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GEOENGINEERING

Revisiting the Economics of Climatic Change*

Juan B. Moreno Cruz** and Sjak Smulders***

This version: October 31, 2008

PRELIMINARY AND INCOMPLETE, Please do not quote

Abstract

There is a serious possibility that simple and reversible measures exist that cool global

temperature and could combat global warming at low cost. Spreading SO2 particles in the

atmosphere is the most promising example, but there are other ones. They all involve

intentional large-scale manipulation of the environment, which is labeled

"geoengineering".

We introduce the concept of “geoengineering” into an analytical model of climate

change. Our small partial equilibrium model simultaneously considers mitigation

(traditional abatement policies) and geoengineering.

We model the technical and economic characteristics of geoengineering in line with the

recent geoengineering literature from physical and environmental management sciences.

We interpret the key economic implication of engineering to be its potential to reduce the

temperature-related damages of climatic change. We investigate (i) under which

circumstances geoengineering makes traditional abatement and mitigation strategies

redundant, (ii) whether geoengineering and mitigation are substitutes or complements in

the reduction of damages, and (iii) whether geoengineering allows for postponing

mitigation (“buying time”).

* We thank David Keith, Timo Goeschl, Mark Jaccard, Robert Oxoby, Scott Taylor and participants at the Grenoble Workshop on Innovation and the Environment, the IEW 2007 meeting at Stanford, and the UNU-MERIT research seminar for comments on a previous version. All mistakes remaining are our own. ** Department of Economics and ISEEE-EESG, University of Calgary. jbmoreno@ucalgary.ca . *** Department of Economics, Tilburg University. Department of Economics and ISEEE-EESG, University of Calgary. j.a.smulders@uvt.nl

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1. Introduction

Scientists have recently worked on, discussed, and experimented with several

technologies that can relatively easily alter global environmental systems. Elements of

these technologies, which come under the label of “geoengineering”, have been put in

practice already, e.g. weather modification at a local scale to boost agricultural

productivity. Geoengineering technologies sometimes appear to be taken from a Jules

Verne book: they range from giant mirrors in the space to block the sun to human

volcanoes that mimic the idea of a giant volcano eruption releasing huge amounts of

sulfur into the atmosphere (as Monte Pinatubo did in 1991 with a three-degree-Celsius

cooling effect for two years (A. Robock, 2005, T. M. L. Wigley et al., 2005)). However,

the scientific principles behind geoengineering technologies are well established.

Moreover, on the economics side, it has been suggested that the cost of geoengineering

could be so low compared to traditional mitigation strategies that they will make climate

change irrelevant (D. W. Keith, 2000)

In this paper we analyze the economics of geoengineering and its implications for climate

change policies that follow from what we consider -from the natural sciences literature-

to be the main characteristics of a geoengineering technology. Before answering the

pressing questions about geoengineering implementation, we adjust the model to include

the idea of geoengineering into the traditional elements of economic models of climate

change, where we stress the differences between the stock of greenhouse gases (GHG)

and the effects of this stock on temperature. This turns out to be the most important

difference given the fact that geoengineering technologies could affect global mean

temperature, but cannot do anything about the concentration of GHG in the atmosphere.

Following this discussion we investigate (i) under which conditions we adopt

geoengineering, (ii) once geoengineering is adopted, under which conditions is abatement

redundant, (iii) whether geoengineering and mitigation should be considered as

complements or substitutes, and finally (iv) whether geoengineering allows for

postponing mitigation (“buying time”).

The uncertainties surrounding the implementation of geoengineering, as well as the

ethical questions around large scale manipulation of the environment, have kept

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geoengineering technologies under the radar of the climate change scientific community.

