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Macroeconomic Analysis 2003
Endogenous Growth: Romer Model
Reference: Jones(2002:chapter 4& 5)
Lecture 6
1
Technology and Growth in AS-AD
AS0
Technology creates
more jobs and income
and raises demand
Price
AS1
P0
a
c
P1
b
A better technology
reduces production cost
and AS shifts out
AD1
AD0
Y0
Lecture 6
Y1
Output
2
Comparison of Production Technology in
Endogenous and Solow Growth Models
 1
Y=AK End. Growth
Y
Solow


Y  AK L
   1
In AK Model
s
'
y
g a
k
y  a  k
y
k
K
Lecture 6
3
Marginal Product of Capital
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.
Y
K
MPK
A
AK Model
 1
Y

 AK  1L
K
    1 Solow Model
K
Lecture 6
4
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
5
Growth of Idea: Number of Patent Rights in the UK
Year
Earliest Patent
Year
Earliest
No (application)
Patent
published
No (applicati
1979
GB 2,000,001
on) published
1980
GB 2,023,381
1991
GB 2,232,862
1981
GB 2,050,131
1992
GB 2,245,131
1982
GB 2,078,071
1993
GB 2,257,003
1983
GB 2,100,561
1994
GB 2,268,036
1984
GB 2,121,661
1995
GB 2,279,218
1985
GB 2,141,611
1996
GB 2,290,445
1986
GB 2,160,751
1997
GB 2,302,005
1987
GB 2,176,681
1998
GB 2,314,495
1988
GB 2.192,121
1999
GB 2,326,809
1989
GB 2,206,271
2000
GB 2,338,877
1990
GB 2,220,118
2001
GB 2,351,428
http://www.patent.gov.uk/patent/history/oldnumbers/after1979.htm
Lecture 6
6
Endogenous Growth Model
Output:
Y K

 ALY 

A = Stock of knowledge
L  Ly
Labour use:
Change in the stock of knowledge:
 LA
A   LA  A LA
A A LA
Growth rate of knowledge: g A  
A
A
Capital Accumulation:
K t  K t 1 1     I
Market clearing:
t
Yt  Ct  I t
Lecture 6
7
Technological progress and Increase in R&D Share
A
A
g A  gn
Assuming
 1
 0


