Transcript Economics 157b Economic History, Policy, and Theory Short

Econ 331b
Kremer’s model
and
Mathematics, economics, science of catastrophes
Basics
1. Production function with labor, land, and technology
2. Diminishing returns leads to Malthusian population
equilibrium.
3. Higher population leads to more rapid technological change.
Fundamental point about technologies: They are ultimate
externality because of non-rivalry.
[Jefferson: “He who receives an idea from me, receives instruction
himself without lessening mine; as he who lights his taper at mine,
receives light without darkening me.”]
This leads to explosive growth in technology.
Jefferson on ideas
If nature has made any one thing less susceptible than all others
of exclusive property, it is the action of an idea, which an
individual may exclusively possess as long as he keeps it to
himself; but the moment it is divulged, it forces itself into the
possession of every one, and the receiver cannot dispossess
himself of it.
Its peculiar character, too, is that no one possesses the less,
because every other possesses the whole of it. He who
receives an idea from me, receives instruction himself without
lessening mine; as he who lights his taper at mine, receives
light without darkening me.
The simplest Kremer model

Y  AL T
1 
Malthusian equilibrium at y , leading to
L  (A / y)
1/(1  )
But assume that technology grows with population:
A / A  Lg
So
L / L  n   1 /(1   )  A / A   Lg /(1   )
So population growth is proportional to population si ze!
Time series: 1,000,000 BP - present
Why does this flatten out in recent years?
Cross section
This is really interesting!
Some interesting conclusions
1. Most important point is to remember that technology is
endogenous, not exogenous. This is a central issue in energy
policy and climate-change policy.
2. How can policy induce more rapid “green” technological
change? Think about this.
3. Kremer suggests that pro-natal population is progressive
rather than regressive. Population is a boon not a bomb.
4. Model misses the historical fact that invention is not just
randomly distributed among people. (Why was Vienna the
greatest center of classical music in all time?) What is the
reason for the agglomeration of invention?
Economics 331b
Tipping points and catastrophes
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Original locally stable
equilibrium
k*
k**
k***
k
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Forcing function tips
function (demography,
global warming, financial
worries, …)
k
k*
k**
k***
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OOPS!!!!!!!
k
k*
k**
k***
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Note: Have new and
different locally stable
equilibrium
k*
k**
k
k***
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Mathematics of dynamics systems
1. Standard linear systems (boring)
2. Unstable dynamics (nuclear reactions)
xt = βxt-1 + εt (β > 0)
3. Unstable dynamics with boundaries (speculation, epidemics)
xt = βxt-1 + εt (β > 0; x min < x < x max )
4. Multiple locally stable equilibria (Solow-Malthus, bank
panics)
5. Hysteresis loops (Phillips curve, Greenland Ice Sheet,
business cycles, snowball earth)
6. Chaotic systems or butterfly effect (weather)
7. Catastrophic disintegration (World Trade Towers, Katrina)
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Examples from climate system
Source: Lenton et al., “Tipping Elements,” PNAS, Feb 2008, 1786.
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Source: T. Lenton et al., “Tipping Elements,” PNAS, Feb. 2008, 1786.
Hysteresis Loops
When you have tipping points, these often lead to “hysteresis
loops.”
These are situations of “path dependence” or where “history
matters.”
Examples:
- In low level Malthusian trap, effect of saving rate will depend
upon which equilibrium you are in.
- When have natural monopoly, “first mover advantage.”
- In macroeconomics, the expectational Phillips curve theory
shows hysteresis loop in inflation.
- In climate system, ice-sheet equilibrium will depend upon
whether in warming or cooling globe.
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Hysteresis loops and Tipping Points for Ice Sheets
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Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,”
Computers
& Geosciences, April 2006, Pages 316-325
Source: GRANTISM model (to examine later).
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Snowball earth (Budyko-Sellars model)
Source: Paul Hoffman (Harvard) and Snowball Earth
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Policy Implications
1. (Economic development) If you are in a low-level
equilibrium, sometimes a “big push” can propel you to the
good equilibrium.
2. (Finance) Government needs to find ways to ensure (or
insure) deposits to prevent a “run on the banks.”
3. (Climate) Policy needs to ensure that system does not move
down the hysteresis loop from which it may be very difficult
to return.
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