Economics 331b The neoclassical growth model
PlusMalthus
1
Agenda for today
Neoclassical growth modelAdd MalthusDiscuss tipping points
2
33
Growth trend, US, 1948-2008
0.0
0.4
0.8
1.2
1.6
2.0
50 55 60 65 70 75 80 85 90 95 00 05
ln(K)ln(Y)ln(hours)
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: 4. Labor supply: New variables
k = K/L = capital-labor ratio; y = Y/L = output per capita;Also, later define “labor-augmenting technological change,”
E = effective labor, 4
/dK dt K sY K
/ n = exogenousL L
; / ; / ;L EL y Y L k K L
n (population growth)
Wage rate (w)
0
5
Exoogenous pop growth
6
1. Economic dynamicsg(k) = g(K) – g(L) = g(K) – n = sY/K - δ – n = sLf(k)/K - δ – nΔk = 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)
4. Then the model works out nicely and fits the historical growth facts.
, ( , ) / ( )
with equilibrium condition:( ) ( ) *
Y F K EL F K Ly Y L f k
s f k n k
7k
y = Y/Ly = f(k)
(n+δ)k
y*
i* = (I/Y)*
k*
i = sf(k)
* ( *) ( ) *k k sf k n k
Now introduce better demography
8
What is the current relationship between income and population
growth?
9
-1
0
1
2
3
4
5 6 7 8 9 10 11
ln per capita income, 2000
Popu
latio
n gro
wth
, 200
7 (%
per
year
)
n (population growth)
Per capita income (y)
0
y* = (Malthusian or subsistence wages)
n=n[f(k)]
10
Unclear future trend of population in high-income
countries
Endogenous pop growth
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)
11
( ) [ ( ) ]with long-run or steady state equilibrium (k*)
0 *
( *) [ ( *) ] *
k sf k n f k k
k k k
sf k n f k k
k
y = Y/L
y = f(k)
i = sf(k)
n[f(k)]k
12
* ( *) [ ( *) ] *k k sf k n f k k
k
y = Y/L
y = f(k)
k***
i = sf(k)
k**k*
Low-level trap
n[f(k)]k
13
High-level equilibrium
* ( *) [ ( *) ] *k k sf k n f k k
kk***k**k* 14
“TIPPING POINT”
Other examples of traps and tipping points
In social systems (“good” and “bad” equilibria)• 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
15
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.
16
17
Hysteresis loops and Tipping Points for Ice Sheets
17Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,” Computers & Geosciences, April 2006, Pages 316-325
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.
18
k
y = Y/L
y = f(k)
k***
i = sf(k)
The Big Push in Economic Development
{n[f(k)]+δ}k
19