g A  gn
L  Ly  LA
 

A  A LA
ss
sR L
gA

A

Lecture 6
A A LA
gA  
A
A
sR ' L
A
LA
A
8
Technological Growth Rate Over Time
A
A
g A  gn
t=0
Lecture 6
Time
9
Level of Technology (Stock of Knowledge) Over Time
A
Level Effect
t=0
Lecture 6
Time
10
Growth Rate of Knowledge and Population
A A L
A
gA  
A
A
By log differentiation: 
LA
A
   1     0
A
LA
g n  1   g A  0
g n
gA 
Knowledge grows at:
1
Higher the growth rate of population
More people can work inLecture
the 6research sector
Stock of knowledge increases and Output rises.
11
Link Between the Growth Rate of Per Capita Output
and Capital Stock and the Knowledge
g y  gk  g A
Y
y
AL
;  g y  gY  g A  g L 
0g
Y
g
A
g
L
Growth rate of per capita output:
g g g
Y
L
A
K
Similarly from k  AL
Growth rate of per capita capital stock:
g
K
g
L
g
Lecture 6
A
12
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
13
http://www.bbc.co.uk/science/
http://www.bbc.co.uk/radio4/science/
Lecture 6
14
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
15
How Human Capital Contributes to the
Economic Growth?
Thinking
New Ideas
Action
Better Tools
Application More and
High Quality
Products
Lecture 6
Formula
Design
Software
Machines
Consultancy
Cars
Computers
Planes
Medicine
Trains etc.
16
Vast areas of Economically Meaningful of Research
http://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)
Social research
Use of scientific knowledge in building Social engineering, Causes of Crimes
tools and in production process; laser,
Personal and communal disorders
radar, automation, cenematograpy
Rights and responsibilities of each
Diagnosis and Treatment of diseases
individuals in a society,
Engineering of sophisticated machines, Wars and conflict resolution
Lecture 6
Buildings
17
Economically Important Innovations: Product of Genius,
Active and Risk-loving People (Forbes Dec 2002)
year
1917
1918
1921
1923
1923
1924
1924
1925
1926
1927
1928
1929
1930
1933
1937
Innovation
Sneakers (Bowerman)
Spectometer, Uranium 235
Tetrathyle lead (Midgley)
Business Management (Sloan)
Multiple camera (Disney)
Mutual funds
Frozen food (Birdseye)
Transistor, digital signal processor (Bell)
Rocket science (Goddard)
TV (Farnsworth)
Penicillin (Fleming)
Synthetic rubber (Newland)
Jet engine (Whittle)
Radio frequency modulation (Armstrong)
Pulse code modulation
Blood bank
1938 Xerography (Carlson)
1939 Automatic transmission (Thompson)
Helicopter (Sikorsky)
year
1940
1942
1945
1948
1949
1947
1951
1952
1955
1956
1958
1959
1961
1962
Innovation
Radar (Watson-Watt)
Electronic digital computer
Nuclear power
LP (Goldmark)
Magnetic core memory (Wang)
Cellular phone (Ring)
Microwave (Spencer)
Instant Photos (Land)
Transistors (Shockley)
Tupperware (Tupper)
Pill (Mccormick and Singer)
FORTRAN (Backus)
Fast food Krock)
Containerised Shipping
Disk drives (Johnson)
Fiber optics (Kapung)
Laser (Patel)
Integrated circuit
diapers (Pampers)
Modem (AT&T)
Lecture 6
year
Innova
1964 Mainframe (IBM)
Mouse
1971 Microprocessor (Noyce)
Answering machine (Pouls
1972 3-D images of body (MRI)
Ethernet -LAN (Metcalf)
Unix/C programming (Ritc
E-entertainment (Bushnell)
1976 DNA (Swansen)
Personal computer chips (J
1979 Spreadsheets (Bricklin and
1984 Dell PC (Dell)
1991 WWW (Bernerslee)
1995 Internet business (Bezos)
1998 Viagra (Ellis and Terrett)
2000 Automated sequencing ma
2001 ?
?
2002 ?
2003 Cloning?
18
Research Intermediate and Final Goods Sectors
New knowledge
derive from existing
stock of knowledge
Research
Intermediate sector
 j  p j x j  rx j
Consultancy
Final goods
Apply knowledge
in production
X
1
y
Y L
Research Sector
Universities: scientific
and technical knowledge
Research centres such as ESRC,
STRC, Bell Lab, microsoft
Software companies
Lecture 6
A
x
j 1
j
Appliers:
BT/BAE
Financial institutions (LSE)
Government organisations
Factories: Rolls Royce
19
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
20
Who Contributes More to Research in the Bigger Economy?
Schools,
Universities
Research Labs
Households
Consumers
Firms –
Investors
Producers
Treasury –
Allocation of
Public Funds
Revenue –
Tax Collector
Research to Improve
the Economy:
The Big Market
Rest of the World
(ROW) –
Trading Partners
Multilateral
Organisation
Lecture 6
Banks –
Central Bank
Commercial Banks
Stock Market
Financial Institutions
Trade Unions
Employer
Unions
Merchants and
Traders
– Wholesalers
– Retailers
21
Final goods sector
Production
1
y
Y L
A
x
j 1
j
where j=1….A index of ideas
1
y
1
1
y
1
y
Y  L x  L x2  ...  L x A
Input Prices = marginal product
Y
w  1   
L
and
1
y
p j  L x
Lecture 6
1
j
22
Intermediate
and
Research
Sectors
Intermediate good sector:
Profit:
 j  p j x j  rx j
MR = MC principle implies that
p' x j x j  px j   r
p 
X = ideas
r = price of ideas
or
1
1
r 
r
p' ( x) x

1
p
 Research sector

dA   L A

A = stock of knowledge
LA= number of people
working in the knowledge
sector
average productivity in the research sector


  A LA
Lecture 6
23
Growth Rate of Knowledge
Growth Rate of knowledge
dA LA
gA 
 1
A A
In Steady State stock of knowledge grows by the growth rate of researchers:
n
gA 
1
Total labour resource can either be used in the knowledge sector or in the
production of final goods sector:
L  Ly  LA
Lecture 6
24
Main Features of the Romer Model
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
 Y
Y
wr   p A  w y  1    but r 
L
L
Lecture 6
2
25
Why Market Under Provides Research?
Intellectual Property right:
Patents
Designs
Trademark
Copyright
CS
Pm
Profit of a
Research firm
MC
o
http://www.intellectual-property.gov.uk/
Lecture 6
Outcome of research
is uncertain at the outset.
Patents provide
Monopoly rights
for research firms.
DWL
MC
Rm
R opt
26
Economic reason for granting a patent right or subsidy
to a research firm
Output:
Y  100L  F 
F = fixed labour
Cost:
Cost function:
C  wL
 Y

C  w
 F
 100

C
w

Constant marginal cost pricing: Y 100  P
C  w
F




Declining average cost:
Y  100 Y 
w
 Y



R

C

Y

w

F

0
Negative profit:
100
 100

Thus marginal cost pricing is not profitable for a research
firm. Government need to subsidise to produce optimal
amount of research.
Lecture 6
27
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
28
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?
Lecture 6
29