Nonetheless lately, scientists have argued that geoengineering needs to be considered as a

potentially serious player in the climate change arena. The series of commentaries on

Nobel Prize winner Paul Crutzen's article in Climatic Change (P. J. Crutzen, 2006)

revealed the multiple questions surrounding geoengineering. It comes across that

whenever defended, research on geoengineering is only proposed as an insurance against

an abrupt climate change happening in the future (see for example (S. H. Schneider,

1996) and (R. J. Cicerone, 2006)). But before we can discuss the risk and uncertainties

over possible scenarios, we need to know what are the qualitative effects of that will be

common in these scenarios. It is this question on the nature of the economic implications

of geoengineering that we want to address in this paper, which is of independent interest

of (and should be addressed before) the question of insurance.

We define geoengineering as an action in which the primary objective is the modification

of the climate system at a large scale (D. W. Keith, 2000). Although this definition is

broad and apply to several technologies, we have a particular one in mind for the sake of

concreteness, viz. the alteration of the reflectiveness of the stratosphere, aiming to

counter effect the increases in the radiative force (leading to increasing temperature) due

to the increase in CO2 concentrations.1 Given the varying tradeoffs between up-front

costs, effectiveness, and adverse environmental consequences, this technology appears to

be optimal in a scientific sense (M. C. MacCracken, 2006).

From a technology perspective geoengineering is distinct from traditional climate change

mitigation strategies (abatement, for short) because its results are immediate and because

rather than reducing greenhouse gases emissions it reduces the impacts of the

concentration level of these gases in the atmosphere. From an economics perspective, two

characteristics make geoengineering special. First, geoengineering is much less costly

than abatement and a single country could easily undertake enough geoengineering to

protect the entire planet against the damage from global warming. In contrast, traditional

abatement strategies are riddle with international coordination and free-riding problems

(T. C. Schelling, 1996). Second, while the marginal cost of any abatement technology

1 This type of intervention is referred to as Solar Radiation Management, but we will refer to it as geoengineering in general.

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increases exponentially, the cost of geoengineering is almost constant on the amount of

“cooling” that has to be done.

Geoengineering sometimes has the connotation of fixing the climate change problem at

zero (or very low) cost and thus making climate change irrelevant (cf the scenario that

(William D. Nordhaus and Joseph Boyer, 2000) label geoengineering). In contrast, in our

model we acknowledge the fact that geoengineering is not a perfect substitute for

traditional mitigation measures: it does not affect the level of concentration of GHG in

the atmosphere, but cools down the planet and reduces the temperature-related damages,

while other problems derived from GHG concentration are not corrected (i.e. ocean

acidification).

We agree with TML Wigley (T. M. L. Wigley, 2006) on his conclusion that

geoengineering works as an instrument that allows us to buy more time, letting

technology evolve to a point in which investments in abatement are achieved at a

relatively low cost. Our model differs from that of TML Wigley in that he assumes

exogenous trajectories for the climate policy, while in this model the interaction between

geoengineering and abatement is the result of an endogenous dynamic optimal decision.

Barrett (2008) can be seen as the first paper dealing with the economics of

geoengineering. He argues that it is essential to study free-riding issues and governance

systems that deal with the question who should be allowed to start using geoengineering,

when and under which conditions. He shares with the community of scientists and of the

general public that geoengineering is potentially very risky (or even immoral) as it

involves the earth system as a whole. We ignore the free-riding, governance and

uncertainty aspects for now, not because we think they are not important (to the

contrary), but because we think we should first clearly set out the concept of

geoengineering, define its characteristics and explore its fundamental impacts on the

economy before we can deal with the more complex issues mentioned.

The rest of the paper is organized as follows. The next section explains which of the

canonical elements of traditional climate change models needs to be changed in order to

incorporate geoengineering. We then present a simple static model of climate change in

which we analyze the static effects of geoengineering in environmental policy. Finally we

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present a dynamic version of the model in which we analyze the transitional path towards

an environmentally sustainable equilibrium, and we highlight the differences with the

traditional results of the environmental economics literature.

2. How Geoengineering affects the Climate-Economy Link

Geoengineering activities are aimed at reducing the intensity with which the sun warms

the planet. Traditional models of climate change correctly assume that there is a

proportionality factor that correlates concentration of GHG and mean temperature in the

globe. However, once we consider geoengineering we have to disentangle the damages

from temperature (e.g. sea level raise) from those of CO2 concentration (e.g. ocean

acidification), because now the proportionality relation between GHG concentrations and

temperature is affected.

