The energy transition in a climate-constrained world: Regional vs. global optimization

Environmental Modelling & Software 44 (2013) 44e61

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The energy transition in a climate-constrained world: Regional vs. global optimizationq Markus Brede a, Bert J.M. de Vries b, * a b

University of Southampton, School of Electronics and Computer Science, Southampton SO17 1BJ, United Kingdom Planbureau voor de Leefomgeving (PBL), P.O. Box 303, NL-3720 AH Bilthoven, Utrecht University, The Netherlands

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 December 2011 Received in revised form 9 July 2012 Accepted 11 July 2012 Available online 7 September 2012

In this paper we present a stylized economy-energy-climate model and discuss the role of the atmosphere, fossil fuels, and a stock of accumulated knowledge about renewable energy technologies in collaboratively and competitively managed worlds. The model highlights that assumptions about the ‘degree of competition’ and about choices of lumping economic regions, and hence their heterogeneity, strongly affect model predictions about the rate of fossil fuel use and, consequently, the rate of climate change. In the model, decisionmakers (actors) make decisions about investment allocations into the goods producing economy and into carbon-based and non-carbon-based (renewable) energy supply, the remainder being for consumption. Actors are faced with the following dilemma situation. Economic growth requires energy and will therefore accelerate fossil fuel depletion and generate growth in carbon emissions, the latter leading to global warming and climate change induced damages. By developing non-carbon energy sources, which come initially at a higher cost than fossil fuels, growth of carbon emissions can be curtailed. Trying to optimize a consumption-related utility, actors base their decisions on the economically most rational investment portfolio for a finite time horizon. However, in their decisionmaking, they are constrained by the choices of other actors. We consider two prototypical situations: (i) a collaborative environment where all actors strive to maximize a world utility e the global optimum e and (ii) a situation where actors optimize the utility of their own country e a solution that corresponds to a Nash equilibrium. The difference between both outcomes can be used to classify the severity of the ‘tragedy of the commons effect’. We present results about the dependence of the severity of this effect on several key parameters (i) the number of actors, (ii) the heterogeneity and severity of expected climate damages, (iii) assumptions about technology diffusion and (iv) fossil fuel depletion. Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved.

Keywords: Climate policy Agent-based modelling Common pool resources

1. Introduction The anticipated human-induced climate change and the resulting societal pressure towards mitigation and adaptation has initiated the development of a series of so-called integrated assessment models (IAMs) to understand the simultaneous dynamics of the climate system, of the economic and energy system and of the socio-cultural and political mechanisms involved (Weber and Hasselmann, 2003; Manne et al., 1998; Nordhaus and Boyer, 2000; Fiddaman, 2002; Weber et al., 2005; Lejour et al., 2006; Bosetti et al., 2006; Waisman, 2012). The IAMs have been and are used to generate large numbers of scenarios of greenhouse q Thematic Issue on Innovative Approaches to Global Change Modelling. * Corresponding author. Tel.: þ31 30 2533684. E-mail address: [email protected] (B.J.M. de Vries).

gas emissions and the subsequent impact on climate (see e.g. (Nakicenovic et al., 2000; IPCC, 2007)). Typically, such scenarios combine assumptions about economic growth patterns with assumptions about energy demand, fuel substitution and depletion, and technology development. In the majority of IAMs, rational economic actors with perfect foresight make investment and consumption decisions that are parameterized on the basis of econometric analyses, and which optimize the (discounted) utility for the world at large (see, e.g., Stern, 2008).1

1 We do not discuss here the category of ‘bottom-up’ IAMs, which tend to focus on techno-economic trend and micro-economic behaviour analyses (see, e.g., Alcamo et al., 1998; Kainuma et al., 2003; van Vuuren et al., 2006). Emission trajectories in these models are based on simulations, not on optimizing an objective function.

1364-8152/$ e see front matter Crown Copyright Ó 2012 Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.envsoft.2012.07.011

M. Brede, B.J.M. de Vries / Environmental Modelling & Software 44 (2013) 44e61

In such top-down models, however, a globally optimal world outcome usually entails suboptimal outcomes from the perspective of some agents who have to sacrifice potential benefits (utility) for the sake of others. In the terminology of the IPCC-SRES scenarios (Nakicenovic et al., 2000), a global optimum fits into a B1-scenario where strong international institutions are able to formulate and implement the necessary cooperation towards sustainability. However, as history shows, policies aimed at global cooperation and fairness meet with large obstacles. Not only is there a risk of failure because of bureaucracy and corruption, but there is also severe competition from consumer- and market-oriented strategies which often are more efficient but tend to enhance inequity and externalize environmental degradation (de Vries and Petersen, 2009). Also, the large heterogeneity in actors’ economic and social situations and in the expected costs and benefits from climate change policies make such global optimal policies difficult to implement, as the past UNFCC-meetings testify. The coordination problems in such a cooperative scenario are well-known from the investigation of Common Pool Resource (CPR) management (Ostrom, 1990; Dietz et al., 2003). At its core is the problem that all actors benefit from being able to freely emit greenhouse gases into the atmosphere, but potential damages of a unit of emissions by one actor are shared by all (though to different degrees). In combination with a positive time preference, the cost-benefit analysis for a single actor yields that the benefits from emissions (i.e. ‘cheap’ carbon-based economic growth and consumption) often outweigh the detrimental impact of climate change induced damages. Naturally, if all actors follow this selfish rationality, a state of the world is achieved in which everybody is worse off than if he had not pursued his own egoistic goals. This situation, which has been well researched in noncooperative game theory, has already been identified for the climate change problem (Kaitala and Pohjola, 1995; Svirezhev et al., 1999; Scheffran and Pickl, 2000; Scheffran, 2002). However, to our best knowledge, it has never been investigated exhaustively in the framework of coupled economy-energy-climate models. Studying the impacts of competition on resource management, is the aim of the present paper. Our study aims to complement the many analyses of optimal emission pathways with IAMs as part of a global optimization.2 We present it here as an innovative way to use (simple) models in the search for strategies that consider simultaneously the costs of the energy transition and of climate change damage as a function of the degree of cooperation. Moreover, present day IAMs have evolved to a high degree of sophistication including modelling of land use and its coupling to climate processes (Bouwman et al., 2006) or economic models that treat the energy sector with far more accuracy then what we present in this paper, cf. (Gerlagh and van der Zwaan, 2004; Edenhofer et al., 2005; Lejour et al., 2006; van Vuuren et al., 2006; Bosetti et al., 2006). However, while establishing strong connections to real world data, this richness in model accuracy and detail is also a weakness. Computational complexities and parameter requirements often don’t allow for an exhaustive investigation of the parameter space. Instead, typically only a handful of predetermined scenarios are investigated. The simple model developed in this paper aims to add insight at this point. Restricting the model structure to the bare ‘essentials’ allows us to systematically investigate key dependencies and experiment with settings like the ‘degree of competition’ which are usually fixed in these scenarios.

2 Bosetti et al. (2006) explore cooperative and non-cooperative solutions in the WITCH-model. The study, however, is limited to one parametrization of the world (e.g. one choice of lumping economic regions).

45

In economic terms the energy-climate dilemma situation can be framed as follows. Countries aim for economic growth in order to increase income available for consumption. Energy is a necessary input. To keep the industry supplied with energy part of the economic output has to be invested into the energy sector.3 In the last century the usual way has been to invest in fossil fuel exploration, exploitation and conversion. With increasing fossil fuel scarcity and the environmental impacts of their use, alternative non-carbon sources are expected to take over in the course of the 21st century in a process denoted as ‘the energy transition’. In our model, the alternatives (wind, solar, nuclear a.o.) are lumped together in a single non-carbon source. Initially, the alternative option requires more investments per unit of energy than the fossil fuel option. This situation is expected to change gradually, as learning by doing allows for improvements in renewable energy technology, a process that will be accelerated by the rise in fossil fuel costs because of depletion. But even with vastly improved technology, renewable energy is still expected to be more expensive than fossil fuels for the decades to come. Hence, a country that opts to build an economy based on energy from fossil fuels can, at least for a while, grow at a faster pace and thus achieve a higher economic output and welfare, because less income needs to be spent on the energy sector and more can be invested into expanding the goods and services producing capital stocks. According to present insights, such a slow transition leads to a large amount of greenhouse gas emissions with a concomitant change in climate, which may cause serious if not catastrophic damages to the economy later on (IPCC, 2007; van Vuuren et al., 2008). However, a country may decide to accelerate the introduction of the more expensive renewable energy if the decisionmakers judge the consequences of climate change damage to be significant or if they anticipate the exhaustion of available sources of fossil fuels. The country then goes faster through the energy transition. The trade-off is that a relatively smaller rate of economic growth is achieved, but that atmospheric gas concentrations remain low enough to significantly reduce negative impacts on the economy later on. Couched in the language of typical dilemma situations that are dealt within game theory, one might call such behaviour a cooperate strategy (considerate behaviour that leads to a global optimum), whereas the strategy in which each country optimizes its own benefits is a defect or competitive strategy (selfish behaviour that is only optimal from the player’s own perspective). Scrutinizing the problem at hand, in this setup there are three stocks that are to be considered: (i) the atmosphere, which is a global common sink, (ii) finite amounts of fossil fuels (oil, gas, coal), that are locally or globally available as resources, and (iii) the knowledge pool in the non-carbon energy sector, that is also locally or globally accessible as a resource. Item (i) has already been discussed above in the context of global commons and climate change. The fossil fuel resource base (ii) may in first instance be considered a resource that can be accessed by all actors with equal rights. Historically, this is unrealistic (Yergin, 1991; Schrijver, 2010). Yet, such an open-access character is to be expected in a globalized world, with a global market for fuels and no trade restrictions. Consequently, the price dynamics of fossil fuels for the decades to come is then dictated by the depletion of the global resource in sequence of (marginal) cost. Countries using more fossil fuels at an earlier point in time benefit

