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

Economics 331b
Population dynamics in economics
1
Course logistics
The enrollment in the course is full. You can participate if you
received an email from me.
There are always appeals for special cases. There is no waiting
list.
2
Schedule
Wednesday (today): Malthus and Cohen
Friday: No class. Nordhaus lecture on Economics of Climate
Change, Yale Climate Institute, 12:00 – 1:15, Kroon Hall
Monday: no class
Wednesday: Solow model with deomgraphy; tipping points
Friday: Kremer model
Presentations: any volunteers for Kremer, demography, or
Cohen would be welcome (Wed and Fri of next week)
3
Importance of population
Obviously important part of social sciences
In environmental economics, part of the stress on natural
systems. Can see in the “Kaya identity”:
Pollution ≡ Pop * (GDP/Pop) * (Pollution/GDP),
This equation is often used for energy, CO2, and other
magnitudes.
Warning: It is an identity, not a behavioral equation. It doesn’t
explain anything.
4
Different world views on population
1. Malthus-Cohen: population bumping against resources.
2. Solow-Demographic transition: Need to make the big push to
get out of the low-level Malthusian trap.
3. Kremer: people are bottled up and just waiting to be the next
Mozart or Einstein.
5
Malthusian economics
Basic propositions:
1. It may safely be pronounced, therefore, that population, when unchecked, goes on
doubling itself every twenty-five years, or increases in a geometrical ratio.
2. It may be fairly pronounced, therefore, that, considering the present average state
of the earth, the means of subsistence, under circumstances the most favourable to
human industry, could not possibly be made to increase faster than in an
arithmetical ratio.
3. Taking the whole earth … and, supposing the present population equal to a
thousand millions, the human species would increase as the numbers, 1, 2, 4, 8,
16, 32, 64, 128, 256, and subsistence as 1, 2, 3, 4, 5, 6, 7, 8, 9. In two centuries the
population would be to the means of subsistence as 256 to 9 ; in three centuries as
4096 to 13, and in two thousand years the difference would be almost incalculable.
4. In this supposition no limits whatever are placed to the produce of the earth. It may
increase for ever and be greater than any assignable quantity; yet still the power
of population being in every period so much superior, the increase of the human
species can only be kept down to the level of the means of subsistence by the
constant operation of the strong law of necessity, acting as a check upon the
greater power.
[This theory led to Darwin, social Darwinism, poorhouses, and many other social
6
ideas.]
Review of basic production theory
Classical production model.
Aggregate production function (for real GDP, Y)
(1) Y = F( K, L)
Standard assumptions: positive marginal product (PMP),
diminishing returns (DR), constant returns to scale (CRTS):
CRTS: mY = F( mK, mL)
PMP: ∂Y/∂K>0; ∂Y/∂L>0
DR: ∂2Y/∂K2<0; ∂2Y/∂L2<0
7
The simplest Malthusian model
Production function:
(1)
Yt = F(Lt )
(1M)
Yt = F(Lt ) = 1 + ln2 (Lt)
Where L = population, B = births, D = deaths, wt = wage rate.
Income:
(2)
wt  Y / Lt
Population dynamics (3) and subsistence assumption (4):
(3)
(3)(4)
Lt / Lt   Lt / t  / Lt  Bt / Lt  Dt / Lt  g (wt )
LLt // LLtg(w
L),t / 
t  *)
/ Lt 0, B
/ Lt 0 Dt / Lt  g (wt )
g (w
g t'(w) 
t
t
t
8
n (population growth)
n=n[w]
Wage
rate (w)
0
w*
(Malthusian
subsistence
wage)
9
Demographic transition
G.T. Miller, Environmental Science
10
Dynamics
1. Long-run equilibrium when population is constant:
(5) P = P* → w = w* → wages at long run subsistence wages.
2. What happens if productivity increases?
-
If productivity takes a jump, then simply increase P (next
slide)
More complicated if have continuous population growth,
then can have a growth equilibrium.
Even more complicated if have demographic transition:
11
MPL, Real wage (w)
Neoclassical distribution of
Sshort-run output/income
Slongrun
w*
MPL’
MPL
L
12
Malthus with continuous growth
Assume Cobb-Douglas production function:
(6) Yt  At Lt
(7)
gY  g A   g L  g A   g ( wt )
> 0 if T.C. strong enough
This is the major anti-Malthus theorem: Rapid technological
change can outstrip population growth even in the
subsistence version.
