Transcript continuous time

coef = 29.981268, se = 1.0345626, t = 28.98
e( hdiscore | X)
96.4363
-90.3541
-3.01368
3.21655
e( lgnppc95 | X )
Exponential Growth
6
4
5000
2
0
Year
21
00
20
50
0
Ln(GNP)
10
8
10000
20
01
GNP
15000
GNP
ln(GNP)
On a graph with a log scale, if a country has GDP with a
constant growth rate its level of GDP lies on a straight line.
Imagine a growth rate for income given by g.
This means that if GDP in time 0 is Y0, then income in time 1 is
Y1 =Y0(1+g)
But then income in time 2 is
Y2 =(Y0(1+g))(1+g) =Y0(1+g)2
More generally, income in time t is written:
Yt = Y0  (1 + g ) t
This type of growth is called “Geometric Growth.” If we take logs of both sides
we find the following linear function:
lnYt = lnY0 + tln(1 + g )
The slope of the function, ln(1 + g ), is approximately equal to g.
A Note on Growth in Continuous Time
In the last slide we treated time as if it was divided into chunks and
we considered growth from year to year. Time, however
is continuous and we may wish to take account of that fact.
In the last slide we said that we could write Yt as:
Yt = Y0  (1 + g ) t
The continuous time version of this equation is:
Yt = Y0  eg  t
If we take logs of this equation we find:
Yt = lnY0 + g  t
Which is again a linear equation with slope of t (no approximation!)
Also, have a look here: http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/andromed.html
Doubling Time: 70 is the magic number!
Say we want to know how long it will take for something to double
when it is growing at growth rate g. How do we work it out?
This is the same as asking for what t does Yt = 2  Y0?
Using the equation Yt = Y0  eg  t we can answer the question by
solving the following equation for t:
2  Y0 = Y0  eg  t
The answer is t=ln(2)/g = .693/g
Hence we can find the answer by dividing .693 by the growth rate
(or approximately by dividing 70 by the percentage growth rate)
MAIN QUESTIONS:
1.
2.
3.
Why did modern economic growth emerge only in the 19th Century?
What is the relationship between population growth and economic growth?
Why is economic growth so concentrated in Europe and European offshoots? Is
this the result of historical accident, first-mover advantage, geography, culture,
social institutions, other factors?
4. Is economic growth now spreading to all regions of the world?
5. What are the engines of economic growth? Accumulation, division of labor, scale,
innovation and diffusion.
6. What are the roles of culture and social stratification in economic development?
Religion and economic organization; Gender roles and inequalities; Ethnicity and
social divisions.
7. What is the role of politics and political institutions in Economic Development?
8. What is the role of economic institutions in economic development? Is modern
economic growth a phenomenon of modern capitalism?
9. Do the rich countries exploit the poor, or do the poor benefit from the rich through
diffusion of technology and inflows of capital?
10. Are there special policies for "catching up growth" for laggard economies? (e.g.
infant-industry protection, or special policies for technological diffusion, etc.).
Alternative Viewpoints:
Importance of economic institutions, political institutions, and incentives:
Mancur Olson
Yours truly
Importance of “culture” of modernization
Max Weber
David Landes
Importance of international environment (geopolitical and economic)
Karl Marx and followers (exploitation, colonialism, dependency)
Moses Abramovitz
Importance of geography (ecology, connectivity)
Jared Diamond
Yours Truly
Need for a Comprehensive Social Theory
Our Approach
Mechanisms of Economic Growth
resource exploitation and depletion
accumulation of capital
division of labor
innovation
Social, Physical, and Geopolitical Context
and the effects on mechanisms of growth
Kinds of Social Institutions
Economic
Political
Cultural (norms, religious beliefs, governed by sanction)
Scientific
Physical Geography:
Proximity
Ecology
Mineral and energy resource
Geopolitical Relations:
Conquest
Imitation
Threat
Social institutions:
Economic
Political
Cultural
Technology:
Science
Belief systems
Innovation and
diffusion
Demography:
Age structure
Mortality
Morbidity
Fertility
Economic and
Social outcomes:
Economic
growth
Distribution of
income