Group Title: Working paper - International Agricultural Trade and Policy Center. University of Florida ; WPTC 06-03
Title: Future of global warming : will it be pollution eliminating technology of environmental catastrophe?
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Title: Future of global warming : will it be pollution eliminating technology of environmental catastrophe?
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I ional Agricultural Trade and Policy Center


WORKING PAPER SERIES


'V


UNIVERSITY OF

SFLORIDA
Institute of Food and Agricultural Sciences


THE FUTURE OF GLOBAL WARMING: WILL IT BE
POLLUTION ELIMINATING TECHNOLOGY OR
ENVIRONMENTAL CATASTROPHE?

By
Ram Ranjan
WPTC 06-03 March 2006









INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER


THE INTERNATIONAL AGRICULTURAL TRADE AND POLICY CENTER
(IATPC)

The International Agricultural Trade and Policy Center (IATPC) was established in 1990
in the Institute of Food and Agriculture Sciences (IFAS) at the University of Florida
(UF). The mission of the Center is to conduct a multi-disciplinary research, education and
outreach program with a major focus on issues that influence competitiveness of specialty
crop agriculture in support of consumers, industry, resource owners and policy makers.
The Center facilitates collaborative research, education and outreach programs across
colleges of the university, with other universities and with state, national and
international organizations. The Center's objectives are to:

* Serve as the University-wide focal point for research on international trade,
domestic and foreign legal and policy issues influencing specialty crop agriculture.
* Support initiatives that enable a better understanding of state, U.S. and international
policy issues impacting the competitiveness of specialty crops locally, nationally,
and internationally.
* Serve as a nation-wide resource for research on public policy issues concerning
specialty crops.
* Disseminate research results to, and interact with, policymakers; research, business,
industry, and resource groups; and state, federal, and international agencies to
facilitate the policy debate on specialty crop issues.









The Future of Global Warming: Will it be Pollution Eliminating
Technology or Environmental Catastrophe?



Ram Ranjan
Postdoctoral Associate
International Agricultural and Trade Policy Center
Department of Food and Resource Economics, University of Florida
Email: rranian(@),ifas.ufl.edu, Ph: (352) 392 188-326; Fax: (352) 392 9898





Selected Paper to be presented at the 3d World Congress ofEnvironmental and
Resource Economics




Abstract

This paper looks at the role of risk perceptions in influencing public policy related to
global warming. In a global optimization framework, the choice between investment in
pollution-eliminating technology and other carbon mitigating polices is shown to be
influenced by the degree of probability weighing of the participating nations. Two main
issues are considered. First, the extent of mitigation efforts such as investment in research
related to technological breakthrough, abatement and emissions is derived for a globally
optimizing manager. Second, the same question is addressed in light of the possibility
that nations may differ in their risk perception over the extent of damages from global
warming and therefore would take differential steps for mitigation. In case of a globally
optimizing manager, relative risk perceptions over catastrophe and technological
breakthroughs lead to substantial difference in policy choices as compared to a case when
risks are not weighed at all. For instance, if the manager fears a high risk of catastrophic
event in future following which later technological breakthroughs may become useless,
his optimal action is to minimize investment in such research efforts. Differential risk
perception is also shown as a possible cause for failure of coordination between rich and
poor nations.










Introduction

Global warming is becoming a cause of greater concern for policy makers with an

increase in the frequency of natural hazards such as hurricanes and melting of polar ice

caps that are supposedly correlated with it. While scientific evidence related to the

causes of global warming increasingly points towards man made emissions, the question

of how and how much effort to put towards mitigation and technology development still

needs to be tackled. One crucial question is over the timing and extent of damages from

global warming. Catastrophic outcomes such as a rise in the sea level, breakdown of the

thermohaline circulation belts, etc. have been predicted to happen with a crossing over of

the thresholds for accumulated atmospheric carbon. Yet, it may be possible to avoid such

disastrous consequences through a combination of available mitigative and adaptive

tools. Pollution eliminating technology is one possibility that holds tremendous potential

for reducing the hazards of global warming significantly. However, most of such efforts

would come at a cost to the society in terms of forgone consumption, plus the uncertainty

associated with the investment in discovery of new technology could be daunting.