2.1. Damages and Geoengineering Intervention.

Damages caused by increases in temperature come in the form of increased precipitation,

more unpredictable weather patterns and storms, sea-level rise, desertification and loss of

fertile soils, etcetera. The key feature of geoengineering that makes it so promising to

combat climate change problems is that it produces a cooling effect: by increasing

reflectivity (albedo) of the atmosphere, incoming sunlight is reflected back and

temperature on earth is reduced. Hence, geoengineering can undo damages from climate

change. However, this is not to say that geoengineering neutralizes all effects of GHG

concentrations. Although it can keep the temperature below dangerous levels and thus

address climate change damages, it cannot, for example, avoid the effects on the

acidification of the oceans caused by GHG accumulation.

The main impact of geoengineering on the economy therefore involves the damage from

temperature change and other climate-related sources. To clarify our argument, we

specify these damages in a way that separates temperature effects from other effects. In

particular, we assume that damages D depend on greenhouse gas concentration S and

geoengineering G in the following way:

1 2 3( , ) ( ) ( ( )) ( ),D S G d S d T S G d G= + − + (D)

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1 1

2 2

3 3

( )0 for ( ) ; 0;

( )0 for ( ) ; 0;

0, 0, 0.

d S S d

d T T d

d d T

′′′ < > < > >

′′′ < > < > >

′′′ ′> > >

The first term at the right-hand side of (D) represents the idea that CO2 concentrations

have other effects than just on temperature, which are on balance positive for small

concentration levels and negative for large ones (H. D. Matthews et al., 2005). The

positive effects stem from a fertilization effect: more CO2 enhances plant growth and thus

boosts productivity in agriculture2 (A. W. King et al., 1997). The negative effects stem

from acidification of oceans and other ecological disruptions which ultimately harm

productivity of the economy (K. Caldeira and M. E. Wickett, 2005). Since the marginal

fertilization effect is decreasing (M. K. Cao and F. I. Woodward, 1998, A. W. King, W.

M. Post and S. D. Wullschleger, 1997), and the marginal acidification effect is likely to

be increasing in S, we assume a critical level S at which a CO2 increase at given

temperature turns from a benefit into a damage.

The second term at the right-hand side of (D) captures the effect of global warming.

Global average temperature is denoted by T. Excessive increases in temperature (as well

as excessive cooling, i.e. temperature below T ) increase damages. CO2 concentrations

increase temperature, which we interpret as the global warming effect of GHG

accumulation, TS>0, while geoengineering produces a cooling effect, TG < 0.3 By

measuring G in terms of CO2 radiative forcing potential, we may write temperature as a

function of S – G, rather than as a seemingly more general function with S and G as

separate arguments.4 [Our choice of units implies T = Θ(S,G) = Θ(S – G,0) and ΘS = –

ΘG. Further it is understood that the increase in the temperature is more or less

proportional to the increase in radiative force.]

2 An experiment carried out by Govindasamy et. Al. (2002) shows that doubling CO2 increases temperature by 2.42 oK. Reducing solar flux by 4.17 W/m2 reduces temperature by 2.40oK, reduces precipitation by 5.8% and increases global biomass from 631.6 Gt-C to 1212.9 Gt-C . Govidasamy et al 2002 3 Supranote 2. 4 Changes in solar flux and atmospheric CO2 content may be considered to be roughly additive and independent of its effects on NPP. Govidasamy et al 2002.

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The benefits from fertilization are assumed to be lower than the damages caused by the

global warming effect, ( )2 1d T T d′ ′ ′> − , so that GHG accumulation is harmful in the

absence of geoengineering.

