Econ 331a. Economics of Energy, Resources, and Climate Change

William Nordhaus

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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

Course introduction

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http://www.econ.yale.edu/~nordhaus/homepage/Energy2014.htm

TOPICS

Tentative Course Topics. • 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 4

Requirements

Course requirements are the following:

• 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:

- 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 demographyFriday 29: Production theory, Malthus, immigration

Monday 1: no classWednesday 3: Carrying capacity, SolowFriday 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 12

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(1) Malthusian

(2) The Mozart effect

Note increase in absolute number of Mozart-scale geniuses as population size increases.

Measure of geniusMozart level

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*“If I could re-do the history of the world, halving population size each year fromthe beginning of time on some random basis, I would not do it for fear of losing Mozart in the process.” Phelps, “Population Increase”

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(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

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 ideas.]

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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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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:

Population dynamics (3) and subsistence assumption (4):

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(3) / / / / / ( ) t t t t t t t t tL L L t L B L D L g w

/ ( ), ( *) 0, '( ) 0t t tL L g w g w g w (4)

(3) / / / / / ( )t t t t t t t t tL L L t L B L D L g w

(2) /t tw Y L

n (population growth)

Wage rate (w)

0

w* (Malthusian subsistence wage)

n=n[w]

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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?

- 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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L

Real wage (w)

MPL1

Malthus in the neoclassical production model

L1*

w*S

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L

Real wage (w)

MPL1

Malthus in the neoclassical production model

L1*

w*

L2*

MPL2

S

Malthus with technological change

Assume Cobb-Douglas production function:

This is the major anti-Malthus theorem: Rapid technological change can outstrip population growth even in the subsistence version.

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1

/

/

(6)

Taking logarithmic derivative:

(7) ( )

And per capita output growth is:

(8) ( 1) ( 1) ( )

Note that > 0 if T.C. strong enough, i.e., (1 ) ( )

t t t t

Y A L A t

Y L A L A t

Y L A t

Y A L T

g g g g g w

g g g g g w

g g g w

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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L

W/P

MPL

We now go back to labor and capital, F(K,L)

Real wages and MPL: graphics

L*

(W/P)*

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L

W/P

MPL

Output = sum of the slices of MPL from 0 to L*

L*

L*

Calculus of marginal and total product

Total product = sum of marginal products up to input level.

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* *

0 0

( , *) ( ) [ ( , )/ ]L L

Y F K L MPL L dL F K L L dL

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L

W/P

MPL

Neoclassical distribution of output/income

L*

(W/P)*

Total wages

Capitalincome*

*More generally, all non-labor income

Can reverse axes and get analogous results for capital.

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L

W/P

MPL

Effect of immigration

L*

(W/P)1

(W/P)2

E1

E2

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.

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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…”

Carrying capacity

The idea of carrying capacityCohen’s descriptionLink to MalthusPopulation externalities

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Background on carrying capacityOriginates in range/wildlife management.

Populations characteristically increase in size in a sigmoid or S-shaped 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.) 36

Logistic curve

Idea is that there is some maximum population, K.Actual approaches as a sigmoid or logistics curve:

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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[ ],

where K is maximum sustainable population,

or carrying capacity.

t t tL rL K L

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:

38Source: J. Cohen, “Population Growth…,” Science, 1995.

Alternative methods for estimating carrying capacity

1. Assume a maximum population density2. Extrapolate population trends. 3. Single factor model (e.g., food supply)4. Single factor as function of multiple inputs 5. Multiple factor constraints (P < β water; P < γ food;

…) 6. 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.:

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:

Which means that carrying capacity grows at 40

/ [ ], where is the earth's carrying capacity. t t t t tL L r Z L Z

, where is a productivity parameter. t tZ L

1/ (1 )/ * / *

t t t tY L w Z A w

/ [1 / (1 )] [1 / (1 .67)] Z A Ag Z Z g g

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

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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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L

Real wage (w)

MPL

Initial equilibrium

S

w*

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L

Real wage (w)

MPL

Impact of additional population

S

w*

S’

w*’

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L

Real wage (w)

PMPL

Congestion externalities of population

S

w*

S’

w*’

SMPL

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:- 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:

4. Labor supply:

* 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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/dK dt K sY K

/ n = exogenousL L

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k

y = Y/L

y = f(k)

(n+δ)k

y*

i* = (I/Y)*

k*

i = sf(k)

* ( *) ( ) *k k sf k n k

Demographic transition

G.T. Miller, Environmental Science 49

Current demography

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-1

0

1

2

3

4

5 6 7 8 9 10 11

ln per capita income, 2000

Pop

ula

tion

gro

wth

, 200

7 (%

per

yea

r)

n (population growth)

Per capita income (y)

0

y* = (Malthusian or subsistence wages)

n=n[f(k)]

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Unclear future trend of population in high-income

countries

Growth dynamics with the demographic transition

Major assumptions of standard model1. Full employment, flexible prices, perfect competition, closed

economy2. Production function: Y = F(K, L) = LF(K/L,1) =Lf(k)3. Capital accumulation: 4. Labor supply:

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)

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( ) [ ( ) ]

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

/dK dt K sY K

/ n = exogenousL L

k

y = Y/L

y = f(k)

k***

i = sf(k)

k**k*

Low-level trap

n[f(k)]k

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High-level equilibrium

* ( *) [ ( *) ] *k k sf k n f k k

k

k***k**k* 54

“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 (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

57Frank 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.”

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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k

y = Y/L

y = f(k)

k***

i = sf(k)

The Big Push in Economic Development

{n[f(k)]+δ}k

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