Consequently, risks of failed investments and of catastrophes play a crucial role in

decision making. However, significantly important than the actual risks is the perception

of such risks borne out by the ambiguity associated with the science of global warming.

A lot of work has been done on comparing the costs and benefits of global

warming mitigation efforts, optimal risk reduction policies and predicting the risks of

damages (Keller et al. 2005, Kelly and Kolstad 1990, and the references therein). Some

approaches have also involved exploring international cooperation to jointly mitigate

global warming through carbon abatement and sequestration (Nordhaus and Yang 1996,









Yang 2003, etc.). Reis (2001) has looked at the possibility of pollution-eliminating

technological breakthrough in an endogenous growth model. Gjerde and Kverndokk

(1999) look at the role played by possibility of catastrophe in shaping optimal abatement

policies. Simultaneous consideration of possibility of both events has not been

considered in the literature so far. Further, work related to the impact of public

perception of risks on public policies to combat global warming has been devoted little

attention. Yet, it is the public opinion formed through risk perception that is going to

have major say in public policies, as governments would seldom against the interests of

the public they represent, if the public itself does not perceive the risks to be a great

threat. To the extent that public perceptions are reflected in governmental policies, the

strategies implemented to mitigate global warming would differ from normative

approaches that suggest decision making based upon objective evaluation of expected

costs and benefits. While there has been some interest in researching the public

perception of risks related to global warming, this research is still being confined to the

field of behavioral psychology or at best at qualitative levels in mainstream

environmental economics.

Bleda and Shackley (2005) argue that businesses would not change their

perceptions towards climate change until affirmative signals are received consistently for

a long period of time. They further argue that reality is perceived by businesses after

being filtered through a reference frame and is not perceived objectively. Consequently,

'experienced reality' may differ from 'actual reality' due to perceptions which are based

upon their interests, expectations, etc. The interpretations of the signals or experiences

are governed by the frame of reference of the receiver and could be resilient to objective









revisions (Daft and Weick, 1984). It is further argued that direct signals of climate

change may be subject to misinterpretation as isolated weather related signals and thus

could be discarded if re-interpretation of these signals requires significant organizational

changes (Berhout et al 2004). Risk perception could also vary based upon gender, race,

education, sex, political affiliation, nationality, etc. Kahan et al. (2005) mention that

whites are more likely to be less risk averse as compared to minorities to certain types of

risks involving abortion, guns, global warming, etc. This phenomenon often termed as

the 'white male effect' is explained by their more individualistic and anti-egalitarian

lifestyles. For instance, in case of global warming, individuals who see the cut-back on

carbon emissions as a threat to their individualistic life styles are more likely to discount

the available information related to global warming. Whereas, individuals who are

egalitarian in nature would be more willing to accept the possibility of global warming as

they would be more concerned about the intergenerational equity.

While it is not clear how risk perception at the local level amongst these various

groups transforms into a collective societal risk perception over global warming, the

impact of such perceptions on public policies cannot be denied and therefore ignored.

Such risk perception could have significant impact on the success or failure of

international collaboration to mitigate global warming through investment in research

related to technology invention or direct carbon abatement and sequestration polices.

The approach in this paper involves modeling the risk of catastrophe and chance

of technological breakthroughs as a Poisson process whose hazard rates are influenced by

the accumulated stock of atmospheric carbon and stock of research in pollution

eliminating technology. In a dynamic programming framework, the total inter-temporal









benefits following a catastrophe or a technological breakthrough are solved for and then

integrated back into the main objective function that seeks to maximize the long term

expected benefits from being in all the possible states of the world. The choice variables

include level of emissions, abatement efforts and the level if investment in research. The

weighing of probabilities is modeled as an inverted s-shaped function following the

literature on risk weighing in behavioral economics.