The third term at the right-hand side of (D) captures the damages caused by

geoengineering alone. Recent numerical simulations on the use of geoengineering show

that geoengineering will affect precipitation patterns and volumes, causing a decrease in

precipitations over land and an increase in precipitations over the ocean (H. D. Matthews

and K. Caldeira, 2007), possibly causing droughts in large regions of the planet.5 It is

expected that the benefits from the cooling effect of geoengineering outweigh the costs

from changes in droughts and precipitation. Although this outcome is extremely

uncertain, since it is based on computer simulations rather observed in real data, we

assume that the marginal benefits of geoengineering exceed the marginal damages (i.e.

we assume 3 2d d T′ ′ ′< ), because this is the only case in which geoengineering can

potentially contribute to climate change policy.

2.2. Carbon Uptake and Geoengineering Intervention.

We now turn to the absorption of carbon from the atmosphere, to be denoted by δ, which

is the second main variable that is affected by both CO2 and geoengineering. Like we did

for climate-related damages, we distinguish between temperature-related, CO2-related,

and geoengineering-related changes in carbon uptake. In particular, we assume the

following:

1 2 3( , ) ( ) ( ( )) ( )S G S T S G Gδ δ δ δ= + − + (δ )

1 2 3( ) 0, ( ) 0, ( ) 0, 0.S T G Tδ δ δ′ ′ ′ ′> < < >

The earth’s biosphere and atmosphere balances the incoming short wave solar radiation

with long wave energy leaving the earth. This process is the combination of, on the one

5 Supranote 2.

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hand, carbon sequestration by plants and oceans, and, on the other hand, heterotrophic

respiration. Oceans and plants take up more CO2 the more of it there is in the atmosphere.

This causes the net primary productivity to increase. Hence, given temperature, carbon

uptake increases with CO2 concentration, which we capture by the term 1( )Sδ , which is

increasing in S. However, at higher temperatures more carbon is released from plants due

to an increase in heterotrophic respiration (Matthews et al. 2005). Hence, given the CO2

stock, carbon uptake reduces with temperature, which we capture by the term 2 ( )Tδ ,

which is decreasing in T. Computer experiments using general circulation models have

shown that the combined effect of an increase in concentration is positive, due in

particular to the fact that the increase in the net primary productivity due to increase in S

is greater than then increase in heterotrophic respiration caused by an increase in T.6

Formally, this requires us to assume 1 2Tδ δ′ ′ ′> .

Lower short wave radiation as caused by geoengineering could reduced reduce carbon

uptake as well, which effect is captured by the term 3( )Gδ , however this effect is very

small compared to the direct temperature effects (B. Govindasamy et al., 2002). This

allow us to impose the condition 3 0δ ′ .

2.3. Implications.

We now combine our assumptions from the previous sections to derive the implications

of changes in CO2 concentrations and geoengineering for damages and carbon uptake.

Lemma 1: If the conditions in section (2.1) hold, then:

0, 0, 0, 0, 0S SS G GG SGD D D D D> > < > < .

If the conditions in section (2.2) hold, then:

0, 0, 0, 0, 0S SS G GG SGδ δ δ δ δ> < > < > .

6 Govidasamy et al 2002 show that Doubling CO2 increases Net primary productivity from 56 to 100 Gt-C/yr, while it associated increase in heterotrophic respiration increases from 50 to 87.5, leaving a net increase in capture of 6.3 Gt-C/yr.

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Proof in the Appendix

3. A Static Model of Abatement and Geoengineering Intervention

We now combine the damage function (D) and absorption function (δ ) with assumptions

on the costs of emissions reduction and geoengineering to build a benchmark model of

climate change economics. To provide the simplest possible benchmark model, we ignore

timing issues and dynamic aspects. The static model of this section allows us to

concentrate on the basic trade-offs in the most elementary framework. The dynamic

version of the model follows in the next section.

To avoid climate and GHG related damage, two strategies stand out. First, environmental

deterioration in general and climate change in particular (increases in S) can be mitigated

by reducing reductions in emissions into the atmosphere (mitigation, or abatement for

short). Second, counteracting measures in the form of geoengineering, G, can be taken.

The differences in impact between changes in S (mitigation) and in G (geoengineering)

on damages are already set out above. Different from abatement, geoengineering

intervention G does not affect the level of environmental services directly; it does,

however, decrease damages in the economy by reducing the radiative force with the same

level of environmental services. We now need to model the economic costs of these two

strategies.

