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

Economics 331b
The neoclassical growth model
Plus
Malthus
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Agenda for today
Neoclassical growth model
Add Malthus
Discuss tipping points
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Growth trend, US, 1948-2008
2.0
ln(K)
ln(Y)
ln(hours)
1.6
1.2
0.8
0.4
0.0
50
55
60
65
70
75
80
85
90
95
00
3
05
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Growth dynamics in neoclassical model*
Major assumptions of standard model
1. Full employment, flexible prices, perfect competition, closed economy
2. Production function: Y = F(K, L) = LF(K/L,1) =Lf(k)
3. Capital accumulation: dK / dt  K  sY   K
4. Labor supply: L / L  n = exogenous
New variables
k = K/L = capital-labor ratio; y = Y/L = output per capita;
Also, later define “labor-augmenting technological change,”
E = effective labor,
L  EL; y  Y / L; k  K / L;
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n (population growth)
0
Exoogenous pop growth
Wage
rate (w)
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1. Economic dynamics
g(k) = g(K) – g(L) = g(K) – n = sY/K - δ – n = sLf(k)/K - δ – n
Δk = sf(k) – (δ + n)k
2. In a steady state equilibrium, k is constant, so
sf(k*) = (n + δ) k*
3. We can make this a “good” model by introducing technological
change (E = efficiency units of labor)
Y  F  K , EL   F(K , L )
y
 Y / L  f (k)
with equilibrium condition:
s f ( k )  (n   ) k *
4. Then the model works out nicely and fits the historical growth facts.
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k  k *  s f ( k *)  (n   ) k *
y*
y = f(k)
y = Y/L
(n+δ)k
i = sf(k)
i* =
(I/Y)*
k*
k
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Now introduce better demography
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Population growth, 2007 (% per year)
What is the current relationship between
income and population growth?
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3
2
1
0
-1
5
6
7
8
9
10
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ln per capita income, 2000
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n (population growth)
Endogenous pop growth
n=n[f(k)]
Per
capita
income
(y)
0
y* =
(Malthusian or
subsistence
wages)
Unclear future trend of
population in high-income
countries
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Growth dynamics with the demographic transition
Major assumptions of standard model
Now add endogenous population:
4M. Population growth: n = n(y) = n[f(k)]; demographic transition
This leads to dynamic equation (set δ = 0 for expository simplicity)
k  s f ( k )  n [ f ( k ) ]k
with long-run or steady state equilibrium (k*)
k  0  k  k* 
s f ( k *)  n [ f ( k *) ] k *
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k  k *  s f ( k *)  n [ f ( k *) ] k *
y = f(k)
n[f(k)]k
y = Y/L
i = sf(k)
k
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y = f(k)
k  k *  s f ( k *)  n [ f ( k *) ] k *
n[f(k)]k
y = Y/L
i = sf(k)
Low-level trap
High-level
equilibrium
k
k*
k**
k***
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“TIPPING POINT”
k
k*
k**
k***
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Other examples of traps and tipping points
In social systems (“good” and “bad” equilibria)
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•
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Bank panics and the U.S. economy of 2007-2009
Steroid equilibrium in sports
Cheating equilibrium (or corruption)
Epidemics in public health
What are examples of moving from high-level to low-level?
In climate systems
• Greenland Ice Sheet and West Antarctic Ice Sheet
• Permafrost melt
• North Atlantic Deepwater Circulation
Very interesting policy implications of tipping/trap systems
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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.
- 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
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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.” This is
intellectual rationale for the bank bailout – move to good
equilibrium.
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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y = Y/L
The Big Push in
Economic
Development
y = f(k)
{n[f(k)]+δ}k
i = sf(k)
k
k***
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