Following the above approach, two main issues are addressed. First, the extent of

mitigation efforts such as investment in research related to technological breakthrough,

abatement and emissions is derived for a globally optimizing manager whose risk

perceptions reflect those of the collective perceptions of the society. Second, the same

question is addressed in light of the possibility that nations may differ in their risk

perception over the extent of damages from global warming and therefore would take

differential steps to mitigate it. In case of a globally optimizing manager, relative risk

perceptions over catastrophe and technological breakthroughs lead to substantial

difference in policy choices as compared to a case when risks are not weighed at all. For

instance, if the manager fears a high risk of catastrophic event in future following which

later technological breakthroughs may become useless, his optimal action is to minimize

investment in such research efforts. This is because later technological breakthroughs are

of no use if a catastrophe happens before them. This highlights the role of risk

perception. A globally coordinated effort when participants tend to weigh the probability

of catastrophes differentially may differ significantly from one where uniformity in risk

perception is assumed. Yet, it is an issue of great practical concern in view of difficulties

faced in coming to a common consensus over the extent of carbon mitigation and other









steps required to expedite pollution eliminating technological breakthroughs. In a global

optimization framework, the choice between investment in pollution-eliminating technology

and other carbon mitigating polices is shown to be influenced by the degree of probability

weighing of the participating nations. Differential risk perception is also shown as a possible

cause for failure of coordination between rich and poor nations to come to terms over an

agreeable carbon mitigation plan.



Model

The modeling approach involves incorporation of risks of global warming related

catastrophes as being endogenous to the stock of carbon accumulated in the atmosphere

and then exploring optimal combination of abatement, research and emissions paths to

influence this stock of carbon. The probabilities of catastrophe and that of discovery in

technology is modeled as a Poisson process. The stock of carbon in the atmosphere

evolves as:

(1) s =e-a-&s

Where e is the emissions per period and a is the abatement of carbon. Stock of carbon

has a natural rate of decay which is governed by the rate at which it gets assimilated into

the deep oceans. Society can also make investment i in research to discover pollution

eliminating technology which would lead to no further stock accumulations. This

investment is considered to be worthwhile, given the possibility of catastrophic changes

in the earth's climate caused by high concentrations of atmospheric carbon. The

possibility of a pollution-eliminating technological breakthrough is modeled as a Poisson

process, characterized by its hazard function:









(2) =a log(i)

where p is the instantaneous probability of a technological breakthrough given that it has

not occurred in the past. The hazard rate is a function of the level of investment in

technological research (i). The methodology used for modeling the probability of

breakthrough and catastrophe in this system is that of a Poisson process, based upon the

work of Clarke and Reed (1994), Reed (1988) and Reed and Heras (1994). Further,

Knowler and Barbier (2005) have applied this approach to model invasive species

management under uncertainty. The probability density function of this technological

progress is given as:

(3) f(p) = pexp(-p(t))

The possibility of a catastrophic change in earth's climate is modeled as a Poisson

process too, characterized by its hazard function :

(4) q = plog(s)

In the above equation c is the instantaneous probability of a catastrophe given that it has

not occurred in the past. The hazard rate is function of the stock of carbon already

accumulated into the atmosphere. The probability density function of this possibility is

given by:

(5) f(q) = exp(-q(t))

In the event of a catastrophe, society suffers damages, d(s) per period for all times to

come. Society's problem is to maximize the expected sum of values in the states

characterized by neither invention nor catastrophe, invention (with the possibility of a

catastrophe) and catastrophe as:









(6) E(v0) + E(v) + E(v2)

where vO is the discounted sum of profits received by society before either a

technological change or a catastrophe happens. vl is the discounted sum of value

received by society in the event of a technological break-through and v2 is the discounted

sum of value received in the event of a catastrophic collapse of the earth's atmosphere

before a breakthrough in technology. The three terms can be further defined as:


(7) vO= (b(e) -c(a) -c(i) -d(e))exp(-rt)dt


In the simplest case when technological change is of the nature that it also eliminates the

possibility of future catastrophe besides eliminating pollution, the value function vl, after

the technological change can be defined as:


(8) vl = jb()exp(-rt)dt, where e is the level of emissions that maximizes societal
0

benefits. Note that, emissions however would not accumulate into the atmosphere, thus,

obviating the need for any abatement. The above formulation is for a case where the

technological change happens at the beginning of time period. The value function after

the occurrence of a catastrophe is defined as:


(9) v2= d(s)exp(-rt)dt, where s is the level of carbon accumulated into the
0

atmosphere. Now, let t be the time when a technological change occurs. Then the value

to the society before such an event occurs is given by:


