Are we going to survive?

Economic models of endogenous growth and evidence from global population and CO2 emission trends

2Andreas HueslerCCSS, 2009-10-24

Outline

Introduction

Economic Model I: IPAT Economic Model II: Cobb-Douglas

Conclusions

Discussion

3Andreas HueslerCCSS, 2009-10-24

Current Economic Footprint

Population (in mio)

Ecological Footprint

Biocapacity Ecological Reserve

High Income Countries 972 6.4 3.7 -2.7

Middle Income Countries 3098 2.2 2.2 -0.0

Low Income Countries 2371 1.0 0.9 -0.1

World 6476 2.7 2.1 -0.6

Soucre

: footp

rintn

etw

ork

.org

4Andreas HueslerCCSS, 2009-10-24

Planetary Boundaries

Soucre

: doi:1

0.1

038

/461

47

2a

5Andreas HueslerCCSS, 2009-10-24

ImPACT equation I: impact P: population A:affluence C:consumption T: technology

Economic Model I

CO2=Population×GDP

Population×EnergyGDP

×CO2Energy

Soucre

: doi: 1

0.1

07

3

6Andreas HueslerCCSS, 2009-10-24

Growth

Growth description:

Solving ODE:

dpdt

∝ p1

p t =p0tc−t −

0

0

=0

rel.

gro

wth

7Andreas HueslerCCSS, 2009-10-24

Results I

≈1.67≈1.72

8Andreas HueslerCCSS, 2009-10-24

Results II: Parameter stability

≈1.67

t c=t

9Andreas HueslerCCSS, 2009-10-24

Results II (cont)

10Andreas HueslerCCSS, 2009-10-24

Economic Models II

Cobb-Douglas: Y: output L: labour K: capital A: technology

Solow equation:

Y t =K t ×[ A t Lt ]1−

dAdt

=b K t ×L t ×A t

dKdt

=sY t =s K t ×A t L t 1−

11Andreas HueslerCCSS, 2009-10-24

Coupling ODE I

Assuming labour is proportional to capital (cf Kremer)

we getdAdt

=a' L t ×A t

dLdt

=b ' L t ×A t 1−

K t ≈L t

12Andreas HueslerCCSS, 2009-10-24

Coupling ODE II

Assuming solutions of the form:

Gives us by coefficient matching

A finite-time singularities can be created from the interplay of several growing variables resulting in a non-trivial behavior: the interplay between different quantities may produce an “explosion” in the population even though the individual dynamics do not!.

A t =A0 tc−t −

L t =L0tc−t −

=11−

=2−−

×

11−

13Andreas HueslerCCSS, 2009-10-24

Coupling ODE III

For the cumulative CO2:

=> φ = -δα+κ

Numerical example:α=0.5, β=0.9, θ=0.9, γ=0.1=> δ=2, κ=1.2=> φ = 0.2 (>0, hence explosive)

dCO2dt

=Y t A t

=A0− L0

1×t c−t

−

14Andreas HueslerCCSS, 2009-10-24

Coupling ODE III (cont)

exponential g

rowth

L~K: δ=2

A: κ=1.2

dCO2/dt: φ=0.2

15Andreas HueslerCCSS, 2009-10-24

Conclusions

Dynamics of CO2 emissions can have complicated dynamics

The (non-linear) dynamics can lead to finite time singularities

Any scenario for future CO2 emissions should take econmic and population dynamics into account.

16Andreas HueslerCCSS, 2009-10-24

References

More references available at:http://www.citeulike.org/user/ahuesler

17Andreas HueslerCCSS, 2009-10-24

Reserve ....

18Andreas HueslerCCSS, 2009-10-24

Case Study: Easter Islands (II)

Colonization Rapid Growth Collapse

Carrying Capacity / Resources

Economic Activity / GDP

Population

400 AD 1600 AD 1750 AD

Soucre

: wikip

edia

, Dia

mond, o

wn g

raphic

19Andreas HueslerCCSS, 2009-10-24

20Andreas HueslerCCSS, 2009-10-24

Source: xkcd.com