3 On the crucial role of energy for the process of economic growth, see for instance (Ayres and Warr, 2005).

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Technological progress (g)

Investments σY

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f energy

Energy fossil sources

Energy renewable sources

(KF )

(KR )

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Learning by doing

Fig. 1. Schematic illustration of the simple economy-energy-climate model, see text.

through cheap prices in comparison to countries who come in later. This formulation assumes that fossil fuel prices are determined by the (marginal) production costs plus a fixed mark-up, in other words: they only reflect (Ricardian) differential rents. This is the procedure usually implemented in IAM-based modelling (Manne et al., 1998; Fiddaman, 2002; Lejour et al., 2006). Resource price dynamics is therefore not explicitly considered in our model. We do not consider the scarcity rent that would raise the market price of fossil fuels exponentially as suggested by the Hotelling rule (Dasgupta and Heal, 1979; Stroebele, 1984). One reason is the lack of evidence that this rule applies in the real world (Perman et al., 2003; Kronenberg, 2008). The second reason is that it requires an explicit treatment of fossil fuel resource owners with enough market power to force such a price rise; to our knowledge, this has so far only been attempted within the framework of the IAM IMACLIM-R model (Waisman, 2012). The knowledge accumulation about non-carbon energy technology is the third (iii) resource. This, too, can be shared to a smaller or larger degree. Knowledge as an open-access resource seems likely in a highly globalized world, although real-world developments will depend on the relative role of governments and private multinational companies. As a consequence, those who have not invested in knowledge accumulation and thus promoted cost reductions from learning-by-doing may benefit from the experiences of the others (Bayoumi et al., 1999; Helpman, 2004). Below, we shall discuss ‘black and white’ situations where the respective resources are either treated as fully open-access or completely protected regional resources. In the ‘real’ world there are rather shades of grey.4 The organization of this paper is as follows. First, we introduce the simple economy-energy-climate model. The model is actor-

4 As indicated before, a completely open-access world would fit into the B1storyline of the IPCC emission scenarios, whereas a fully blocked situation would make up an A2-world.

based in the sense used by Hasselmann and Kovalevsky (2013). We use an iterative procedure to construct competitive and collaborative solutions. In the next section we discuss the dependence of the results on the degree of competition, and study the degree to which the open-access character of the three relevant resources influences the attractiveness of competitive and cooperative strategies. For this purpose we introduce the loss in utility in a competitively managed world with respect to its value in a fully cooperatively managed world. In Section 3 we then investigate the dependence of this utility loss on the heterogeneity in actor size or heterogeneity in regional climate impacts. We conclude with a discussion of our main results and implications for the development and use of IAM’s. 1.1. The economy-energy-climate model To keep computing requirements for the optimization experiments within a manageable range, we restrict this analysis to a simple model economy, consisting of a goods production sector and an energy sector (de Vries, 1998), see Fig. 1 for an illustration.5 Emissions from the energy system provide a link with a very simple climate model, with changes in earth temperature feeding back on the economy. Goods are produced by the input of a goods producing capital stock (which comprises factories, machines, etc.) and labour. Goods production is modelled by a CobbeDouglas production function with elasticity g ¼ 1/2

Y ¼ egðtt0 Þ Y0 K g L1g DðDTÞfenergy ;

(1)

where t0 is the start year of the simulation, K is the goods producing capital stock, L ¼ 0.25P the labour force (assumed to be always one quarter of the population P), D($) a damage function that

5 See (Fiddaman, 2002) for an analysis of simple economy-energy-climate models.

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characterizes damages to the economy from global warming per degree Kelvin of increased average temperature, Y0 a proportionality constant and g a (not endogenously modelled) growth rate. For all our simulations we set g ¼ 0.007. Because it is possible in the simulation that the energy production capacity does not match energy demand, we introduce the factor fenergy to explore the effects of energy over- or under-supply on goods production. Damages are modelled as a linear function of temperature rise, i.e.

DðDTÞ ¼ 1  aDT;

(3)

(4)

where dK ¼ 1/10 is the depreciation rate of goods producing equipment. The required energy supply of the economy is assumed to be proportional to goods production, i.e. Edemand ¼ eY. We realize that this is an incorrect assumption in view of the long-term decline in energy-intensity (GJ/$) for most countries. However, in view of computing requirements, we have omitted autonomous and priceinduced energy-efficiency improvements (de Vries, 1998; van Vuuren et al., 2006). One justification for this approach is in the use of a simple macro-economic model, in which one aspect of dematerialization, namely the structural change towards a service economy, cannot be simulated. Although this surely overestimates energy use per unit of goods production, we argue that it does not impact upon the key point of our experiments. Energy can be generated from fossil fuels or renewable energy sources (we assume renewable to be equivalent to non-carbon throughout the paper). Capital stocks (fossil fuel fired power plants, solar panels, wind turbines, etc.) for the generation of energy from these sources are subject to the evolution:

dKR ¼ sR Y  dR KR ; dt

dKF ¼ sF Y  dF KF dt

(6)

for energy generation from fossil fuels (F). The quantities sR and sF are the investment allocations and dR and dF the depreciation rates of the respective capital stocks. Energy output is obtained from

Esupply ¼ DðDTÞðfF KF þ fR KR Þ;

with C/P per capita income. There is a rather large spread among regions; here we neglect country differences and use the parameter values that give the best fit for the world data.8 Given a savings rate sY the goods producing capital stock is subject to the following dynamics:

dK ¼ sY Y  dK K; dt

for energy generation from renewable sources (R), and:

(7)

(2)

with one parameter a that quantifies the amount of damage caused per unit increase of temperature.6 It is further worthwhile to note that our model does not include the possibility of adaptation to climate change.7 Generally, this option will be available to a larger extent for rich than for poor countries. The population and thus the labour force are assumed to have a growth rate which decreases with income. The functional dependence of population growth on income is derived from historic data. The following functional description is found to be a reasonable fit for the data:

dP ¼ aPðC=PÞb : dt

47

(5)

6 We do not yet consider more elaborate formulations that include possible adjustment of the economic system to temperature rise (Hallegatte, 2005). 7 In first instance one may consider the adaptation as being part of the damage multiplier: more and cheap adaptation implies a lower a-value. 8 Using OECD-data (OECD, 2008) for population and GDP growth, the world data can be reproduced very well for a ¼ 0.75 and b ¼ 0.97 for the historical period 1970e2005 and the OECD-scenario period 2005e2050.