(10) vO = p exp(-p(t))exp(-q(t))(b(e) c(a) d(e) c(i))exp(-rt)dt ,
o o

where p exp(-p(t)) exp(-q(t)) is the probability that the technological change happens at








time t and the environmental catastrophe happens after time t. After integration by parts,

this can be further written as:


(11) vO = exp(-p(t) q(t)) (b(e)- c(a) d(e) c(i)) exp(-rt)dt
0 P(t) + q(t)

Similarly, if t be the time when a catastrophe occurs, and a technological change happens

after time t, then the value to the society before such an event is given by:


(12) vO = j exp(-q(t))exp(-p()) ((e) c(a) -d(e) c(i))exp(-rt)dt where
Lo o Jo

q exp(-q(t))exp(-p(t))is the probability that the environmental catastrophe happens at

time t, and the technological change happens after time t. After integration by parts, this

can be further written as:


(13) vO = f exp(-p(t) q(t)) (b(e)- c(a)- d(e)- c(i)) exp(-rt)dt
0 P(t) + 4(t)

Therefore, the expected value to the society, before any of the two events occur is given

by:


vO = p exp(t q(t)) (b(e) c(a) d(e) c(i)) exp(-rt)dt +
(14) exp(- (t)- + (t)
exp(- p(t) q(t)) (b(e) c(a)- d(e) c(i)) exp(-rt)dt
{0 p(t) + c(t)

After simplification (14) can be further re-written as:


(15) vO = exp(-p(t) -q(t))(b(e) c(a) d(e) c(i))exp(-rt)dt


Similarly, vl and v2 can be defined as:










(16) vli= pexp(-p(t))exp(-rt)dt
0 r

The equation of motion for atmospheric carbon accumulation after the technological

innovation is given by:

(17) s = s


(18) v2 = d(s)cexp(-q(t))exp(-rt)dt
0


= s(t)2 q exp(-q(t)) exp(-rt)dt
0

= (t)2 exp(-rt)dt = s(T)2 exp(-t)2 exp(-rt)dt = s(T)
o o r+23

where T is the time of collapse

Society's problem is to maximize the sum of vO, vl & v2 given the constraints posed by

the equations of motion for carbon stock and the hazard functions for technological

discovery and the environmental catastrophe. The current value Hamiltonian is given by:

b(e)
exp(-p(t) q(t))(b(e) c(a) d(e) c(i)) + )p exp(-p) d(s)c exp(-q) +
(19) r
S(-e a &s) + Aalog(i) + AJ3 log(s)

Where 1, A2,and A3 are the shadow prices of stock of carbon, stock of cumulative

probability of invention and stock of cumulative risk of catastrophe. One would expect

the shadow prices, A, and A3 to be negative as they are 'bads'. First order conditions

w.r.t.:

(20) e => b'(e) d'(e) exp(-p q) + A1 0

(21) a=> -c'(a)exp(-p-q) -A =0










(22) i=> -c'(i)exp(-p q) + -+ vl exp(-p) 0
i i

The first order conditions require dedication of emissions, abatement and investment

efforts to a point where there marginal utility equals their shadow prices. This ensures

long term optimization of the societal benefits.



More interpretation of the shadow prices themselves could be had from observing their

equations of motion over time. No arbitrage conditions are given by:


(23) =r -(- d'(s) exp(-q) d'(s) exp(-q) + 3)
r r s s

(24) = rA, + exp(-p(t))(b(e) c(a) d(e) c(i))vlp exp(-p)


(25) A = rA3 + exp(-q(t))(b(e) c(a) d(s) exp(-q)
r

Rate of growth of shadow price of stock of carbon is positively related to the stock of

damages as given by equation (23). It is also negatively influenced by the shadow price

of stock of cumulative hazard rate. This should be obvious as a higher A3 would imply a

higher risk of catastrophe which would require 4 to be lowered for adequate

optimization. Shadow price of invention chances, as given by (24) above grow positively

with an increase in vl as an increase in value after invention would make postponing it

costlier. Finally, (25) presents the growth path for shadow price of cumulative risk of

catastrophe as increasing in stock of carbon, which is again obvious.

