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

Econ 331a. Economics of Energy, Resources,
and Climate Change
William Nordhaus
Contents:
1. Introduction to course material (this duplicates the materials under
“Basics” on the course web site.
2. Preliminary lectures on population through week 2+. Note that
these are likely to be modified as we go along.
3. Course web site:
http://www.econ.yale.edu/~nordhaus/homepage/Energy2014.htm
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Course introduction
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http://www.econ.yale.edu/~nordhaus/homepage/Energy2014.htm
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TOPICS
Tentative Course Topics.
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Alternative views of population
Economics of exhaustible resources
Energy policy
Discounting
Behavior environmental economics
Impacts of climate change
Cost of reducing emissions
Integrated assessment climate-economic models
Decision making under uncertainty
Economics of innovation and energy policy
Economic theory of treaties and climate change
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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
A 3-hour final examination
All readings are electronic.
A few problem sets on model building
In-class self-graded quizzes most classes (including today)
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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 from Econ
We will use the following all the time:
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Growth theory (neoclassical and advanced)
Theory of externalities
Core micro, particularly production theory
Simple game theory
Calculus (multivariate, simple integral, logs, simple
differential equations, Lagrangeans, NO matrix algebra)
Note: you are advised to have access to a textbook on
intermediate macro and intermediate micro.
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Enrollment
We have decided upon vote of the class not to limit enrollment.
Students should be aware that due to shortages of teaching
fellows, the services provided may be constrained.
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Schedule
Wednesday 27: Introduction to demography
Friday 29: Production theory, Malthus, immigration
Monday 1: no class
Wednesday 3: Carrying capacity, Solow
Friday 5: Kremer model
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First in-class problem
I will pass out a sheet of paper. On one page answer the
following as best you can:
What is the most important economic effect of higher
population growth over the next half-century or so?
I want your answer. Don’t refer to the Internet, just to your
ideas.
10 minutes.
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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 or Steve Jobs.
4. Modern demography: With declining populations and low
mortality rate, growing fiscal burdens and declining
innovation.
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Demographic transition
G.T. Miller, Environmental Science
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(1) Malthusian
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(2) The Mozart effect
*“If I could re-do the history of the world,
halving population size each year from
the beginning of time on some random basis,
I would not do it for fear of losing Mozart in
the process.” Phelps, “Population Increase”
Note increase in absolute
number of Mozart-scale
geniuses as population
size increases.
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Mozart
level
Measure of genius
(3) Declining population: Geezertown
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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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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.]
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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The simplest Malthusian model
Production function:
(1)
Yt = F(Lt ; Tt)
Where L = population, T = land (terra), wt = wage rate, no
technological change
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
Malthus with technological change
Assume Cobb-Douglas production function:
(6) Yt  At L t T 1t 
Taking logarithmic derivative:
(7) gY  g A   g L  g A   g ( wt )
And per capita output growth is:
(8) gY / L  g A  (  1) g L  g A  (  1) g ( wt )
Note that gY / L > 0 if T.C. strong enough, i.e., g A  (1   ) g ( wt )
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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Immigration
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What are the
macroeconomic
effects of
immigration?
Alfred Stieglitz
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W/P
We now go back to labor
and capital, F(K,L)
Real wages and MPL:
graphics
(W/P)*
MPL
L*
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L
W/P
L*
Output = sum of the slices
of MPL from 0 to L*
MPL
L
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L*
Calculus of marginal and total product
Total product = sum of marginal products up to input level.
Y  F(K , L*) 
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L*
L*
0
0
 MPL(L)dL   [F(K , L) / L]dL
Neoclassical distribution of
output/income
W/P
*More generally,
all non-labor
income
Capital
income*
Can reverse axes
and get analogous
results for capital.
(W/P)*
Total wages
MPL
L*
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L
W/P
(W/P)1
Effect of immigration
E1
E2
(W/P)2
Assume immigrants are
perfect substitutes for L
Results:
1. Wage rate falls.
2. Output and national
income rise.
3. Capital income rises.
4. More generally, income of
substitutes fall and
complements rise.
5. Empirical studies suggest
that low-skilled and
Hispanic workers are hurt
by Mexican immigration.
MPL
L*
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L
National Academy of Sciences study
(The New Americans)
“Immigration over the 1980s increased the labor supply of all
workers by about 4 percent. On the basis of evidence from the
literature on labor demand, this increase could have reduced
the wages of all competing native-born workers by about 1 or
2 percent. Meanwhile, noncompeting native-born workers
would have seen their wages increase…”
“Based on previous estimates of responses of wages to changes
in supply, the supply increase due to immigration lowered
the wages of high school dropouts by about 5 percent…”
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Carrying capacity
The idea of carrying capacity
Cohen’s description
Link to Malthus
Population externalities
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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
1.
2.
3.
4.
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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Population externalities
Cohen discusses the idea that children have externalities.
What might these be?
- Pecuniary externality (like immigration)
- Negative (crowding, use of resources)
- Positive (Einstein effect)
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Initial equilibrium
Real
wage (w)
S
w*
MPL
L
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Impact of additional population
Real
wage (w)
S
S’
w*
w*’
MPL
L
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Congestion externalities of
population
Real
wage (w)
S
S’
w*
w*’
SMPL
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PMPL
L
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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Demographic transition
G.T. Miller, Environmental Science
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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
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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
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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 *
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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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•
•
•
•
Bank panics and the U.S. economy of 2007-2009
Steroid equilibrium in sports
Cheating equilibrium (or corruption)
Epidemics in public health (e.g., Ebola)
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.”
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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