i.e. both capital stocks produce with productivities fF and fR and are, as is the economic capital stock K, subject to climate change related damages. The energy capital stock productivities are assumed to decline for energy from fossil fuel resources with cumulated output due to depletion and to increase with cumulated output for non-carbon resources due to learning by doing. The details of the simple depletion and learning by doing mechanisms are given in Appendix A. For the initial experiments in the following section, the model is calibrated in such a way that fossil fuel depletion does not play a role. The energy over- or under-supply multiplier is calculated from the energy demand and the available supply by fenergy ¼ 1 if Edemand < Esupply and fenergy ¼ Esupply/Edemand otherwise. Thus, in an energy shortage situation economic output declines proportional to the energy supply/demand ratio, neglecting all kinds of energy system features. The energy supply/demand ratio allows us to identify situations of very rapid, and therefore tense, transition dynamics. CO2 emissions are proportional to the amount of energy generated from fossil fuels, i.e. E ¼ eKF, where e is a proportionality constant. Emissions lead to global warming and temperature increases DT, which are modelled in a simplified way following (Janssen and de Vries, 1998), see Appendix B for details. Given investments into the economic capital, and into the two different sources of energy supply, the remainder of the goods production sC ¼ 1  sY  sR  sF is available for consumption C. Hence, C ¼ sCY. To account for declining marginal utility of consumption, the actors’ objective is formulated in terms of a utility U according to U ¼ log C. The model is formulated in discrete timesteps of length 5 years, i.e. all continuous equations are used in their discretized form as difference equations. 1.2. Actor behaviour Actors that manage a country are assumed to follow strategies that optimize a discounted time-averaged population weighted per capita utility function:

ZT UðC; PÞ ¼ 0

edt PðtÞlog½CðtÞ=PðtÞdt=

ZT PðtÞdt:

(8)

0

In the following the pure time preference discount rate d is chosen equal to zero. We distinguish two extremes: (i) actors optimize a country specific utility function Ui ¼ U(Ci, Pi), where the index i specifies the consumption and population in country i and (ii) actors strife to optimize the world utility function P P Pi Þ. The latter is equivalent to global planning in U ¼ Uð Ci ; i i managed world, the former to regional planning in a cooperatively a competitively managed world. Naturally, the difference between competitive and cooperative strategies vanishes if we set the number of countries N to 1. In a competitive world, actors are coupled in three important ways: (i) possible damages of greenhouse gas emissions through global warming, (ii) effects of learning by doing, such that countries

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who adopt a technology later benefit from the knowledge stock accumulated by others, and (iii) the exploitation of finite resources. We model these interactions as a non-cooperative Nash Game and our solutions are open loop Nash equilibria. This implies that actors decide on planning strategies over the entire time horizon at the outset of the game. Actors then adhere to these strategies over the entire time horizon and there are no opportunities for strategy shift once an equilibrium strategy has been decided on. The algorithm to find the equilibria is implemented as an iterated negotiation process, where countries gradually adapt to their respective decisionmaking. Note, that this negotiation process takes places only once before the actual decisions are implemented. Assuming N > 1 countries with decision vectors Di ðtÞ ¼ ðsYi ðtÞ; sRi ðtÞ; sFi ðtÞ; sCi ðtÞÞ, i ¼ 1,.,N and t ¼ 0,.,T, we consider the following iterated procedure. Let the decisions of country i at negotiation stage k be Dki . Then, the decisions of country i at iteration k þ 1 are obtained by optimizing country i’s utility function Ui, assuming that the other countries j s i follow the decisions fDkj gjsi . This process is repeated to convergence, i.e. until no country can improve its decisions any more. The process is similar to the one adopted in Bosetti et al. (2006). In general, the detailed course of negotiations and the paths of equilibration depend on initial conditions. It should be noted that the outcome of the trajectory represents a series of investment decisions in the N countries considered for the full time horizon and that the results are thus comparable to the ones from standard IAM dynamic optimization runs for N ¼ 1 (e.g. (Manne et al., 1998; Nordhaus and Boyer, 2000)). The problem at hand constitutes an infinite-dimensional optimization problem, solutions for which are very hard to obtain. To reduce the complexity and make the problem amenable to numerical treatment, the decision vectors have been discretized into 5 year time intervals during which investment decisions are held constant. This choice of discretization results in discontinuous derivatives in the evolution of capital stocks and output variables. Simulations are performed for 150 years, but shown for only 100 years to avoid finite-time horizon effects. We are interested in the effects of competition on the energy transition and climate change, that is, in the behaviour of the system for N > 1. If countries are competitively managed, the degree of competition in the system is a monotonically growing function of the number of competing countries. To allow for a comparison between situations with different numbers of countries, parameters and initial conditions are chosen in such a way that the global, i.e. summed over all countries, stocks of population and capital, of available resource and of possible total economic activity are independent of the number of countries. Simulating a cooperative world is then equivalent to simulating a single country (N ¼ 1) with stocks equal to the sum of the country stocks. Such a single-world cooperative strategy is the globally optimum decision strategy that can be obtained in a world where everybody strifes for the globally optimal transition. 2. The commons effect: how many countries and how much resource access? In this section we first concentrate on the role of the atmosphere as a CPR and consider the other two resources: fossil fuels and knowledge about renewable energy technology, as non-tradable non-exchangeable resources. Thus, each country has abundant but finite fossil fuel resources available to itself, and similarly it has only access to the knowledge it has gained itself from accumulated production in its own country. Such a setting is achieved by tuning the emissions constant as (see also Appendix C):

e ¼ e1 =N;

(9)

where e1 is the emissions constant for the one country situation and N gives the number of independently managed countries. In all experiments we verified the independence of the setup on N by making sure that simulations for an optimized world-utility give results that are independent of N. The optimized world-utility corresponds to a cooperative optimization strategy. We will use the relative ratio between the utility U1 that is obtained for N ¼ 1 and the utility UN achieved for N > 1, UN/U1, as an indicator or measure of the loss of possible utility caused by competitive management. Stated differently, we consider the relative ratio as an indicator of the ‘tragedy of the commons’ (ToC) or commons effect. 2.1. The atmosphere as an open-access common pool resource From the experience about common pool resource use in climate-change related and other contexts (Ostrom, 1990; Scheffran, 2002; Dietz et al., 2003) one expects that the difference between cooperative and competitive resource use grows with the amount of competition about the resource. Thus, the more countries, the more pronounced one expects the ToC effect. This is illustrated by the simulation results displayed in Fig. 2, which give the dependence of the relative utility UN/U1 on the number of competing equal-sized countries for different climate change damage assumptions. Thus, the relative utility is an indicator of the loss in over-all utility that is found when N > 1 countries start from an initial state (cf. Fig. 2) to negotiate and converge to an investment strategy that is optimal from each country’s own perspective. Note that each country has only access to its own fossil fuel and knowledge stocks in these first experiments. The relative utilities decline gradually with the number of actors, until a threshold number of competitors Nc is reached. After this threshold level of competition is crossed, i.e. for N > Nc, utilities converge to a level that is independent of N. The threshold is reached for smaller Nc if climate damages are milder, but the utility gap between the situation just below and just above the threshold is smaller. In Figs. 3 and 4 the investment choices and the corresponding economic developments on the number of actors for the highest damage scenario with a ¼ 0.1 are shown (see also Fig. 2). The data are given for N ¼ 2 (virtually no difference to globally optimal behaviour), N ¼ 8 (considerable utility loss due to competition), N ¼ 14 (strong utility loss due to competition, but still below threshold) and N ¼ 16 (above threshold, behaviour then remains the same for larger N). These s-trajectories are the outcome of the utility-maximizing strategies followed in these worlds. Let us first have a closer look at the investment allocations sF(t) and sR(t) into the energy sectors (see Fig. 3). In a world that is managed close to global optimality (N ¼ 2), an instant energy transition is undertaken: because the anticipated impacts of global warming are severe, no investments into the fossil fuel based energy sector are made at all. Instead, the optimal strategy is to invest heavily into renewable energy: investments are initially very large and only saturate after roughly 20 years when the transition away from fossil fuels has been achieved (see the panel for the fossil fuels/renewables supply mix ratio rfoss in Fig. 4). This is reflected in the evolution of the respective capital stocks KF(t) and KR(t). Without further investments into the fossil fuel energy sector, KF declines exponentially with the capital depreciation rate dKF . The renewable energy producing capital stock initially grows very rapidly, until around year 20, after which investments into the renewable energy sector stabilize at about sR ¼ 0.15 at which the energy sector tracks economic growth. The timely energy transition allows for a fast stabilization of CO2 emissions, such that global

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1.1 1

rel. utility

0.9 0.8 0.7 0.6 0.5

a=.03 a=.05 a=.07 a=.10

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2

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8

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N Fig. 2. The commons effect for different damage expectations. All countries are identical, emissions per country are scaled (eN ¼ e1/N, see Equation (9)) Fuel trade and knowledge exchange are not possible. Results are shown for four categories of climate change damage (a ¼ 0.03: mild, to a ¼ 0.1: severe). One typically finds a threshold number of competing regions Nc, such that for N  Nc all countries undergo an energy transition and for N > Nc economies remain essentially fossil fuel based at the end of the simulation. The larger the damage, the less ‘severe’ is the commons effect for N > Nc, but the larger is also the utility gap at the transition. Since the atmosphere is the only resource treated as a common pool, for N > Nc countries are effectively decoupled and hence utilities are independent of N.