Alternate scenarios:

While the above model assumed simplification in terms of post-breakthrough or

catastrophe scenario, it is possible for catastrophe to take place even after a technological









breakthrough or a breakthrough to take place after a catastrophe. Consider a case when

technological change leads to elimination of pollution but does not eliminate the risk of

catastrophe. vO and v2 remain the same as before however vl is now redefined as:

o- s(T)72 1
(26) vl = p exp(- p) b(e) exp(q(t)) exp(-rt)dt + f exp(-q(t)) exp(-rt)dt
Sr+2

Another situation is where catastrophe does not eliminate the possibility of technological

change later on. Under this scenario, vO remains the same as before, vl is given by the

above equation and v2 is now redefined as:

(27)


v2= { exp(-q) {-d(s)exp(p(t))exp(-rt)dt + ) exp(-p(t))exp(-rt)dt
r

We will consider these possibilities for detailed exposition in the numerical simulation

section. So far we have not incorporated the probability weighing aspect in the

optimization problem. In the next section we look at how collective weighing of risks

could be incorporated to be reflected in the risk weighing by the global planner or a

country level planner.


Subjective Weighing of Risks

We now add the behavioral economics element into the model. Based on

accumulated evidence in economics and psychology literature (see summary in Hurley

and Shogren, 2005), assume the planner assigns higher weights to low probabilities of an

event and lower weights to high probabilities of the same event (also see Starmer, 2000).

We add these weights to the hazard rate p(x), which represents the probability of the

event happening at time t, given that it did not happen previously. Let the weighing









function follow an inverse S-shape. Following Prelec (1998), we use a two-parameter

weighting function

(28) w(p) = e (-1np)

where 0 is the parameter that primarily determines elevation, and y is the parameter that

primarily determines curvature. Elevation reflects the inflection (reference) point at

which a person switches from overestimating low probability events to underestimating

high probability events, i.e., the degree of over- and underestimation; curvature captures

the idea that people become less sensitive to changes in probability the further they are

from the inflection point (Tversky and Kahneman, 1992; Gonzales and Wu, 1999).

Depending on the values of 0 and y the path of the hazard rate can differ from the

traditional expected utility model. By adding a subjective weighing that discounts high

probabilities, a planner cares less about high risks of loss. The inflexion point of the

inverted s-shaped curve is critical and can only be determined empirically. Weighing of

hazard rates implies that predominance is given to the probability of the event happening

at time t, given they would survive until that time. In an exponential distribution, this

hazard rate is constant (but could be endogenous). Figure below shows the subjective

weighing of hazard rates.

INSERT FIGURE 1 HERE


Numerical Simulation:


We perform numerical simulations with hypothetical parameters to study the evolution of

optimal control policies. Choice of parameters reflects the non-linearity involved with

various costs and benefits functions. Figure 2 shows the value functions before









breakthrough or catastrophe (vO), after breakthrough (vl) and after catastrophe (v2).

Note that the value function after technological breakthrough (vl) is lower than one

before either of the events (vO) as the former is weighed by the probability of a

technological breakthrough. Also, the value after a catastrophe has negative value all

throughout due to damages from accumulated stock of carbon in the atmosphere.

INSERT FIGURE 2 HERE

Figure 3 shows the survival probabilities (or the probability of surviving until a given

time) for environmental catastrophe. The base case scenario predicts the lowest survival

probability for any given time period. Survival probability increases with an increase in

perceived chance of technological breakthrough. Due to a high chance of technological

breakthrough, emissions actually increase substantially initially (as shown in Figure 4).

When risk perception is high over catastrophe or over both catastrophe and technological

breakthrough, survival probability from catastrophe is pushed even farther up. This is

primarily achieved through increased abatement and reduced emissions compared to the

earlier cases. When the risk of future catastrophe remains even after a technological

breakthrough (as specified in equation 26), the survival probability is the highest which is

achieved through very high level of abatement compared to the rest of the cases.

