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

Economics 331b
Spring 2011
Tentative Course Topics.
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Population dynamics and Malthus’s theory
Economics of exhaustible resources
Energy policy
Discounting
Geosciences
Impacts of climate change
Cost of reducing emissions
Integrated assessment climate-economic models
Decision making under uncertainty
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Requirements
Course requirements are the following:
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One term paper at end of course (15 pages)
A midterm examination in week 7 or 8
A 3-hour final examination
No textbook. All readings are electronic.
Be prepared for class.
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Meeting times
Generally, lectures are on Monday and Wednesday.
Fridays will be sections, occasional lectures, special topics.
You must be available on Fridays to take the course.
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Prerequisites
We will use the following all the time:
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Growth theory (neoclassical and advanced)
Theory of externalities
Core micro
Calculus (multivariate, simple integral, logs, simple
differential equations, Lagrangeans, NO matrix algebra)
Note: you should have access to a textbook on intermediate
macro and intermediate micro.
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First two weeks: The “population problem”
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Basics of demography
Malthusian theories
Kremer’s technological story
The “aging society” and its challenges
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Basics of demography
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Birth rates
Mortality rates
Survival rates
Life expectancy
Support ratio
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Issues Raised in Malthusian models
What are the dynamics of human population growth?
What is the demographic transition?
The interesting case of a low-level trap, and how to get out of it
(a generic multiple equilibrium like bank panics).
Are humans doomed to return to the stone age because of
resource exhaustion?
Why do some people think this is all irrelevant because the
problem is population decline and an aging population.
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Two Views of the Demographic Fate of the World
1. The Malthusian view – population filling up the world.
2. The Aging Society
What is your view?
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(1) Malthusian
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(2) Geezertown
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Economics 331b
Population dynamics in economics
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Schedule
Wednesday 12:Malthus
Friday14: Cohen
Monday 17: no class
Wednesday 19: Solow model with demography; tipping points
Friday 21: Kremer model
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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.
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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.
4. Modern demography: With declining populations and low
mortality rate, growth fiscal burdens and declining
innovation.
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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
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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
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The simplest Malthusian model
Production function:
(1)
Yt = F(Lt ; Tt)
Where L = population, T = land (terra), wt = wage rate.
Income = wages:
wt  Y / Lt
(2)
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
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n (population growth)
n=n[w]
Wage
rate (w)
0
w*
(Malthusian
subsistence
wage)
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Dynamics
1. Long-run equilibrium when technology is constant:
(5) L = L* → w = w* → wages at long run subsistence wages.
2. What happens if productivity increases?
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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:
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Malthus in the neoclassical
production model
Real
wage (w)
S
w*
MPL1
L1*
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L
Malthus in the neoclassical
production model
Real
wage (w)
S
w*
MPL2
MPL1
L1*
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L2*
L
Demographic transition
G.T. Miller, Environmental Science
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Malthus with continuous growth
Assume Cobb-Douglas production function:
(6) Yt  At L t T 1t 
(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.
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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.
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Agenda for today
The idea of carrying capacity
Cohen’s description
Link to Malthus
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Background on carrying capacity
Originates in range/wildlife management.
Populations characteristically increase in size in a sigmoid or Sshaped fashion. When a few individuals are introduced into, or
enter, an unoccupied area population growth is slow at first . . . ,
then becomes very rapid, increasing in exponential or compound
interest fashion . . . , and finally slows down as the environmental
resistance increases . . . until a more or less equilibrium level is
reached around which the population size fluctuates more or less
irregularly according to the constancy or variability of the
environment. The upper level beyond which no major increase can
occur (assuming no major changes in environment) represents the
upper asymptote of the S-shaped curve and has been aptly called
the “carrying capacity” or the saturation level. (Odum, Fundamentals
of Ecology)
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Ehrlichs on human populations
The key to understanding overpopulation is not population
density but the numbers of people in an area relative to its resources
and the capacity of the environment to sustain human activities; that
is, to the area’s carrying capacity.
When is an area overpopulated? When its population can’t be
maintained without rapidly depleting nonrenewable resources (or
converting renewable resources into nonrenewable ones) and
without degrading the capacity of the environment to support the
population. In short, if the long-term carrying capacity of an area is
clearly being degraded by its current human occupants, that area is
overpopulated.
By this standard, the entire planet and virtually every nation is
already vastly overpopulated.
(Ehrlich and Ehrlich The population explosion.)
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Logistic curve
Idea is that there is some maximum population, K.
Actual approaches as a sigmoid or logistics curve:
L t  rL t [ K  L t ],
where K is maximum sustainable population,
or carrying capacity.
Where does K come from?
Is it static or dynamic?
Is r always positive?
How do r and K respond to
changes in technology?
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Carrying Capacity
Demographers have sometimes assumed this applies to the upper limit
on human populations that the earth can support. (maximum
supportable human population).
Estimates of maximum possible population:
Source: J. Cohen, “Population Growth…,” Science, 1995.
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Alternative methods for estimating carrying
capacity
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2.
3.
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5.
6.
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]
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Carrying Capacity from Cohen
Basic idea is that there is an upper limit on the population that
the earth can support.
This is Cohen’s interpretation of Malthus with dynamic c.c.:
L t / L t  r [Zt  L t ], where Zt is the earth's carrying capacity.
Z t   L t, where  is a productivity parameter.
What is economic interpretation here? [This is the art in
economic science!]
One possibility is the Z = maximum L at subsistence wages,
which would be MPL(K)=w*, or in C-D framework:
Yt / Lt  w*  Z t   At / w*
1/ (1 )
Which means that carrying capacity grows at
gZ  Z / Z  [1/ (1   )]g A  [1/ (1  .67)]g A
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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.
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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
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Verdict on carrying capacity
My economist’s take on this:
1. Useful only in very limited environment (fruit flies in a jar).
2. Particularly limited for human populations:
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Because it depends so crucially on technologies
Because human population growth does not respond
mechanically and in Malthusian manner to
income/resources.
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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
* For those who are rusty on the neoclassical model, see handout as well as
chapters from Mankiw on the course web site.
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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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