warming remains limited to a DT ¼ 0.5 temperature increase (see the panel for the temperature increase r in Fig. 4). As the number of competing countries increases, the energy transition becomes more and more delayed. Investments into fossil fuel capital stocks KF(t) are declining more slowly, whereas investments into renewable energy capital stocks KR(t) take off at a (much) lower rate. The mechanism behind this is roughly the following. If other countries emit a certain amount of CO2, a given country is faced with a certain amount of damages that it cannot influence by its own decisions. To adapt to these damages, i.e., to sustain a certain consumption/output level despite the climate change induced capital and productivity destruction, the country will have to accelerate the buildup of its economy in the initial stages of the time period considered. This allows for earlier consumption, when productivities are not yet influenced by the expected damages. This is only possible by using more cheap fossil energy earlier on, which in turn leads to larger emissions. If every country follows this rationale, an emission-increasing spiral is started that is only bounded by the amount of additional damages a country’s emissions cause to its own economy. Thus, the aim of long-term utility maximization in each country induces the ToC effect. It gets worse the more independent actors there are, because more countries increases the emissions baseline each country is faced with when making its decisions (see the investment decisions for N ¼ 8 and N ¼ 14 in Fig. 3). Altogether, for N < Nc an (albeit delayed) energy transition is still undertaken and a stabilization of emissions and temperature increases is achieved. The temperature levels at which stabilization is achieved, however, are higher for worlds with more competing regions.

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Fig. 4. Evolution of the production capital stock and per capita production, of the energy capital stocks, and of the fossil fuel/renewables supply mix ratio, and the effect on the climate (temperature change). The curves correspond to the investment decisions shown in Fig. 3. The damage constant is a ¼ 0.1 (severe damages), other parameters as in Fig. 2.

When the number of countries surpasses a certain threshold number Nc, curbing emissions by using renewable energy is no longer a viable strategy as long as fossil fuel reserves are not exhausted. In the latter case (see N ¼ 16 in Fig. 3), actors mainly build their energy sectors on fossil fuels and only complement the latter by a certain amount of renewables that are required to counteract fossil fuel depletion. These investments into the renewable energy sector, however, are made at an early stage of economic development. The reason behind this choice is the learning by doing effect that rewards early investments by a prolonged time of benefits from the learning later. On the other hand, investments into the fossil fuel energy sector are massively ramped up towards the end of the 100 year time window. This is caused by the increasing effects of fossil fuel depletion and climate change

related damages to the outputs of the capital stocks in the energy sector. These energy investment allocations also impact on the growth strategy for the goods producing sector and the distribution of consumption over time. Using a nearly cooperative strategy (N ¼ 2), the high initial investments into renewable energy capital reduce the investment goods available for the goods producing sector. However, with the learning by doing and the continuation of the energy transition, the investments into the energy sector decline from around year 20 onwards and output is used first to further boost economic output and then increasingly for consumption. With more countries in the world, each country plans for an early rapid growth phase of the economy and correspondingly very low initial levels of consumption once the actors perceive the

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opportunity to avoid large future climate change. After this early rapid expansion the goods production sector (note in particular also the evolution of K and C/P in Fig. 4) saturates around year 20, when the expansion of the economy is increasingly driven by population growth while the expansion of the capital stock K more and more lags behind. The latter is partly due to the need for investments into the renewable energy capital because of depletion of fossil fuels. When the number of countries exceeds the threshold (N > Nc), they all attempt to sustain consumption levels for an increasing population and growing levels of climate damage. Indeed, this is a characteristic collapse scenario which has probably occurred quite often in past societies (Costanza et al., 2007). 2.2. An open world economy: the role of fossil fuel access and knowledge exchange What happens when fossil fuels are considered as a tradable commodity and knowledge about non-carbon energy technologies as a stock which diffuses instantly throughout the world? In our model, we do not explicitly simulate trade processes. Instead we make the assumption that, in a world with trade in fossil fuels and/ or exchange of knowledge about renewable energy sources, the depletion and learning by doing multipliers are determined by the accumulated fossil fuel use and installed renewable energy capital in all countries. We can expect a different outcome in such an open world economy. We present the results of a couple of simulation experiments in a multi-country setting with N ¼ 10, i.e. somewhere between the intermediate cases discussed previously (N ¼ 8 and N ¼ 14). In order to separate out the effects of using the atmosphere as a common sink we set damages from global warming to zero (a ¼ 0) in our first experiments. The difference with previous simulation experiments is that energy cost and the effects of learning by doing are calculated on the basis of world, not country production (cf. Appendix A). Countries are now coupled in two ways: (i) by a globally finite amount of fossil fuels and (ii) by a global knowledge stock from renewable energy production experience. We use the following coding for the experiments. The letters I for Individual (non-tradable/exchangeable), S for shared (freely accessible to all), F for fossil fuel stocks and T for renewable (non-carbon) energy technology knowledge stocks are used to compare four different situations:  (IFIT) Every country has its own stock of fossil fuels and has to develop its own renewable energy technology (taking the threshold functions used to model the stocks, the depletion transition sets in at xF ¼ F (for fossil fuels) and at xR ¼ R (for renewable energy technologies) in each country e see Appendix A). This was the starting point for the experiments presented in the previous section;  (SFIT) All countries share one global stock of fossil fuels (depletion of which sets in at xF ¼ NF) that can be traded, but countries have only access to the knowledge about renewable energy technologies built up in their own country;  (IFST) All knowledge that is acquired about renewable energy technologies is freely accessible to all, but each country has its own source of fossil fuels that cannot be traded with other countries (and of which depletion sets in at xF ¼ F);  (SFST) Both fossil fuels and knowledge about renewable energy technologies can be traded/exchanged freely. A summary of the optimal investment and development pathways for N ¼ 10 independent and economically equivalent regions is depicted in Figs. 5 and 6. It turns out that, apart from the average relative utilities UN/U1, a good indicator of the qualitative differences between different scenarios is the cumulated use of fossil

51

fuels. Accordingly, relative accumulated amounts of fossil fuel used (normalized by the fossil fuel use in the N ¼ 1 scenario) and the changes in relative utilities when the number of regions is increased, are shown in Fig. 7. The data displayed in Figs. 5 and 6 and particularly those shown in Fig. 7 allow some qualitative conclusions about the effects of an open world economy on actor strategies. Let us now investigate the four possible scenarios IFIT, SFIT, IFST and SFST in more detail. The first case is IFIT (red curves). It is to be compared with the results in Fig. 3, with the difference that there is now no anticipated climate change and hence a slower transition towards renewable energy. Around the year 40 the economy slowly moves towards a steady-state with a slow further transition from fossil fuels to renewable energy sources. It is associated with a buildup of economic output at a moderate pace, that also allows for relatively high levels of consumption in the early time periods. The result of this development path is an economy that achieves a high level of utility (U z 54.8) with an overall low use of the fossil fuel stock (see Fig. 7, N ¼ 1). The second case is SFIT (green curves). Here, the competition for the use of an initially cheap global stock of fossil fuels generates pressure towards an earlier exhaustion of the limited fossil fuel reserves. Each country can now make use of the global stock of fossil fuel. This makes the energy transition less smooth, because each country tries to use fossil fuels as long as they are still cheap, with the result that its cost increase around year 60 is rather sudden and so is the subsequent necessary investment boom in renewable energy capital. The profiles of investment in production capital and of consumption are similar to the IFIT-case. Also the achieved level of utility is only marginally smaller (U z 54.7) than in the IFIT scenario due to the logarithmic relationship between consumption and utility. However, fossil fuel use is up to one quarter larger than in the IFIT scenario and increases with the number of countries competing for the global stock (Fig. 7). In the IFST scenario (blue curves), the sharing of knowledge about renewable energy technology also leads to a delay of the energy transition which necessitates a more extensive and prolonged use of fossil fuels. This can be explained as follows. Using the knowledge stock acquired by competitors allows for a prolonged use of cheap fossil fuels and thus gives freedom to invest into other sectors and expanding the economy at a faster pace. In contrast, building up knowledge about renewable energy use is costly, since renewable energy sources have a large capital-output ratio, initially. Hence, in the iterated negotiation process, agents gradually postpone their countries’ energy transitions to later and later times as they seek to benefit from other countries renewable energy investments. The process is only stopped when any further postponement causes a severe increase in the cost of the already largely depleted fossil fuel stocks. In the actual negotiations, this ‘after you’ policy is evident in many countries who see the benefits of waiting for new technologies to emerge and become cheaper (van Vuuren et al., 2004). In this waiting game in the IFST case, available individual fossil fuel reserves are stretched for as long as possible. This is achieved by lower investments into goods production, i.e. correspondingly slower economic development. Accordingly, consumption is very pronounced in the earlier years. Eventually, when fossil fuel reserves expire, costs of further fossil fuel use become too large at around year t ¼ 60. Then, a steep transition (and hence a transition where nobody can take unfair advantage of knowledge spillovers) towards renewable energy sources is undertaken. Such a sharp transition requires the concentration of all investments in the renewable energy sector. This causes a dip in investments into goods production, and hence a short phase of stagnation of production. Goods production never reaches the same level as in the reference scenario (IFIT), the average utility level is

