Assume the following continuously compounded growth rates for use in the Kaya Id

Question

Assume the following continuously compounded growth rates for use in the Kaya Identity:
p = 0.00747
a = 0.0317
EI = -0.0233
CI = 0.000984
C2010 = 8 GtC
(a) Using the base case rates above, in what year will annual carbon emissions reach 20 GtC?
(b) Suppose a commitment is made to reduce carbon intensity at a continuous rate of 2% with all other rates as in the base case. What would annual carbon emissions be in 2050?
(c) Choose one term in the Kaya Identity, and write one or two sentences defining it and explaining what the sign of its rate of change means.

Explanation / Answer

(a)
CO2 Emissions, F = Population * (GDP/Population) * (Energy/GDP) * (CO2 /Energy)

p = world population
a = GDP/population
EI = energy intensity of world GDP
CI = carbon intensity of energy

Continuously compounded growth rate
rp = 0.00747
ra = 0.0317
rEI = -0.0233
rCI = 0.000984

continuously compounded growth rate of CO2 emission, rF = rp +ra +rEI +rCI=
0.00747+0.0317-0.0233+0.000984 = 0.016854

At time t, Ft = F0*exp(rF*t)
F0 = 8GtC, Ft = 20GtC
t = 1/rF*(ln(Ft/F0))=1/0.016854*(ln(20/8))=54.4yr
So year = 2010+54.4=2064.4 year the carbon emission reaches 20Gtc

(b)
(b) Suppose a commitment is made to reduce carbon intensity at a continuous rate of 2% with all other rates

as in the base case. What would annual carbon emissions be in 2050?

rCI = - 0.02

continuously compounded growth rate of CO2 emission, rF = rp +ra +rEI +rCI=
0.00747+0.0317-0.0233 - 0.02 = -0.00413

At time t, Ft = F0*exp(rF*t)
F0 = 8GtC, t = 2050-2010=40yrs
Ft = F0*exp(rF*t) = 8*exp(-0.00413*40)=6.78GtC

(c) Choose one term in the Kaya Identity, and write one or two sentences defining it and explaining what the

sign of its rate of change means.

CI is carbon intensity of energy. It is amount of carbon emitted per unit of energy consumed.
The positive sign indicates that the amount of carbon increases as the energy is being utilized.

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