metadata: authors: 0: author: Satija,Gaurav
1: author: Steinbuks,Jevgenijs
2: author: Zhao, Fu
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docna: 0: docna: Sustainability of solar electricity : the
            role of endogenous resource substitution and market mediated responses
docty: Policy Research Working Paper
subtopic: Mining & Extractive Industry (Non-Energy),Oil Refining & Gas Industry,Rural and Renewable Energy,Energy Policies & Economics,Solar Energy,Energy Demand,Energy and Environment,Energy and Mining,Renewable Energy
teratopic: Energy,Rural Development,Industry,Environment
abstracts: cdata!: This study seeks to understand how
            materials scarcity and competition from alternative uses
            affects the potential for widespread deployment of solar
            electricity in the long run, in light of related technology
            and policy uncertainties. Simulation results of a computable
            partial equilibrium model predict a considerable expansion
            of solar electricity generation worldwide in the near
            decades, as generation technologies improve and production
            costs fall. Increasing materials scarcity becomes a
            significant constraint for further expansion of solar
            generation, which grows considerably slower in the second
            half of the coming century. Solar generation capacity
            increases with higher energy demand, squeezing consumption
            in industries that compete for scarce minerals. Stringent
            climate policies hamper growth in intermittent solar
            photovoltaics backed by fossil fuel powered plants, but lead
            to a small increase in non-intermittent concentrated solar
            power technology. By the end of the coming century, solar
            electricity remains a marginal source of global electricity
            supply even in the world of higher energy demand, strict
            carbon regulations, and generation efficiency improvements.
repnme: repnme: Sustainability of solar electricity : the
            role of endogenous resource substitution and market mediated responses
display_title: Sustainability of solar electricity
            : the role of endogenous resource substitution and market
            mediated responses
listing_relative_url: /research/2015/01/23884211/sustainability-solar-electricity-role-endogenous-resource-substitution-market-mediated-responses
topicv3: Solar Energy m1326390 528,Energy and Extractives m1326595 507,Power and Electricity Sector m1327094 515,Silver m1503519 2937,Natural Gas m1583894 4712
publishtoextweb_dt: 2015-01-26T00:00:00Z
historic_topic: Energy,Rural Development,Industry,Environment
no_of_pages: 40
author_keys: 0: author_key: 1281706
1: author_key: 666646
model_extractions: WPS7178 Policy Research Working Paper 7178

# Sustainability of Solar Electricity

The Role of Endogenous Resource Substitution and Market Mediated Responses _Jevgenijs Steinbuks Gaurav Satija Fu Zhao_ Development Research Group Environment and Energy Team January 2015
Policy Research Working Paper 7178

# **Abstract**

This study seeks to understand how materials scarcity and competition from alternative uses affects the potential for widespread deployment of solar electricity in the long run, in light of related technology and policy uncertainties. Simulation results of a computable partial equilibrium model predict a considerable expansion of solar electricity generation worldwide in the near decades, as generation technologies improve and production costs fall. Increasing materials scarcity becomes a significant constraint for further expansion of solar generation, which grows considerably slower in the second half of the coming century. Solar generation capacity increases with higher energy demand, squeezing consumption in industries that compete for scarce minerals. Stringent climate policies hamper growth in intermittent solar photovoltaics backed by fossil fuel powered plants, but lead to a small increase in non-intermittent concentrated solar power technology. By the end of the coming century, solar electricity remains a marginal source of global electricity supply even in the world of higher energy demand, strict carbon regulations, and generation efficiency improvements.

This paper is a product of the Environment and Energy Team, Development Research Group. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The authors may be contacted at jsteinbuks@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Sustainability of Solar Electricity: The Role of Endogenous Resource Substitution and Market Mediated Responses<sup>_∗_</sup> Jevgenijs Steinbuks<sup>_†_</sup> , Gaurav Satija<sup>_‡_</sup> , and Fu Zhao<sup>_§_</sup> January 23, 2015

# 1 Introduction

It is widely recognized in the economic literature that the provision of high quality public goods and services (Anand and Ravallion 1993, Kremer 1993, Besley and Ghatak 2006) and, particularly, energy services (Ferguson et al. 2000, Toman and Jemelkova 2003, Barnes and Toman 2006, Chakravorty et al. 2014), has a profound impact on economic development. The challenges to providing energy services are also widely recognized (Barnes 2007, Brew-Hammond 2010, Deichmann et al. 2011). Extension of traditional power supply systems tends to be uneconomic in developing countries when loads are small due to low population density and/or low consumption per user. Traditional smallscale generation (in particular, with small to medium size diesel generators) also tends to be uneconomic due to high fuel costs.

