Economic Modelling
Lecture 6
Human Capital, Technology (Knowledge),
R& D and Economic Growth
1
Exogenous Technology in the Solow Model
Total multi-factor productivity or Solow residual
g a  g y g  1 n
k
Higher saving rate does not lead to higher growth rate (because of
diminishing marginal productivity of capital)
g  y  g a  g  1 n
y
Assuming output and capital grow at the same rate.
ga
g n 
1 
does not explain technological growth, it is exogenous.
2
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
– Rockets, Cars, computers, trains, planes, medicine,
TV, Phone Internet, Rockets; high yielding varieties of
crops, cloning (?)
3
How Human Capital Contributes to the
Economic Growth?
Thinking
New Ideas
Action
Better Tools
Application More and
High Quality
Products
Formula
Design
Software
Machines
Consultancy
Cars
Computers
Planes
Medicine
Trains etc.
4
Role of Human Capital in Production
Y=f(k,h3)
y3
Y=f(k,h2)
y2
Y=f(k,h1)
y1
k1
k2
k3
It is possible to have increasing returns to scale with human capital in production.
5
i
Simple version of the Lucas Model
1
Y  K  hL 
 = fraction of time spent on working
(1-) fraction of time spent on studying
h = is human capital per worker, it depends on (1-)
L = labour supply –(assume this as given)
If K=100, L=100 h=3  =0.8, =0.3
0.7
0
.
3
Y  100 0.8 * 3 *100
 100(2.4) 0.7
= 185 where with

1


Y K L
=100.
6
Constant, Increasing and Decreasing Returns to Scale
• Y = AKαLβ
• Constant Return to Scale: α + β = 1
• When capital and labour inputs are increased by a
certain factor t, output also increases by the factor of t.
• Increasing Return to Scale: α + β > 1
• If adding capital and labour input by a factor of t would
increase output by more than factor of t.
•
• Decreasing Return to Scale: α + β < 1
• When adding inputs by factor t causes output to
increase by less than factor of t.
7
Saving, Capital Accumulation and Output with
Increasing return to Scale: AK Model
Y  AK
y
Higher saving rate
implies higher rate of
growth of output.
Y  Ak
 1
In AK Model
s
'
y
g a
k
y  a  k
y
k
k
8
Comparison of Production Technology in
Endogenous and Solow Growth Models
 1
Y=AK End. Growth
Y
Solow


Y  AK L
In AK Model
s
'
y
g a
k
y  a  k
y
k
   1
Three Sectors in the Romer’s Endogenous Growth
Model
Research Sector:
Universities/ research labs produce ideas
K
Intermediate sector:
Takes those ideas to make tools and machines
Final Goods sector use those ideas
to produce consumer goods.
9
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.
MPK
Y
A
K
AK Model
 1
Y

 AK  1L
K
    1 Solow Model
K
10
How does the technological advancement affect the per
capita capital and per capita output in the steady state?
y  k
2 2
y2
Advanced Technology
i  n   k
2
2
S  sy  sk
2
2
2
Primitive Technology
y  k
1 1
y1
S  sy  sk
1
1
k1
k2
k
K
L
11
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
Y1
Output
12
Endogenous Growth Model
Output:
YK

 ALY 

A = Stock of knowledge
L  Ly  LA
Labour use:
The stock of knowledge rises if more people do research:

 

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
t
Yt  Ct  I t
Market clearing:
Here technology is endogenous to efforts in production and
13
application of research.
Increase in Real Wage Rate with Human
Capital
w2
w1
Technological
advancement raises
wage rate but reduces
Work hours.
MPKh2
MPKh1
14
Constant Marginal Product of Capital with
Human Capital
r
MPKh3
MPKh1
k1
MPKh2
k2
k3
15
What Can Policy Do to Improve the
Human Capital and Technology?
Skilled and Unskilled Labour In Production, UK 2000
3 SkLab
41%
2 UnSkLab
59%
16
The proportion of all adults of working age in the UK and England
with no formal qualifications: 1985 - 2002 (www.defs.gov.uk)
45
40
35
United Kingdom %age
England %age
25
20
15
10
5
1985
1990
1995
1996
1997
1998
1999
2000
2001
autumn
spring
autumn
spring
autumn
spring
autumn
spring
autumn
spring
autumn
spring
autumn
spring
autumn
spring
spring
0
spring
per cent.
30
2002
17
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/
Outcome of research
is uncertain at the outset.
Patents provide
Monopoly rights
for research firms.
DWL
MC
Rm
R opt
18
Economic reason for granting a patent right or subsidy
to a research firm (See Jones (2003) Problem 4.3)
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

Negative profit:   R  C  100 Y  w 100  F   0


Thus marginal cost pricing is not profitable for a research
firm. Government need to subsidise to produce optimal
amount of research.
19
References
•
•
•
Blanchard (13)
Aghion and Howitt ( 1998) Endogenous Growth Theory, MIT Press.
Abramovitz, Moses (1986). Catching up, forging ahead and falling behind. Journal
of Economic History, 46(2), June, 386-406.
•
Barro R. J.(1998) Determinant of Economic Growth: A Cross Country Empirical
Study, Cambridge MA:MIT Press.
•
Barro R. and Sala-I-Martin (1995) Economic Growth, McGraw Hill.
•
Jones C. I. (1995) R & D-Based Models of Economic Growth, Journal of Political
Economy, 103:4:759-784
•
Lucas R.E. (1988) "On the Mechanics of Economic Development", Journal of
Monetary Economics, 22, 3-42.
•
Cameron Gavin (2003) Why Did UK Manufacturing Productivity
Growth Slow Down in the 1970s and Speed Up in the 1980s?Economica, 70:121-141
•
•
Romer, Paul (1989) Endogenous Technological Change, Journal of
Political Economy, vol. 98, no. 5. Pt. 2, pp. S71-S102.
Temple, Jonathan R. W. (2001). Growth effects of education and social
capital in the OECD countries. OECD Economic Studies, 33, 57-101.
20
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
1938
1939
Innovation
year
Sneakers
Spectometer, Uranium 235
Tetrathyle lead
Business Management
Multiple camera
Mutual funds
Frozen food
Transistor, digital signal processor
Rocket science
TV
Penicillin
Synthetic rubber
Jet engine
Radio frequency modulation
Pulse code modulation
Blood bank
Xerography
Automatic transmission
Helicopter
1940
1942
1945
1948
1949
1947
1951
1955
1956
1958
1959
1961
1962
Innovation
Radar
Electronic digital computer
Nuclear power
LP
Magnetic core memory
Cellular phone
Microwave
Instant Photos
Transistors
Tupperware
Pill
Fast food
Containerised Shipping
Disk drives
Fiber optics
Laser
Integrated circuit
diapers
Modem
year
Innovation
1964 Mainframe
Mouse
1971 Microprocessor
Answering machine
1972 3-D images of body (MRI)
Ethernet -LAN
Unix/C programming
E-entertainment
1976 DNA
Personal computer chips
1979 Spreadsheets
1984 Dell PC
1991 WWW
1995 Internet business
1998 Viagra
2000 Automated sequencing m
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