Our assumptions on the cost of abatement will be standard: we assume that the marginal

cost of abatement is a strictly increasing, strictly convex function of abatement, ( ),C A

wtih 0,AC > 0.AAC > 7

With respect to the costs of geoengineering, we allow for fixed costs and variable costs.

The fixed cost of geoengineering, to be denoted by IG, concerns the cost of developing

and testing geoengineering technologies. Moreover, the operating cost of geoengineering

is likely to be independent of the intensity of geoengineering, so this should be included

7 The notation YX represents the partial derivative of X with respect to Y.

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in the fixed cost IG as well. For example, while the amount of particles to be put into the

atmosphere depends on the amount of cooling to be geoengineered, the cost of operation

is almost independent of the amount of particles to be spread (“sending the plane to the

stratosphere”). The technical operation costs are small and largely independent of the

amount of cooling to be produced (D. W. Keith, 2000). Nevertheless, there may be non-

zero increasing marginal costs associated with geoengineering, mainly outside the realm

of operating costs. These costs arise from the effects that geoengineering can have other

than those on temperature. We think these are mainly health effects, following Crutzen

(2006), who warns for the health and air quality effects of SO2 concentrations at low

levels, and assuming that this can be extended to any type of particles used for the

geoengineering. We denote the variable cost of abatement by M , with M = 0 for G = 0,

and assume that the marginal costs of geoengineering are increasing and convex,

0,GM ≥ 0.GGM ≥

3.1. The structure of the model

We now study optimal abatement and geoengineering. Consider an economy in which a

benevolent social planner minimizes the costs of climate change to society by choosing

the flow of atmospheric CO2 equivalent emissions (S), the amount of abatement (A), and

the level of geoengineering, (G). The social planner's problem is given by the following

minimization program:

{ }

( ) ( ), ,

min ( ) , 1( 0) GA G SC A M G D S G G I+ + + > (OF)

subject to

( )0 ,A E S Gδ= − (SD)

where IG represents the fixed cost of geoengineering and 1(.) is an indicator function

which take the value 1 if G > 0. In the current static model, carbon uptake variable

( , )S Gδ should be interpreted as the emissions that do not enter the atmosphere due to

natural absorption processes, therefore equation (SD) imposes environmental

sustainability as an equilibrium condition, such that emissions net of abatement are equal

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to the absorption capacity level of the atmosphere. Recall that the absorption capacity of

the environment is a function of the CO2 concentrations (S) and the level of

geoengineering (G) as explained in the previous section.

3.2. The impact of geoengineering on optimal abatement and CO2 concentrations

Using traditional optimization techniques, we find that the optimal choice of abatement

(A) and CO2 concentration (S) requires the following equilibrium conditions (see

appendix for details):

( )( , )AC a S Gτ = (MAC)

( )( )

,,

S

S

D S GS G

τδ

= (MD)

where

( )0( , ) ,a S G E S Gδ≡ − (SD’)

is the level of abatement needed to satisfy the sustainability constraint (SD), and τ is the

Lagrange multiplier associated to the sustainability constraint. As usual, τ has the

interpretation of the pollution tax to which firms equate the marginal abatement cost, as

in equation (MAC). In the optimum, the pollution tax has to equal marginal damages net

of the contribution of increased CO2 concentration to the absorption capacity, as in

equation (MD).

Equations (MAC) and (MD) determine the optimal CO2 concentration, S, and pollution

tax, τ, for a given level of geoengineering. Figure 1 depicts this optimum. We are

interested in comparing a situation with and without geoengineering so as to analyze the

effects of the introduction of geoengineering in the economy. We analyze the experiment

in which we move form no geoengineering to an exogenous level of geoengineering G >

0, that we assume to be small. We report the results from this experiment in our first

proposition.