Renewable energy can help accelerate access to energy, particularly for the 1.4 billion people without access to electricity (IPCC 2011). In many developing

> _∗_ We thank Uwe Deichmann, David Newbery, Michael Pollitt, Michael Toman, Wally Tyner, and the participants of the USAEE Annual Meetings and Energy & Environment Research Seminars at the World Bank and the University of Cambridge for helpful comments. We also appreciate nancial support from Purdue Global Policy Research Institute, the National Science Foundation (award ENG-1336534), and the World Bank Research Support Budget.

> _†_ Steinbuks: Development Research Group, The World Bank. Email: jsteinbuks@worldbank.org.

> _‡_ Satija: Department of Agricultural Economics, University of Maryland.

> _§_ Zhao: School of Mechanical Engineering and Division of Environmental and Ecological Engineering, Purdue University.

1
countries, both decentralized grids based on renewable energy and the inclusion of renewable energy in centralized energy grids have expanded (Baumert et al. 2005, Nouni et al. 2009, Deichmann et al. 2011). Solar photovoltaics (PV) and concentrated solar power (CSP) have emerged as particularly promising renewable technologies for addressing the energy/development nexus, while also mitigating greenhouse gas emissions. Both PV and CSP are carbon-free renewable technologies that are highly modular and thus relatively easy to build to scale and to maintain. PV in particular can be a very cost-competitive source of electric power in smaller-scale rural and peri-urban applications.<sup>1</sup> The attractiveness of solar electricity as a source of renewable energy has increased recently due to signicant cost reductions from advances in technologies and economies of scale in production. The fact that PV generated electricity has reached or become close to parity at the busbar in several countries has stimulated new investment in grid-based PV as well as more decentralized applications (Byrne et al. 2010). The total installed PV capacity in the world has increased from 1.5 GW in 2000 to 39.5 GW in 2010, which corresponds to an annual growth rate of 40% (REN21 2010). In addition, many developed and some developing countries have introduced policies (e.g. feed-in taris, higher electricity purchasing price, and rebates on installation) to further encourage the development of the solar PV market (Schmalensee 2011).

Though solar electricity has been seen by many to be an economically and environmentally attractive energy solution, it has its own challenges. In the next few decades, regulatory and institutional barriers can impede solar energy deployment, as can integration and transmission issues. In the longer term, the deployment potential of solar PV is aected by technological uncertainties and raw material scarcities. The economics literature on solar PV deployment has mainly focused on the short- and medium-term challenges related to regulation, integration and transmission constraints (for an excellent survey of these issues, see Baker et al. 2013). The long-run issues related to solar electricity deployment, such as technological uncertainties and material scarcities have largely been neglected in the economics literature, and remain an important gap to be lled.<sup>2</sup>

> 1In addition, non-electrical solar technologies also oer opportunities for modernization of energy services, for example, for water heating and crop drying (GNESD 2007).

> 2These issues are well recognized in environmental science and policy literatures (Jacobson and Delucchi 2011). This research adopts a longer-run perspective and largely revolves around the integrated assessment models (for a survey of solar PV in energy-economy integrated assessment models, see Baker et al. 2013), life-cycle assessment models (Fthenakis, Wang and Kim 2009) and expert elicitation surveys (Bosetti et al. 2012).

2
The focus of this study is on one so far neglected long-run challenge related to the production of solar generation capacity itself. The way a solar PV panel works, photons in sunlight hit the panel surface and are absorbed by semiconducting materials. Semiconducting materials presently used for solar PVs include monocrystalline silicon, polycrystalline silicon, ribbon silicon (usually referred to as crystalline silicon type), amorphous silicon, cadmium telluride, and copper indium gallium selenide/sulde (usually referred to as thin lm PVs). The former type dominates the market now, but the share of the latter is increasing. Manufacturing of either type of solar PV panels competes with other semiconductor-intensive industries for raw materials and resources. For example, in 2006, the booming solar panel production led to a short supply of polysilicon wafers resulting in a signicant price hike, which aected both the solar PV industry and computer chip manufacturers (LaPedus 2006). This competition is even more relevant for thin lm solar PVs. The production of thin lm PV panels directly competes for indium with the manufacturing of liquid crystal displays (Kapilevich and Skumanich 2009, Fthenakis 2009, Fthenakis, Mason and Zweibel 2009).<sup>3</sup> Many raw materials needed to produce PV cells have low natural reserves. For example, indium has an economical reserve of 2,800 tons and there is serious concern about its depletion (USGS 2009). The increasing demand for such PV raw materials in the globalized world economy leads to greater resource scarcity and higher prices, which can hinder the further cost reduction potential of PV panels and challenge its economic sustainability. While it will be possible to increase supply of these metals, it is very likely that more complicated processes will be needed to extract additional quantities. This will not only increase the production cost, but also lead to larger environmental footprints.