52

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Fig. 5. Comparison of optimal investment decisions if the finite amount of fossil fuels and the knowledge stock are treated as assigned to the separate countries (IFIT, red line) or as global stocks that are accessible to each country at no additional cost (SFIT, green line; IFST, blue line, SFST magenta line). The simulations are carried out for N ¼ 10 identical countries. All regions are characterized by the same parameters. Note that the climate system is not treated as a commons, i.e. there is no climate change induced damage. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

U z 54.4  0.1. Cumulative fossil fuel use is significantly higher than in the IFIT-case. The last case is the SFST scenario (magenta curve). The effects of treating fossil fuels and knowledge as accessible to all are combined. The competition for the global stock of fossil fuels is fiercer than in the SFIT case. A delayed energy transition and initially complete reliance on fossil fuels permit a high rate of economic growth early on. The fossil fuel capital stock keeps expanding and no investments into renewable energy capital are made. However, when fossil fuel depletion starts requiring ever more investments, a sharp and sudden transition to a renewable energy based economy is needed to sustain energy supply and, with it, economic activity. The need for very large energy investments leads to an approximately 20-year recession period from year t ¼ 60 to year t ¼ 80, during which investments in goods production markedly dip and there is a temporary energy supply shortage (Fig. 8). There is an around 7% loss in utility levels as compared to the IFIT-scenario and the cumulative amount of fossil fuels used is more than twice as large as in the IFIT-scenario (Fig. 6). It makes up for a recognizable storyline: early accelerated growth caused by competition for a finite common resource and delayed investments into the renewable energy sector to avoid other’s benefiting from knowledge spillovers causes energy shortages and economic downfall when the transition to renewable energy becomes a necessity e and this despite long term planning with complete foresight! The outcome of the SFST-case suggests already that the impact of climate change will be more serious in an open world economy

because of the larger fossil fuel use. We therefore explore one last scenario, in which fossil fuels and knowledge about renewable energy technology are considered freely accessible to all and there are mild damages from climate change anticipated (a ¼ 0.03). We refer to it as SFSTSD e shared fuel, shared technology and shared damages. The main difference to the previous simulations with fossil fuels and knowledge allocated to each country separately, is that utilities keep decreasing after the threshold at N ¼ 4, cf. Fig. 2. The reason becomes clear from the above discussion: a delay in the energy transition causes significantly higher cumulative fossil fuel use and thus more carbon is emitted into the atmosphere, leading to significantly larger temperature increases from global warming. The loss in utility is significant, reaching almost one third for large numbers of countries (Fig. 7). It is useful to summarize the outcomes in more general terms. First, treating the finite amount of fossil fuel resources, the learning by doing knowledge stock or both combined as freely tradable/ exchangeable entails a decline of relative utilities because of a postponed energy transition. This effect becomes the more severe the larger the number of competing regions. However, compared to the threshold effect when treating the atmosphere as a common pool (see Subsection 2.1), the decline of relative utilities with the number of competing countries is gradual and smooth. The reason is that countries in the first two situations are not faced with an ‘energy transition’ or ‘no energy transition’ choice. Essentially, treating fossil fuels or the renewable energy knowledge stock as freely accessible to all has the same ToC-effect: the early use of fossil fuels is promoted. As a consequence, the transition from fossil

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t Fig. 6. Comparison of the capital stock paths if the finite amount of fossil fuels and the ‘knowledge stock’ are treated as assigned to the separate countries (IFIT, red line) or as global stocks that are accessible to each country at no additional cost (SFIT, green line; IFST, blue line, SFST magenta line). For the investment decisions and parameters see Fig. 5. Note that there is no climate change induced damage assumed in these experiments (a ¼ 0). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

fuel use towards renewable energy use becomes very sudden and threshold-like at a certain point in time (see below). Second, the combination of the effects of treating fossil fuels and knowledge of renewable energy technologies as freely accessible to all is non-linear, entailing a much steeper decline in utility than when each effect is considered individually. The effect of treating more stocks as shared generally is an enhanced (significantly suboptimal) use of fossil fuels. Third, when climate change damages are included, the threshold behaviour separates a regime with early strong investments into the renewable energy sector (N  4) and a regime with early extensive fossil fuel use and a fossil fuel scarcity induced transition to a renewable energy reliant economy only at later times. Treating the atmosphere as a common pool results in an additional non-linear decrease of utilities with the number of independent regions. In particular, utilities keep decaying after the threshold, i.e. even if the economies do not attempt an energy transition any more, utilities still decay with N because of increased competition and increasingly suboptimal use of the fossil fuel stock. 2.3. The commons effect: does it matter how rich the world is? In the simulations shown so far we assumed the countries to have equal and rather large capital stock and output levels. In our model, economic growth occurs because the goods producing capital stock increases due to investments from savings. This leads to higher capital-labour (K/L) ratios which permit a higher labour

productivity. If the capital stock grows faster than the labour force, which in our model is taken proportional to population, income per capita will increase. With our parametrization, the capital-labour ratio in the collaboratively managed world always saturates at approximately K/L z 4, which can thus be considered a maximum value for a maturely developed world. We present a series of experiments in which we keep the initial population the same but adjust the initial value of the capital stock. Defining Kmax ¼ 4L as the maximum attainable capital stock, we investigate the relative utility loss in competitively managed worlds with initially all countries rich, medium or poor. As before in Fig. 2, the ratio of average utilities in competitive and collaborative worlds UN/U1 is considered the relevant indicator and shown in Fig. 9 as a function of the number of countries. It is seen that independent of the initial capital-labour ratio there is a decline in average utilities with the number of independent regions but the severity of the effect differs for the rich, medium and poor worlds. High income (rich) worlds suffer less from the commons effect, in the sense that the threshold from the situation where all countries undergo an energy transition to the situation where no energy transition is attempted by any country occurs for larger N than in a world of low-income (poor) countries. Also, compared to the benchmark case of one centrally governed world, the initial decline of utilities is slower. Thus, worlds with larger available capital stocks suffer less from competitive behaviour than worlds where capital scarcity limits the options for future development.

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N Fig. 7. (Top) Relative amount of fossil fuel used in the 100 year period (normalized by xF) and (Bottom) relative utility achieved in the 100 year period in simulations with different numbers of regions and different scenarios. Note that for N ¼ 1 IFIT, SFIT, IFST, and SFST coincide e these scenarios also define the optimal level of fossil fuel use. SFSTSD is the combined case where fossil fuel stocks and renewable energy knowledge are treated as accessible to all countries and damages from climate change (a ¼ 0.03) are included (this results in the steep transition at N ¼ 4). Note also, that for all scenarios fossil fuel use increases drastically above optimal levels as the number of competing regions N increases; a steep transition between a ‘relatively cooperative regime’ and an ‘uncooperative’ regime, however, only occurs when climate change is included.

This outcome is easy to understand. Poor countries need to buildup their goods producing capital stocks to reach the optimal capital labour ratio. As income per capita is initially small, these countries also face pressures from population growth. Undertaking an energy transition will delay the build-up of the goods producing capital stocks and thus slow down labour productivity growth and the demographic transition. This should be avoided because the resulting larger population renders it very hard to achieve acceptable per capita incomes later on. In contrast, in the beginning a rich country already has large goods producing capital stocks, thus also large per capita incomes and an only slowly growing population. Available capital stocks then allow for per capita incomes to be kept high while incurring the costs of an energy transition. The net effect of the counteracting forces of population growth and economic development is that the balance between larger per capita incomes and the benefits from an early energy transition are shifted in favour of the first in a poor country, while being in favour of the second in affluent countries. Hence the economic value of fossil

In the previous subsections, we explored the development path of a world with countries that pursue either a completely individually oriented competitive strategy (‘defect’ in game theory

1.1 developing (K0=.1 Kmax) transition (K0=.5 Kmax) developed (K0=.9 Kmax)

1

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Fig. 8. Energy demand/supply ratio over time for different numbers of competing regions for SFST (similar, but even more drastic for SFSTSD). The initial oversupply (and the minor wobbles) are an artifact of the discretization of time into intervals of DT ¼ 5 timesteps e the initially fast buildup of the economy requires a steeply growing energy supply. Note that for the optimal scenario (N ¼ 1) no energy shortage is encountered. However, if competition increases, the very steep temporal transition from a fossil fuel based economy towards a renewable energy based economy first results in an energy oversupply, then a severe energy shortage and then an oversupply again. The first oversupply is a mitigation response to an expected crisis, the unavoidable crisis stems from the unwillingness to let others profit from accumulated knowledge, and the later oversupply is again a result of the discretization and the supply requirements of a very fast growing economy after the transition.