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Proposition 1: Suppose an interior optimum choice of abatement and CO2 concentration

exist, then, in comparison to the optimum without geoengineering, the introduction of

geoengineering induces

(i) a lower optimal pollution tax,

(ii) less abatement in the optimum, and

(iii) higher (lower) CO2 concentration in the optimum if the following inequality holds (is

violated):

SG A SGG

AA S

D CC

δ δδ

− +> . (*)

Proof . Total differentiation of (MAC) and (MB) gives 2A SG SG AA S G

SS AA S A SS

dS C D CdG D C C

δ δ δδ δ

− −=

+ −,

2

( ) ( ) 0S A SG SG G SS A SSAA

SS AA S A SS

d C D D CCdG D C Cτ δ δ δ δ

δ δ− + −

= − <+ −

and 1 0AA

dA ddG C dG

τ= < . Existence of

an interior solution requires the second order condition to be satisfied, which requires that the denominator term, 2

SS AA S A SSD C Cδ δ+ − , is positive. QED

To illustrate these results we can use a standard diagram of pollution versus taxes. We

can depict equations (MAC) and (MD) in the S vs. τ space.

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Figure 1. Geoengineering effects on the Static Equilibrium

Initially the economy is in an equilibrium where there is no geoengineering intervention

(Point A). Geoengineering shifts the marginal damage cost curve down, since the cooling

effect of geoengineering reduces marginal damages. It also shifts the marginal abatement

cost curve down: the cooling effect of geoengineering boosts carbon uptake (through

reduced heterotrophic respiration) and implies that less abatement costs have to be

incurred to neutralize emissions. Natural abatement (δ) substitutes for human made

abatement (A). With both curves shifting down, the overall impact is that the pollution tax

falls, so that abatement activities fall, but the effect on CO2 is ambiguous.

Geoengineering reduces the need to tax emissions for three reasons. The cooling effect of

geoengineering makes increases in temperature through CO2 accumulation less harmful,

first through lowering marginal damages ( 0SGD < ) and, second, through increasing the

marginal rate of carbon absorption ( 0SGδ > ). Third, the cooling effect of geoengineering

increases total carbon uptake through diminished heterotrophic respiration ( 0Gδ > ). All

these effects lower the social cost of carbon and result in a optimal lower carbon tax.

With lower carbon taxes, traditional mitigation measures are less needed.

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The effect of geoengineering on CO2 concentration itself is ambiguous. On the one hand,

the lower social cost of carbon induces lower abatement and thus increases CO2

concentration. On the other hand, improved carbon uptake from the atmosphere decreases

CO2 concentration in the atmosphere. Indeed, according to the inequality in (*), if the

change in carbon uptake as a result of geoengineering (δG) is small, the first effect

dominates and geoengineering makes it optimal to allow for higher CO2 concentrations

than without geoengineering.

3.3. The optimal level of geoengineering

We now confront costs and benefits of geoengineering to discuss its optimal level. The

first order condition for optimal choice of geoengineering activities G is given by:

( ) ( ) ( ), ,G G GD S G S G M Gτδ− + = (OG)

The left-hand side of this equation represents the marginal benefits from geoengineering:

cooling reduces damages ( 0GD < ) and improves the absorption of carbon ( 0Gδ > ),

which has a social cost τ. The right-hand side of the equation represents the marginal

costs of geoengineering.

Eliminating τ between equations (OG) and (MD), we can find an implicit function that

relates the optimal value of G as a function of S, which implies the following:

Lemma 2: If geoengineering is worthwhile to be introduced, the optimal level of

geoengineering increases with CO2 concentration: that is ( )*G g S= with ( )g S

increasing in S.

Proof in the Appendix

An increase in the CO2 concentration raises the benefits of geoengineering since CO2-

induced higher temperature is associated with higher marginal damages, which

geoengineering can offset. Hence, higher CO2 justifies more geoengineering.

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We can now substitute G = g(S) into (MAC) and (MD), and depict the resulting

expressions in the (S, τ ) plane, as in Figure 1. Point B in the figure represents the

optimum with optimized geoengineering, and can be compared to the optimum without

geoengineering, point A.

