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Economic Modelling

Lecture 6

Human Capital, Technology (Knowledge),

R& D and Economic Growth

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Exogenous Technology in the Solow Model

Higher saving rate does not lead to higher growth rate (because of

diminishing marginal productivity of capital)

ngagyyg 1

Assuming output and capital grow at the same rate.

1agng

does not explain technological growth, it is exogenous.

Total multi-factor productivity or Solow residual

nkgygag 1

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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 (?)

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How Human Capital Contributes to the Economic Growth?

Thinking New Ideas Formula Design Software

Action Better Tools Machines Consultancy

Application More and High Quality Products

Cars Computers Planes Medicine Trains etc.

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Role of Human Capital in Production

k1 k2k3

Y=f(k,h1)

Y=f(k,h2)

Y=f(k,h3)

y1

y2

y3i

It is possible to have increasing returns to scale with human capital in production.

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Simple version of the Lucas Model

1hLKY

= fraction of time spent on working (1-) fraction of time spent on studyingh = is human capital per worker, it depends on (1-)L = labour supply –(assume this as given)

7.0)4.2(1007.0100*3*8.03.0100 Y

If K=100, L=100 h=3 =0.8, =0.3

= 185 where with

1LKY =100.

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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.

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Saving, Capital Accumulation and Output with Increasing return to Scale: AK Model

AKY

k

y

1

AkY

kkay

y

kysag '

In AK Model

Higher saving rateimplies higher rate of growth of output.

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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

1Three Sectors in the Romer’s Endogenous Growth ModelResearch Sector: Universities/ research labs produce ideas

Intermediate sector: Takes those ideas to make tools and machines

Final Goods sector use those ideas to produce consumer goods.

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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

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How does the technological advancement affect the per capita capital and per capita output in the steady state?

11

sksyS

22ky

1y

L

Kk

222

sksyS

22kni

2y

1k 2k

Primitive Technology

Advanced Technology

11ky

12

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

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Output: YALKY

A = Stock of knowledge

Labour use: Ay LLL The stock of knowledge rises if more people do research:

AA LALA

Growth rate of knowledge: A

LA

A

Ag AA

Capital Accumulation:

tItKtK 11

Market clearing: ttt ICY Here technology is endogenous to efforts in production and application of research.

Endogenous Growth Model

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MPKh1

MPKh2w1

w2

Increase in Real Wage Rate with Human Capital

Technologicaladvancement raises

wage rate but reducesWork hours.

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r

MPKh1 MPKh2

MPKh3

k3k2k1

Constant Marginal Product of Capital with Human Capital

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Skilled and Unskilled Labour In Production, UK 2000

2 UnSkLab59%

3 SkLab41%

What Can Policy Do to Improve the Human Capital and Technology?

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The proportion of all adults of working age in the UK and England with no formal qualifications: 1985 - 2002 (www.defs.gov.uk)

0

5

10

15

20

25

30

35

40

45

sprin

g

sprin

g

sprin

g

autu

mn

sprin

g

autu

mn

sprin

g

autu

mn

sprin

g

autu

mn

sprin

g

autu

mn

sprin

g

autu

mn

sprin

g

autu

mn

sprin

g

autu

mn

1985 1990 1995 1996 1997 1998 1999 2000 2001 2002

per

cen

t.

United Kingdom %age England %age

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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/

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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 (See Jones (2003) Problem 4.3)

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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 ProductivityGrowth 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.

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

year Innovation year Innovation year Innovation1917 Sneakers 1940 Radar1918 Spectometer, Uranium 235 1942 Electronic digital computer 1964 Mainframe1921 Tetrathyle lead 1945 Nuclear power Mouse1923 Business Management 1948 LP 1971 Microprocessor1923 Multiple camera 1949 Magnetic core memory Answering machine1924 Mutual funds 1947 Cellular phone 1972 3-D images of body (MRI)1924 Frozen food Microwave Ethernet -LAN1925 Transistor, digital signal processor Instant Photos Unix/C programming1926 Rocket science Transistors E-entertainment1927 TV Tupperware 1976 DNA1928 Penicillin 1951 Pill Personal computer chips1929 Synthetic rubber 1955 Fast food 1979 Spreadsheets1930 Jet engine 1956 Containerised Shipping 1984 Dell PC1933 Radio frequency modulation Disk drives 1991 WWW1937 Pulse code modulation Fiber optics 1995 Internet business

Blood bank 1958 Laser 1998 Viagra1938 Xerography 1959 Integrated circuit 2000 Automated sequencing machine1939 Automatic transmission 1961 diapers

Helicopter 1962 Modem

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