same research work, whi h may provide

negative externality.

y There is ³too little´ research because of monopoly power due to patent

r ights though prof it incentives are vital for innovation of new ideas.

romer model final

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