It should be noted that when geoengineering is optimized, the optimal tax level is greater

than zero, which implies as positive level of abatement. As is clear from (MAC) and

(MD), this follows from our assumptions 0, 0, 0A S SC D δ> > > . In our framework, a zero

optimal carbon tax would result only if marginal abatement costs would be zero (CA = 0),

but then climate change would have been costless even without geoengineering. A zero

optimal tax (i.e. no social cost of carbon) would also appear because of geoengineering if

geoengineering perfectly offset the damages from GHG accumulation, i.e. if DS = 0. For

zero (or small) levels of geoengineering, we have assumed DS > 0. However, with

intensive geoengineering, we could have 0SD ≤ . We formalize this in the following

proposition:

Proposition 2. With optimum levels of geoengineering, the pollution tax is strictly

positive if and only if 1 2( ) ( ( ( ))) ( ( )) 0d S d T S g S T S g S′ ′ ′+ − − > .

The possibility of a non-positive tax can no longer ruled out, since geoengineering can

offset the damage from global warming: after stabilizing temperature (at T so that

2 0d ′ = ), increases in CO2 concentration improve welfare (i.e. reduce damages) through

the fertilization effect ( 1 ( ) 0d S′ < provided S S< ). The surprise is perhaps that with

optimized geoengineering the cost of carbon can still be positive. Indeed, since

geoengineering is subject to increasing marginal cost, stabilizing temperature for a large

CO2 level might be too costly. Moreover, too large a stock of CO2 makes acidification

problems dominate the fertilization effect.

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3.4. Geoengineering adoption and Pollution Saving Technical Change Interaction

So far we have ignored the fixed cost of geoengineering, IG. This cost can be interpreted

as the cost of introducing geoengineering. Once introduced, it is optimal to choose G =

g(S) and to choose τ and S corresponding to point B in Figure 1. The area OBI represents

the total flow cost (M+C+D) in the optimum with geoengineering. Without

geoengineering, total flow cost is represented by area OAI. Hence the welfare gains from

the adoption of geoengineering are given by boomerang shaped area ODACIB.

Geoengineering is optimally introduced in the economy if and only if the benefits from

its implementation exceed its costs, including fixed costs, or equivalently, IG < ODACIB.

We can now identify forces that reduce the welfare gains of geoengineering introduction.

Any force that shifts down the MAC or MD curve reduces the gains from

geoengineering. We focus on technical change that reduces marginal abatement costs.

To do this, we introduce a technology parameter in the cost function, C(A,H). The

technology-shift parameter H allows us to study pollution-saving technological change.

We assume that technological changes decreases the marginal abatement cost, 0AHC < .

Obviously, this technological change is always beneficial, so to allow for the possibility

of endogenous technology, we assume that the economy can only implement the

technological change if it incurs a fix cost, IH.

The social planner problem is given by

{ }( ) ( )

, ,min ( , ) , 1( 0) 1( 0)G HA G S

C A H M G D S G G I H I+ + + > + > (OF’)

Think of an economy in which geoengineering and pollution saving technological change

are available. A central planner decides whether to adopt zero, one or two technologies.

This decision comes to comparing the welfare gain and the fixed costs of adoption.

Figure 2, shows the situation we describe.

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Figure 2. Results of the static model of geoengineering and technical change

Society will choose the option that maximizes welfare gains net of fix costs between four

possibilities. It either adopts geoengineering, adopt the new technology or adopt both. It

can also decide to adopt none of them. Each option carries different levels of welfare

gains and costs. The adoption of both technologies comes with welfare gains “OAIG”,

and costs IH + IG. Adopting only geoengineering comes with welfare gains “OAIB” and

costs IG. Adoption of the pollution saving technology brings welfare gains “FAI” and

costs IH.

Our assumptions about geoengineering are that the benefits from its implementation are

proportional to the damages of the economy, as well as the indirect effects described

above. Therefore, when a pollution saving technology is adopted by the economy, there is

a reduction on the welfare gains of geoengineering. The opposite is also true, when

geoengineering is implemented in the economy, some fraction of the benefits from

abatement are already being ripped off. Assuming that society is shortsighted and do not

see that the pollution saving technology is available then society might choose the option

of only geoengineering, but it might be possible that “FAI” - IH > “OAIB” - IG.