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language) or a completely cooperative strategy. As mentioned before, in the real world one rather expects shades of grey between both extremes. The reasons to rather not expect fully competitive behaviours are manifold. They range from ethical concerns, different perceptions of fairness, altruism and bounded rationality in decisionmaking (Gintis, 2000) to the possibility of coalition formation and bargaining for agreements that foresee payment transfers between countries to ensure cooperative behaviour (Kaitala and Pohjola, 1995). While the second poses an interesting problem that we shall explore in more detail in another study, in the present work we focus on a summary inclusion of altruistic behaviours into decisionmaking. Would it matter if a country considers also the well-being of the world-at-large, besides its own national interests, even if it is costly? Such a form of altruism is a modification of an individualistic strategy that can be introduced in a straightforward way by redefining country i’s goal functions as:

~ ; P Þ ¼ aU UðC i i

X j

Cj ;

X  Pj þ ð1  aÞUðCi ; Pi Þ;

(10)

j

P P where, as before, the first term Uð Ci ; Pi Þ denotes the worldi By interpolating how utility and U(Ci, Pi) country i’s owni utility. much regard a country pays to the world as a whole as opposed to its own individual interests, the parameter a specifies the degree to which altruistic concerns effect a country’s decisionmaking. A value a ¼ 0 represents a country that does not pay attention to the welfare of the rest of the world, i.e. the fully competitive country as defined above and a ¼ 1 specifies a fully cooperative country that strifes to maximize the world utility. We present results for a world consisting of N ¼ 8 economically equivalent countries that strife to optimize their goal functions in a non-cooperative way, according to the negotiation dynamics described in Subsection 1.2. Fig. 10 summarizes the dependence of relative utilities and the relative amounts of fossil fuel used as a function of the altruism parameter a, under the assumption of mild climate change (a ¼ 0.03). As expected, we find that relative utilities for a ¼ 0 (no altruism) and a ¼ 1 (complete altruism) coincide with the simulations described in Subsection 2.1 (IFITSD). A comparison with simulations carried out previously (cf. Fig. 2) confirms that a setup with a ¼ 0 corresponds to a Nash equilibrium solution where no country undertakes an energy transition and economies are managed mainly on the basis of fossil fuels. However, it is noteworthy that in the interval in between, i.e. for 0 < a < 1, the dependence of utilities on the altruism parameter is not smooth. Up to around a < 0.3 countries don’t change their decisions, even though the utility of others formally enters the goal

function. The respective curve for relative world emissions confirms that no country undertakes an energy transition in this regime. At a ¼ 0.3 a threshold is reached. Countries weighing concerns for the world for more than 30% in their goal function undertake energy transitions, albeit at first inefficiently and too late to avoid serious climate change impacts (DT z 4 K). Accordingly, for a  0.3 cumulative fossil fuel use and hence carbon emission trajectories start to decline. There is also a gradual improvement in average utilities for larger a. In effect, this situation is similar to the situation of decreasing competition discussed earlier in this section: an increasing degree of altruism leads to decisions in favour of earlier and earlier energy transitions that finally approach the (world-) optimum solution. 3. Heterogeneity: two-country worlds with different sizes, climate impacts and income levels In this section we investigate the impact of different sources of heterogeneity in country characteristics on the utility loss of regional vs. global strategies. We perform experiments with a two-country world (N ¼ 2), in which we systematically tune country sizes (here treated as equivalent to population sizes) while keeping the overall population in the world constant. The next subsection is then devoted to an investigation of the impact of heterogeneity of climate damages. The experiments are again performed for a two-country world, in which the ratio between the damage constants of the two countries is systematically tuned, while the overall amount of damage in the world is held constant. We finish this section with a brief exploration of the role of income differences in a two-country world. 3.1. Countries of different sizes Imagine the world consists of one rich and one poor country. How would the ToC effect work out in such a world? Such a world consists of two independent countries that are in the same state of economic development.9 Different sizes of the regions are modelled by different initial population sizes while keeping the initial world population constant. The relative size of the populations, p ¼ P1(0)/P2(0), is used as the indicator. To make sure that the countries are in the same state of economic development, we ensure that regions have the same capital-labour ratios, proportionate initial capital stocks for goods production and the same relative sizes of the energy sectors.

9 The influence of the state of the economic development on the commons effect has already been discussed in Subsection 2.3.

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pop. size ratio Fig. 11. Relative utility (normalized by optimal utility for a cooperative equal-size country world) vs. the ratio of the population sizes p in a two-country world. To make sure that the situations are comparable, the size of the world is held constant and regions are initially in economically equivalent circumstances. See also the panels in Fig. 12 for more analysis.

One expects that the treatment of the fossil fuel resources as well as the knowledge stock about renewable energy technologies built up from learning by doing will influence the relative performance of economic regions of different size. For instance, if knowledge is not freely available to all, a small region with a smaller

population will find it more difficult to accumulate enough knowledge of its own to make energy production from renewable sources viable. One then expects that regions perform worse the smaller they are. As this effect can be easily predicted, we concentrate in the following on the situation where fossil fuel and knowledge stocks are both treated as freely accessible to all so that smaller regions are not a priori disadvantaged. Fig. 11 shows the dependence of the larger and the smaller countries’ relative utilities on the ratio of the initial population sizes p. To measure the loss of utility due to competitive management, as before we normalize utilities by the maximum attainable utility in a cooperatively managed world with the same climate damages per unit of emissions. It is seen that for values of the size parameter p above 0.8 there is not much difference to a world of equal-sized countries. When the ratio further drops and the disparity in size increases, the utilities for the large and the small country start to diverge. The smaller country benefits while the larger country loses out. The reason is easily understandable from our previous discussion: the smaller a country is, the relatively larger the emissions baseline (caused by the other country) it considers as a given in its decisionmaking in each iteration. Hence, if the small country emits more greenhouse gases, the impact on itself remains small in comparison to the emissions caused by the rest of the world cq. the large country. Consequently a decisionmaker in a small country will perceive it as optimal to emit a relatively larger amount of CO2 than a decisionmaker in a large country. Hence, overall emissions tend to be larger than overall emissions in a world composed of two countries of equal size. The beneficiary is the small country: it

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maintains a high share of fossil fuel in its energy supply or even does not undertake an energy transition at all if it is small enough. As in the real world, small countries are natural free riders. The loser is the large country: because of its larger size, its emissions impact on itself to a large degree, and it considers it the most prudent policy to stringently restrict its own emissions. Yet, it suffers from the damages caused by the smaller countries’ emissions. If the size ratio further declines, the utility loss for the large country decreases again because the small country becomes too unimportant and the world has become effectively a one-country world. The panels in Fig. 11 illustrate the corresponding investment allocations for the small (green curve) and the large country (red curve). As discussed above, the larger country undertakes an immediate energy transition with very large initial investments into the renewable energy sector. Accordingly, the buildup of the goods producing capital stock in the large country is delayed and

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damage ratio Fig. 13. (Top) Dependence of relative utilities (normalized by optimal utility if countries suffer equal damages) on the ratio of the damage coefficients for the two countries for cooperative and competitive management. (Bottom) Dependence of the relative (normalized by xF) fossil fuel use on the ratio of the damage coefficients for the competitive management (for cooperative management fossil fuel use is always minimal). The country that suffers smaller damages uses increasingly more fossil fuel, i.e. it delays the energy transition and for small enough damage does not undertake it at all. Eventually encountered small damages are compensated by larger investments into the fossil fuel sector. In contrast, the country that suffers larger damages is forced into an accelerated energy transition and has to spend a larger fraction of its income on compensating for damages in the energy sector to provide energy for a growing population.