This study thus seeks to understand how materials scarcity and competition from alternative uses aects the potential of widespread deployment of solar electricity in the long run, in light of technology and policy uncertainties related to deployment of dierent solar electricity generation technologies. To address these issues related to long-run implications of widespread deployment of solar electricity, we adopt a dynamic partial equilibrium modeling approach, which explicitly accounts for endogenous resource substitution upstream and market

> 3This point has been largely ignored in environmental policy literature. For example, one recent study concluded that the development of a large global PV system is not likely to be limited by the scarcity or cost of raw materials (Wadia et al. 2009). This study however, assumes that all critical materials are being allocated solely for the purposes of solar PV, and ignores the eect of market mediated responses.

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mediated responses downstream. The model provides the computational basis to illustrate quantitatively, albeit in quite stylized fashion, the potential interactions among solar electricity generation and other relevant industries and elucidate policy challenges to large-scale solar electricity deployment in the long run. It is a dynamic, long-run, perfect foresight partial equilibrium framework, which chooses optimal scarce resource extraction policies that maximize the discounted net present value of the services from electricity (generated from both conventional thermal and solar electric power plants) and the industries, which compete with solar electricity for scarce minerals, such as e.g., articles of silver and consumer electronics.

Our modeling approach is related to a number of earlier studies that looked at similar problems. Perhaps the most closely related paper is Chakravorty et al. (1997), who develop a perfect foresight model in which the optimal supply of scarce fossil fuels is endogenously determined through competition with renewables, particularly solar energy. Unlike our paper, Chakravorty et al. (1997) do not account for either materials scarcity in solar generation itself or for the signicance of market mediated responses in non-energy industries. A more recent study by Chakravorty, Magné and Moreaux (2012) does account for endogenous substitution along fossil and non-fossil resource grades in a comprehensive dynamic partial equilibrium model aimed at investigating the long-term perspectives of nuclear energy. Finally, several recent studies employ dynamic partial equilibrium models with endogenous resource extraction and market mediated responses to analyze economic constraints to biofuels deployment (Chakravorty, Hubert, Moreaux and Nøstbakken 2012, Cai et al. 2014).

We solve the model over the 200 year period 2010 - 2209, focusing analysis on the next century, and calibrating the baseline to reect developments over the years that have already transpired. While we are under no illusions that our highly stylized baseline will be accurately predictive, it serves as an important point of reference for understanding the signicance of depletable resource constraints and market mediated responses along the socially optimal deployment path of solar electricity. Though we do not explicitly incorporate uncertainty at the optimization stage of the model, we do examine a combination of factors corresponding to the most important sources of uncertainty aecting deployment of solar electricity. Specically, we consider comparative dynamic eects of higher demand for energy services, global greenhouse gas (GHG) emissions regulations, and cost reduction in solar electricity generation technologies.

We show in our model baseline that global solar electricity production grows 4
considerably in next few decades, fostered by improved generation technologies and falling production costs. However, materials scarcities become a signicant constraint for further expansion of solar generation, which grows considerably more slowly in the second half of the coming century. Higher energy demand results in further expansion of solar electricity generation technologies but leads to even greater materials scarcities, which translate into output declines in industries that compete for scarce minerals, such as consumer electronics. Introduction of a GHG emissions constraint hampers further deployment of intermittent solar photovoltaics backed by fossil fuel powered electric plants, but leads to a small increase in non-intermittent concentrated solar power technology. A drastic cost reduction in CSP generation technology generates a further boost of solar electricity. Nonetheless, with all factors combined, solar electricity remains a marginal source of total electricity generation by the end of the coming century.

# 2 Model Description

In this section, we describe a deterministic, discrete dynamic, multi-sector, nite horizon computable partial equilibrium model for optimal deployment of renewable electricity under natural resource and technology constraints. The model focuses on allocation of scarce natural resources across the competing uses. It is based on the economic theory of depletable resources with grade selection and endogenous substitution, extended to incorporate stock-dependent inuences on supply and technological improvements in downstream industries, which act as a backstop to further extraction less ecient inputs.<sup>4</sup> Figure 1 shows the model structure.