We summarize the results of this section in the following proposition:

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Proposition 3. Geoengineering is worthwhile to be introduced if and only if IG <

ODACIB. Lower costs of abatement ceteris paribus reduce the desirability of

geoengineering introducion. Geoengineering ceteris paribus reduces the desirability of

introducing a pollution-saving technology.

Proof. In text.

4. A Dynamic Model of Abatement and Geoengineering Intervention

We now study the dynamics and timing issues. The dynamic model that we propose in

this section has a steady state that coincides with the static model of the previous section,

but also has transitional dynamics towards this steady state that allow us to draw

conclusion about the effect of geoengineering on the timing of abatement and the time

profile of the optimal carbon tax.

Damages depend on the stock of GHGs which accumulates over time as long as net

emissions, 0E A− , exceed absorption ( ),S Gδ . The problem is

{ }

( ) ( ) ( )( ),

0

min , t

A GC A M G D S G e dtρ

∞−+ +∫ (DOF)

Subject to

( )0 ,S E A S Gδ= − − given S(0) = S0 (DRC)

Baseline emissions, denoted by 0E , are exogenously given and assumed to be constant

over time for simplicity (but it is straight forward to allow for asymptotically constant

baseline emissions). Notice that now the variables are functions of time; however, we do

not make explicit reference to time dependence to avoid notation clutter.

19

4.1. Geoengineering and abatement interaction

Using the maximum principle to solve for the optimal behavior of this dynamic system,

we find the following conditions:

( )AC A τ= (MAC)

( ) ( ) ( ), ,G G GD S G S G M Gτδ− + = (OG)

( )( ) ( ), ,S SS G D S Gτ δ ρ τ= + − (MDD)

where τ λ= − , and λ is the co-state variable of the CO2-stock accumulation equation

(DRC). It should be noted that the optimality conditions for the flow variables, abatement

and geoengineering, as given by equations (MAC) and (OG), are the same as in the

previous section. As a result, τ has the same interpretation of the carbon tax and social

cost of carbon, as above. The new condition is (MDD), which can be interpreted as an

arbitrage rule for the investment in a cleaner atmosphere. For a constant pollution tax,

(MDD) reduces to its counterpart in the static model, (MD), apart from the constant

discount rate. Hence, we can conclude the following:

Lemma 3 In a steady state with 0Sτ = = , the steady state of the dynamic model and the

static model coincide if ρ = 0. For constant ρ, the qualitative properties of the steady state

and the static model are the same.

Intuitively, with a zero discount rate, short run costs and long-run benefits gets equal

weights in the optimization problem so that the trade-offs occur as if the timing of costs

and benefits does not play a role, exactly like in the static model.

As a result, we can apply propositions 1 and 2 to the steady state: we find that in the

steady state, geoengineering reduces the carbon tax and abatement and has an ambiguous

effect on S (as in proposition 1) and that the tax can still be positive (but does not need to

be).

20

We analyze the dynamics of the system in three different situations. First, we have the

system in the absence of geoengineering. Second, we add geoengineering to the system at

date T1, when the economy does not foresee the arrival of geoengineering. Third, the

economy knows of the arrival at date T1 of geoengineering at a given future date T2. The

dynamics of the system are depicted in Figure 3, which is the phase diagram that directly

follows from the dynamic system. This system is saddle point stable. In the absence of

geoengineering, the saddle path leads to a steady state like “1”.

Proposition 4: Unexpected introduction of geoengineering leads to a reduction of the

short-run tax and an increasing tax after introduction. The announcement of a future

introduction of geoengineering leads to a drop in the tax rate at the time of

announcement, and to a phase of declining taxes between announcement and

introduction.

Proof. directly follows from phase diagram.

Figure 3. Dynamics of the Optimal System in the Presence of Geoengineering.

21

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