57

what is left for consumption is quite low in the first decades. Overall, the share of consumption is markedly lower in the first 50 years and relatively stronger in the last 50 years. Conversely, the smaller country does not undertake an energy transition. It can take a free ride by benefiting from fossil fuel abundance, which shows up as fast initial growth in the goods producing sector. In summary, the simulations show that in a competitively managed world with significant country size differences the larger countries have lower economic growth as they lose out to the selfish behaviour of the small countries that lack an incentive for a transition to renewable non-carbon energy sources. 3.2. Countries experiencing different climate impacts It is becoming clear that future climate change will not impact people in the world in the same way (IPCC, 2007). Some may hardly be affected, others will suffer severely. In this subsection we investigate the impact of heterogeneity in climate change impacts in cooperatively and competitively managed worlds. Our model world consist again of two countries, N ¼ 2, with the same economic starting conditions but with different degrees of damage from climate change (cf. Equation (2)). Fossil fuels and knowledge about renewable energy technology are shared and climate damage is assumed to be mild (a ¼ 0.03). We use the ratio of the damage multipliers r ¼ a1/a2 of the respective countries as a measure of heterogeneity. We make sure that the average damage, i.e. the two countries combined, is constant. More precisely, for a given damage ratio r ¼ a1/a2 we set a1 ¼ 2r/(1 þ r) and a2 ¼ 2/(1 þ r). Figs. 13 and 14 summarize the results of the experiments. In the top panel of Fig. 13, the dependence of relative utilities for the large and small damage countries on the ratio of the damage constants r for the countries are given in cooperatively and competitively managed worlds. First, one notes that also in the cooperatively managed world the utilities achieved in the small and the large damage country differ, but only by an amount that grows linearly with decreasing damage ratio r. Consequently, the utility difference between both countries is narrow over the whole parameter range. As the results in Fig. 14 show both countries always undergo an instant energy transition towards renewable energy use. That is, in the cooperatively managed world no investments into the fossil fuel-based energy sector are undertaken at all. Initially, the country with smaller damages invests more into economic growth and consumes significantly less, while consumption in the large damage country is shifted towards earlier periods. Both countries invest almost equal shares into the renewables energy sector, but larger contributions towards learning-by-doing come from the small damage country, because it can grow a larger economy. In the competitively managed world, the country with smaller damages increasingly lacks incentives to undergo an energy transition when its relative damage becomes smaller as compared to the country with larger damage. As a consequence, for nearly the whole simulated time period it relies on fossil fuels and contributes heavily towards global warming, thereby causing damages to the large damage country. Hence the large damage country is forced into an early accelerated energy transition and needs to invest a large and over time increasing share of its income into maintaining the energy sector. 3.3. Optimal strategies in a world with one rich and one poor country A third form of heterogeneity we test is a difference in income. How does the commons effect unfold in a world of large income inequality? For this purpose we again construct a world consisting

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0.45

0.5

0.4

0.45

0.35

σY

σC

0.55

0.4

0.3 large, comp. small, comp. large, coop. small, coop.

0.35

large, comp. small, comp. large, coop. small, coop.

0.25

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0.2 0

20

40

60

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100

0

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100

80

100

t

0.18

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σR

σF

t

60

0.08 0.06

large, comp. small, comp. large, coop. small, coop.

0.2 0.15

large, comp. small, comp. large, coop. small, coop.

0.04 0.02

0.1 0.05

0

0 0

20

40

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80

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0

20

t

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t

Fig. 14. Comparison of investment decisions in a competitively and a collaboratively managed world consisting of one country that suffers small damages (damage coefficient a ¼ 0.03 0.1) and one country that suffers large damages (damage coefficient a ¼ 0.03 1.9). The damage ratio is r ¼ 10/19.

small. In contrast, the richer and larger economy has higher fuel use and carbon emissions and the decisionmaker follows allocations similar to a global decisionmaker. As a result, a larger utility loss for the larger country is to be expected and found. Secondly, the poor country faces the challenge to increase its goods producing sector and increasing the capital-labour ratio will

1 developed developing 0.98

rel. utilities

of two countries, N ¼ 2, that are in different stages of economic development. Again, we assume that fossil fuels and knowledge about renewable energy technology are shared and climate change damages are mild (a ¼ 0.03) (SFSTSD). As in Subsection 2.3, different income levels are simulated with different initial capitallabour ratios. We implement this by tuning the initial capital stock of the poor country, e.g., K2(t ¼ 0) for country 2, while keeping the initial state of the economy of the rich country constant (K1(t ¼ 0) ¼ 1000). The initial populations for both countries are taken equal at Pi(t ¼ 0) ¼ 1000, i ¼ 1,2. Hence, the initial capital stock ratio k ¼ K2(t ¼ 0)/K1(t ¼ 0) is an indicator for the degree of income inequality in the model world. Note, that this experiment does not reflect different partitionings of the same world. Rather, worlds of different sizes are compared, and the optimal development path of the cooperative world has to be determined for every comp coop =Ui , i ¼ 1,2, then measures the ratio k. The utility ratio, Ui effect of competition on achievable utilities. In Fig. 15 we report the dependence of the relative utilities of the rich and the poor country on the initial development ratio k. As in previous comparative graphs, for k ¼ 1 the simulation reproduces the simulation of a world with two equal countries and a competitive strategy. Generally speaking, relative utilities are a monotonically declining function of the income disparity ratio. Comparing the utility losses in the rich and the poor country, we find as a rule of thumb that the rich country loses out more than the poor country. This can be understood from similar arguments to those advanced in Subsection 2.3 and from country size-related considerations discussed in Subsection 3.1. First, the poor country initially has a smaller economy. Hence, the impact of its emissions on its own economy is initially relatively

0.96

0.94

0.92

0.9 0

0.2

0.4

0.6

0.8

1

capital size ratio Fig. 15. Dependence of relative utilities (normalized by optimal utilities achieved in a cooperative situation) of the developed and the developing country on the ratio of initial capital stocks K2(t ¼ 0)/K1(t ¼ 0) between the countries. All resource stocks are treated as common pools, climate damages are mild (a ¼ 0.03).

M. Brede, B.J.M. de Vries / Environmental Modelling & Software 44 (2013) 44e61

be the dominating consideration in the early time period. This can only be done by relying on cheap fossil fuel. In other words, for the poor country carbon emissions have a larger intrinsic value than for the rich country and it will therefore aim at using more fossil fuel and undertake a later energy transition than the rich country. As a consequence, the rich country contributes most to the cost reduction of renewable energy through learning by doing, while the poor country benefits from slower depletion of fossil fuel stocks and from the build-up of knowledge about renewable energy technology. Of course, from an equity point-of-view this is precisely the kind of fairness that one would provide for the poor in a B1world e think of the Millennium Development Goals, for instance. A corollary to this finding is that the benefit of shared learning by doing gets lost when the knowledge stock is not shared and that it will therefore be optimal policy for the poor country to undertake an even slower transition to renewable energy. Similarly, outcomes change when the fossil fuel resource base is not accessible for all countries. 4. Summary and discussion In this paper we have explored long-term optimal investment allocations in a simple economy-energy-climate model with an emphasis on the difference between two distinct possibilities: (i) a world where countries are managed independently and decisionmakers of individual countries pursue the maximization of consumption of their own country and (ii) a world where all decisionmakers strife to optimize a world utility function such as to maximize the income of an average citizen of the world independent of where he lives. The two are referred to as competitively and cooperatively managed worlds. Simulations are then carried out for one given world, partitioned into two or more independent countries. In these experiments we study the role of competition with respect to fossil fuel use, developing an alternative, renewable noncarbon energy source and climate change. To evaluate results, we analyse the utility relative to the utility in a single, cooperatively managed world as a measure of the commons effect. As one may expect, the incentive to undertake the energy transition and thus prevent serious climate change damage decreases with an increasing number of countries. This contrasts with the assumption of a central cooperative world-planning agency, underlying most previous economy-energy-climate model simulations. The way the world is managed has important implications for projections of future economic growth, the corresponding energy use and the probability to avert climate change. Importantly, whether and the extent to which climate change can be averted depends on the degree of competition in the use of the atmosphere. The relationship between competition and the prevention of serious climate change is smooth for a small number of countries, but a threshold is passed at some critical level of competition, i.e. a certain number of (identical) countries, and economies suffer large damages from global warming. Below the threshold, countries undertake an energy transition from fossil fuel to renewable energy based economies. When there are more countries each optimizing their own utility, competition delays and thus reduces the efficiency of the transition. Beyond the threshold no energy transition is undertaken and actors opt to base their economies on fossil fuels and bear the associated costs of climate change. This threshold level for competition depends on the expected severity of climate damages. For mild damages the threshold occurs already at levels of less than six countries, while for severe damages more competition can be tolerated before the threshold is passed. One possible solution that overcomes the ill-effects of noncooperation is solidarity and concern for others, irrespective of one’s own utility. We studied effects of solidarity by including an