13
Modern Malthusians
Left-wing neo-Malthusians: This school that believes we are
heading to low consumption because we are exhausting our
limited resources (alt., climate change, …). See Limits to
Growth, P Ehrlich, The Population Bomb
Right-wing neo-Malthusians: This school believe that the
“underclass” is breeding us into misery due to overly
generous welfare programs. See Charles Murray, Losing
Ground: American Social Policy 1950–1980.
14
Carrying Capacity
Basic idea from ecology: the maximum number of individuals that the
environmental resources of a given region can support.
Demographers have sometimes assumed this applies to the upper limit
on human populations that the earth can support. (maximum
supportable human population).
15
Source: J. Cohen, “Population Growth…,” Science, 1995.
Agenda for today
Cohen and the idea of carrying capacity
The neoclassical growth model:
- the basics from macro
- adding endogenous population growth
Nonlinear dynamics and tipping points
Schedule presentations
16
Alternative methods for estimating carrying
capacity
1.
2.
3.
4.
5.
6.
Just assume a maximum population density
Extrapolate population trends.
Single factor model (e.g., food supply)
Single factor as function of multiple inputs
Multiple factor constraints (P < β water; P < γ food; …)
Multiple dynamic and stochastic constraints
(P(t) < β water(t) + ε(t) ; P(t) < γ food(t) +ς(t) ; …]
[Source: As described in Cohen]
17
Carrying Capacity from Cohen
Basic idea is that there is an upper limit on the population that
the earth can support.
This is a variant of Malthus as follows:
(8)
Lt / Lt  r[Zt  Lt ], where Zt is the earth's carrying capacity.
(9) Zt   Lt , where  is a productivity parameter.
Not clear how to interpret (9). One possibility is the maximum L
at subsistence wages, which would be MPL(Z)=w*, or in C-D
framework:
(10) Yt / Lt  w*  Z t   At / w*
1/(1 )
Which means that carrying capacity grows at
(11) [1/ (1   )]g A  [1/ (1  .67)]g A  3  2  6% per year!!!
18
Economic interpretation
of carrying capacity theories
Carrying capacity is a concept foreign to economic
demography. Is it a normative concept? A descriptive
concept?
As descriptive, it seems related to Malthusian subsistence
wage.
•
•
Carrying capacity changes over time with technological change.
Basic trends in U.S. and rest of world outside of Africa is that technological
shifts have outweighed diminishing returns. I.e., clear evidence that
because of technological change, carrying capacity has increased over
time.
As normative, it seems inferior to concept of optimum
population.
• This would be some social welfare function as U(C, L), maximized
over L
• However, introducing L gives serious difficulties to Pareto criterion,
which is central normative criterion of economics
19
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
* For those who are rusty on the neoclassical model, see handout as well as
chapters from Mankiw on the course web site.
20
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
21
Demographic transition
G.T. Miller, Environmental Science
22
Population growth, 2007 (% per year)
Current demography
4
3
2
1
0
-1
5
6
7
8
9
10
11
ln per capita income, 2000
23
n (population growth)
n=n[f(k)]
Per
capita
income
(y)
0
y* =
(Malthusian or
subsistence
wages)
Unclear future trend of
population in high-income
countries
24
Growth dynamics with the demographic transition
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
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 *
25
y = f(k)
“TIPPING POINT”
n[f(k)]k
y = Y/L
i = sf(k)
Low-level trap
High-level
equilibrium
k
k*
k**
k***
26
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
In climate systems (see next slide)
Very interesting policy implications of tipping/trap systems
27
Original locally stable
equilibrium
k*
k**
k***
k
28
Forcing function tips
function (demography,
global warming, financial
worries, …)
k
k*
k**
k***
29
OOPS!!!!!!!
k
k*
k**
k***
30
Note: Have new and
different locally stable
equilibrium
k*
k**
k
k***
31
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)
32
Examples from climate system
Source: Lenton et al., “Tipping Elements,” PNAS, Feb 2008, 1786.
33
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.
35
Hysteresis loops and Tipping Points for Ice Sheets
36
Frank Pattyn, “GRANTISM: Model of Greenland and Antrarctica,”
Computers
& Geosciences, April 2006, Pages 316-325
Source: GRANTISM model (to examine later).
36
Snowball earth (Budyko-Sellars model)
Source: Paul Hoffman (Harvard) and Snowball Earth
37
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.
38
y = Y/L
The Big Push
in Economic
Development
y = f(k)
{n[f(k)]+δ}k
i = sf(k)
k
k***
39