INSERT FIGURES 3 ,4 and 5 HERE

Investment in technological research is highest in the base case, and lowest in the cases

when the perceived risk of a breakthrough is higher. When the perceived risk of a

catastrophe is higher, the investment is lower than the base case, which seems

counterintuitive. However, this anomaly is due the comparative costs and their

effectiveness of various control options that have been assumed. Note that investment in









research falls drastically with an increase in the risk of catastrophe as a catastrophe would

negate all the investment towards technological breakthrough if technological

breakthrough happens after the catastrophe. This highlights a very important challenge

to policy formulation related to investment; a very high perceived risk of catastrophe may

discourage investment in discovery of technology that could become ineffective after the

catastrophe. This of course is related to the nature of catastrophe that follows a crossing

of the environmental threshold for atmospheric carbon. Sharp shifts in the environmental

balance, (such as a rapid rise of the sea level) may render pollution -eliminating

technology useless as the focus may shift towards adaptive measures. When the

technological breakthrough is of the nature that sucks out accumulated carbon from the

atmosphere, thus helping revert back the catastrophic consequences of a threshold

breaching, investment in such research would be encouraged. However, it is unlikely

that a rise in the sea level or a break down of the thermohaline circulation belt could be

reverted back. Consequently, such possibilities are negligible.

INSERT Figure 6 HERE

Figure 7 shows the possibility of a technological breakthrough which is highest in the

base case and increases as the risk of catastrophe increases. In case when the risk

perception is high for the both the events of breakthrough and catastrophe, the risk

perception over catastrophe dominates.

INSERT FIGURE 7 HERE


Case of Two Countries with Differential Risk Perception

Consider now that there are two countries (developing and developed) that differ in their

risk perception over the catastrophe and also over the probability that a pollution









eliminating technology could be discovered in the near future. The developing country

has lower benefits from emission, higher damages from catastrophe, higher costs of

abatement and investment in technology.

Figure 8 shows the emission paths of the two countries when their welfare is

jointly managed by a global optimizer who assigns equal weights to both of them.

Emissions of the developed country are higher than those of the developing country due

to their higher benefits from emissions. This maintains even as the risk perception of a

catastrophe is high. However, abatement by the developed country too is higher than the

developing country as determined by its low relatively lower costs of abatement. This is

shown in figure 9 below.

INSERT 8 and 9 HERE

The developed country also makes higher investment in research for technological

breakthrough as shown in figure 10. However, this is not always the case as it turns out

that risk perception can alter the roles of the two sides. When the risk perception over

catastrophes for the developing world is higher and the globally optimizing planner

assigns a slightly higher weight to its welfare (w=.6) as compared to the developed world,

the investment patterns change dramatically. It is now the developing country that is

taking more investments in research all throughout.

INSERT FIGURE 10 HERE

Conclusion

Quite a few key results emerge from the above analysis. While the tradeoff between

abatement efforts, reduction of emissions and investment in research is obviously linked

to their relative costs and benefits, some results are more highlighted than others.









Consider the influence of high perceived chance of technological breakthrough, which

leads to both higher emissions and abatement as compared to the base case. Whereas,

when catastrophic risks are hard to eliminate (continued risks case), the situation

obviously warrants highest levels of abatement. Similarly, if risk perception over

catastrophe is very high, it might discourage investment in pollution eliminating research

if breakthroughs after catastrophe are deemed to be useless. International cooperation is

heavily influenced by how welfare of countries is weighted in the global scheme and how

different countries perceive the risks of catastrophe.

It would be highly desirable to understand the risk perceptions of different

countries and their hopes over future pollution-eliminating technological advances. It is

also possible that weighing of probabilities over these key events is used as a strategic

tool to while negotiating deals over emissions reductions between nations. For instance,

by pretending that a country does not actually believe in the risks of catastrophe, it could

extract out a much milder emissions plan as compared to other nations.









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Appendix


Functional Forms and Parameter Values for the Global Planner Case:


Benefits from emission b0e + ble2 bO = 5, bl= .5



Cost of abatement cOa + cla2 cO =.2,cl =.5



Cost of innovation cOi + cli2 cO = 1, cl = .5



Damages from emissions dOe + dle2 dO =.5,dl =.01



Damages from stock s2 (t) -s2 (t)



Hazard function for c = p log(s(t)) = .05
catastrophe


Hazard function for p = a log(2.71828 + i(t)) a = .05
technological breakthrough


Weighing of Catastrophic risks -02(-log(alog(2.71,2+, 2 02= .5 y2 = .5
(high risk perception of
catastrophe case)

Weighing of technological -e1(-log(alog(2.7121+ .1 1111 yl = .5 01 = .5
possibilities
(high risk perception of tech.
breakthrough case)
Discount rate r .1