59

altruism-parameter in the competitive decisionmakers’ goal functions. In worlds influenced by different degrees of altruism, the above threshold effect is recovered: weighing world concerns up to a threshold percentage of around 30% in goal functions leaves the development paths virtually unaltered. Only above the threshold, larger degrees of altruism gradually allow improvements in world management. Both the thresholds in the dependence of utilities on competition and on altruism point towards important nonlinearities in the world system, when competition is considered. A second key finding is that future development paths are strongly impacted by whether fossil fuel resources and knowledge about renewable energy technology are open-access stocks available to all or not e even without considering the role of the atmosphere as a global common sink. It appears a reasonable scenario for a highly globalized 21st century world that demand for fossil fuels is met from the total stock without access restrictions to any country and that knowledge about renewable energy is, within limits, freely accessible to all. In such situations competition leads to inefficient resource use patterns. In particular, competition for fossil fuel resources induces planning strategies that focus heavily on early, fossil-fuel based economic growth. Fossil fuel reliance continues up to or beyond a point where a transition to the initially more costly renewable resource would have been economically rational. As a consequence, countries are forced into significantly steeper energy transitions with associated demand-supply tensions. From a resource depletion and climate change perspective, these high-consumption strategies are unsustainable in a very literal way. Future policies, both national and global, have to consider the large differences in size, income levels and climate change impacts that exist in the world. We therefore investigated the role of such differences between countries in a series of simulation experiments in two-country worlds. Because their own efforts at mitigating climate change are relatively less important, smaller countries tend to behave as free riders. A poor country with an initially low capitallabour ratio will focus first on increasing its labour productivity. This is achieved by utilising cheap fossil fuels. Considerations of a transition to more capital-intensive renewable energy become secondary. A country that is expected to suffer much less from climate change than other countries is also expected to postpone the energy transition. Generally speaking, the outcomes of the model experiments indicate that these forms of heterogeneity emphasis the effects of competition, entailing correspondingly larger losses of utility in competitively managed heterogeneous worlds than in homogeneous worlds. During the last decade, it has become increasingly clear that climate policy can only be effective if it involves the majority of large greenhouse gas emitters and if the essential role of energy in economic development is adequately addressed. Our model simulations indicate that creating alliances and negotiation blocks such as the EU is an important strategy to reduce the risk that the energy transition to non-carbon sources starts too late to prevent serious climate change impacts. In an open world economy where everyone has access to high-quality fossil fuels and to knowledge about renewable energy technology, there is presumedly more economic growth, but our simulations indicate that the fiercer competition tends to cause a decline in long-term welfare even with no or minor climate change impacts. It suggests the relevance of a global resource scarcity policy and of independent ‘Alleingang’ policies as part of the economy-energy-climate quandary. A third conclusion, confirmed in game-theoretic analyses, is that small and/or poor countries have rather strong incentives to apply competitive strategies, which makes it important to engage them early on in globally coordinated energy-climate policies. Finally, the larger the anticipated negative climate change impacts, the larger

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the welfare losses of competitive strategies in an open world economy. We think that these insights should be borne in mind when judging the outcomes of IAM-based global optimization policies and that, as a next step, this kind of regional vs. global trade-offs should be included in the IAMs. Appendix A For simplicity, in this model the effects of depletion of a finite resource of fossil fuel and of an increasing productivity of renewable energy resources due to learning by doing are described by threshold functions parametrized by









0 FR ðxÞ ¼ F0R þ FN R  FR

 1=ptan1 ðgR ðx  xR ÞÞ þ 1=2

(11)

and N 0 FF ðxÞ ¼ FN F þ FF  FF

 1=ptan1 ðgF ðx  xF ÞÞ þ 1=2

(12)

0 N where f0R and fN R (fF and fF ) are the initial and asymptotic productivities of renewable (fossil) energy generation, xR the amount of cumulated output x where a transition towards enhanced productivities of renewable energy generation sets in, xF the transition point where depletion of fossil fuels becomes noticeable, and gR and gF are the respective steepnesses of the transitions. The introduction of the inverse tangent functions is based on purely heuristic grounds because they can be used to parametrize the expected tendencies. We have also experimented with other functional forms (parametrizations based on logistic functions or heavyside functions). The qualitative results presented in the paper have proved robust to such changes.

Appendix B Essentially, the atmospheric carbon concentration is based on carbon emissions which decay according to five processes with weights ci, i ¼ 1,.,5 and lifetimes ai, i ¼ 1,.,5 according to MaierReimer and Hasselmann (1987):

Zt pCO2 ðtÞ ¼ pCO2 ðt0 Þ þ 0:47 t0

! 5 X st : dsEðsÞ c1 þ ci exp ai 

(13)

i¼2

The shares of the different lifetime classes are c1e5 ¼ 0.13, 0.2, 0.32, 0.25, and 0.1 while the corresponding atmospheric lifetimes are a25 ¼ 363, 74, 17, and 2 years. From these CO2 concentrations the potential equilibrium change of the mean global surface temperature is calculated as

DTp ðtÞ ¼

DT2 CO2 ln2

ln

pCO2 ðtÞ ; pCO2 ð0Þ

(14)

where DTCO2 , the climate sensitivity, is the mean global equilibrium surface temperature change for a doubled CO2 concentration. In the following we use DT2 CO2 ¼ 3K which corresponds to the best estimate of (IPCC, 2007). Inertia in the system, which stems mainly from the heat capacity of the oceans, leads to a lag of the actual adaptation of global surface temperatures, which we model according to

  dDT ¼ b DTp  DT ; dt

(15)

with the timescale 1/b for equilibration estimated at around 20 years.

Appendix C Unless otherwise stated, we always parametrize our simulation experiments as follows. Countries are assigned an initial capital stock K(0) ¼ 500 and have an initial population of P(0) ¼ 1000 inhabitants. Energy capital stocks are parametrized such that the initial economy is sufficiently supplied with energy (demand/ supply ratio fenergy ¼ 1) and a fraction of 1/10 of the initial energy supply is generated from renewable energy sources. Scaling of country sizes is achieved by introducing effective emissions constants according to Equation (9) and by an appropriate scaling of the threshold for fossil fuel abundance (xF ¼ NF0 with F0 ¼ 100,000) and the threshold for the effectiveness of learning by doing (xR ¼ NR0 with R0 ¼ 20,000). If fossil fuels are not treated as openly accessible by all countries (referred to as ‘IF’ scenarios), each individual country n is allocated a threshold xnF ¼ F0 ; n ¼ 1; .; N. Similarly, if knowledge about renewable resource use is considered as non-exchangeable between countries (referred to as ‘IT’ scenarios), each country is allocated a learning by doing threshold xnR ¼ R0 ; n ¼ 1; .; N. A summary of the settings of all simulation experiments discussed in this paper is given in Table 1.

Table 1 Overview over the settings of all simulation experiments described in the paper. Experiment

Countries Illustrated Section Climate Fossil N in figures damage a fuels xF

IFITSD IFIT no D SFIT no D IFST no D SFSTSD Varying K(0) Altruism Large vs. small Different a Rich vs. poor

1..18 10 10 10 10 1..7 8 2

2,3,4 5,6,7 5,6,7 5,6,7 5,6,7,8 9 10 11,12

2.1 2.2 2.2 2.2 2.2 2.3 2.4 3.1

0.03e0.1 0.03 0.03 0.03 0.03 0.03 0.03 0.03

N xnF ¼ F0 xF ¼ NF0 xnF ¼ F0 xF ¼ NF0 xF ¼ NF0 xF ¼ NF0 xF ¼ NF0

2 2

13,14 15

3.2 3.3

0.03 0.03

xF ¼ NF0 xR ¼ NR0 xF ¼ NF0 xR ¼ NR0

Technology xR xnR xnR xnR xR xR xR xR xR

¼ R0 ¼ R0 ¼ R0 ¼ NR0 ¼ NR0 ¼ NR0 ¼ NR0 ¼ NR0

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Further reading Sterman, J., Fiddaman, T., Franck, T., Jones, A., McCauley, S., Rice, P., Sawin, E., Siegel, L., 2013. Management flight simulators to support climate negotiations. Environmental Modelling & Software 44, 122e135.