Initial value of hazard rate pO .1



Initial value of hazard rate qO .1



Initial value of stock of carbon sO 30



Decay rate of stock of carbon 6 .001




Parameters for the two country case:

Parameters Country -Developed Country--Developing




Benefits from emission bO = 7, bl =.9 bO = 5, bl =.5




Cost of abatement ca0 =.2, cal =.2 ca0 = .5,cal = .5




Cost of innovation ciO =. 1, cil =. 5 ciO = .2, cil =.7




Damages from emissions dO= 5,dl =.01 dO= 7,dl= .05









Damages from stock s2 (t) s2 (t)




Hazard function for c = log(s(t)) = .05
catastrophe



Hazard function for p = alog(2.71828 + i(t)) a = .05
technological breakthrough



Weighing of Catastrophic risks -82(-log(alog(2.71828+i(t)))2 02 = 1 y2 = 1
(base case)



Weighing of technological -81(-log(alog(2.71828+i(t))))Y1 y = 1 O1 = 1
possibilities
(base case)


Weighing of technological yl = .4 01 = .4 yl = .4 01 = .4
possibilities and catastrophe
(high chance oftech. 02 = .99 72 = .99 02 = .99 72 = .99
breakthrough)

Weighing of technological yl = .9 01 = .9 yl = .9 01 = .9
possibilities and catastrophe
(w=.6 and high perception of 02 = .99 /2 = .99 02 = .4 y2 =.4
catastrophe by the developing
country)








Figure 1: Inverted S-Shaped Weighing of Probability of an Event


Weighted Probability

1\


Probability


0.2 0.4 0.6 0.8


Note: Parameters in the function: w(p) = e ( lnp) 0 .5, y


0.O















Figure 2: Value Functions under Base Case


6 --*-v0(t)--value before either event takes place
-m--v1(t)--value after a tech. breakthrough

5 ^ v2(t)--value after a catastrophe


4


3


2








1T
-1


-2


-3

Time










Figure 3: Survival Probability of Catastrophe


1 11 21


Time













Figure 4: Time Path of Emissions


--e(t)--base case

-- e(t)--high risk perception of catastrophe

e(t)--high perception of chance of breakthrough

e(t)--high risk perception over both events


Time


1











Figure 5: Time Paths of Abatement Efforts


25




20




15




10 -




5


--a(t)--base case
-*-a(t)--high risk perception of catastrophe
a(t)--high perception of chance of breakthrough
a(t)--high chance of both events
-- continued-risk-unweighted


1 2 3 4 5 6 7 8

Time
















Figure 6: Time Path of Research Investment





35

--i(t)--base case

3 -l-i(t)--high risk perception of catastrophe
i(t)--high perception of chance of breakthrough

2 5 i(t)--high chance of both events



2 -



15







05



0-
1 21 41

Time














Figure 7: Probability of Technological Breakthrough over Time








0.9
-*-exp(-p(t))-high perception of chance of technological breakthrough

0.8 -U-exp(-p(t))-high perception of risk of catastrophe

exp(-p(t))--base case

0.7 exp(-p(t))-high risk perception over both events



0.6



0.5



0.4 -



0.3



0.2



0.1
1 21

Time












Figure 8: Emissions-Two Countries






0.95


0.85


0.75


0.65


-*-developing country (base case)


-u-developed country (base case)


developing country (high risk perception of tech. breakthrough)


developed country (high risk perception of tech. breakthrough)


5

Time


0.55


0.45


0.35


0.25-


0.15


0.05


-0.05 1


9













Figure 9: Abatement-Two Countries


-*-developing country (base case)

c- -*-developed country (base case)

developing country (high risk perception of tech breakthrough)

developed country (high risk perception of tech breakthrough)




















i i ^ ^ < ^ ^ ^ ^ ^ ^ ^ ^ ^ < ^ >


Time














Figure 10: Investment: Two Countries


-*-developing country (base case)
-*-developed country (base case)
10 developing country (high perception of tech breakthrough)

developed country (high perception of tech breakthrough)
-- developing country (w=.6,high risk perception of catastrophe for developing world)
8 --developed country (w=.6, high riskperception of catastrophe for the developing world)


1 21 41 61

Time




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