There are three scarce primary resources in our model (see the bottom part of Figure 1) - fossil fuels, other minerals, and capital. The supply price of the former two resources is determined endogenously and depends on the quantity of resources available for extraction during a specic time period. The rental value of the capital stock is exogenous in this partial equilibrium model of nat-

> 4For the notable early contributions to the economic theory of depletable resources with grade selection see Herndahl (1967), Solow and Wan (1976), Kemp and Long (1980), Slade (1988) and Chakravorty and Krulce (1994). The endogenous resource substitution approach was pioneered by Nordhaus (1973) and subsequently extended by Chakravorty et al. (1997). The theory of nonrenewable resource supply with stock-dependent inuences was developed by Pindyck (1978), and subsequently extended by Pindyck (1982), Krautkraemer (1988), Swierzbinski and Mendelsohn (1989) and Cairns and Van Quyen (1998).

5
ural resource extraction and substitution. Each of three primary resources has dierent grades, whereby the word grade is used as a proxy for dierent cost and eciency characteristics of a resource utilization in a particular production sector. Other primary resources, such as labor, human capital, and land, have a relatively small contribution in electricity generation and are assumed to have perfectly elastic supply in the long run.

We analyze dierent electricity generation technologies, which compete for baseload in electricity dispatch. As our model is concerned with the environmental aspects of electricity generation, we dierentiate between the technologies based on their carbon content (see the middle part of Figure 1).<sup>5</sup> Conventional thermal (i.e., coal, oil, or natural gas-red) power plants combine capital and fossil fuels to produce electricity high in carbon content. Intermittent renewable electric plants (e.g., conventional solar photovoltaics) use primary capital and other minerals embodied in parts of the capital stock in the form of semi-conducting materials. We also consider emerging intermittent renewable technologies (e.g., organic solar photovoltaics) that employ only capital and do not depend on other minerals. Though intermittent renewable electricity is zero carbon itself (post deployment), it has to be combined with other generation technologies (most typically natural gas back-up generation) to maintain reliability of power supply (Gowrisankaran et al. 2011, Joskow 2011). The resulting mix is therefore not entirely carbon neutral, though it has lower carbon content than conventional fossil generation technologies. Finally, we consider an emerging non-intermittent renewable electricity technology (e.g., concentrated solar power with storage), which employs only capital and delivers zero carbon electricity. This emerging technology can be regarded as a clean backstop technology independent of exhaustible primary resources. Other conventional electricity generation technologies, such as hydroelectric and nuclear plants are considered integral and non-competing parts of the baseload, and are not included in the model.

We also analyze consumer goods (e.g., consumer electronics), whose production employs primary capital and other minerals embodied in parts of the capital stock in the form of semi-conducting materials. These consumer goods

> 5For simplicity we do not dierentiate between carbon and other environmental pollutants. While this assumption does not aect our core results, it prevents us from analyzing some interesting aspects of carbon regulation arising from non-separability of carbon and other pollutants in electricity generation (Agee et al. 2014). For example, a carbon emissions cap may result in an endogenous substitution between dierent grades of fossil fuels, leading to increased emissions of other pollutants, such as SOx and NOx (unless these emissions also are capped).

6
<!-- Start of picture text --> Welfare<br>Consumer Other Goods Electricity<br>Goods and Services<br>Zero Carbon Low Carbon<br>Electricity Electricity<br>with Storage<br>Zero Carbon High Carbon<br>Electricity w/o Storage Electricity<br>Other Capital Fossil<br>Minerals Stock Fuels<br><!-- End of picture text --> Figure 1: Structure of the Economy compete for scarce minerals with mineral-dependent electricity generation technologies. To complete the demand system we also include exogenous supply of other goods and services. The objective function of the model places value on the utility from consumption of consumer electronics, electricity, other minerals (e.g., gold and silver), and other goods and services net of exogenous costs (e.g., land rents, operation and maintenance, and capital adjustment costs) incurred in their production (see the upper part of Figure 1).

The key model equations are described below, with more complete information on equations, variables, and parameter values oered in the technical appendix.

# 2.1 Resource Use

Let there be _i_ exhaustible primary resources (e.g., fossil fuels, other minerals) with _j_ grades (e.g., coal, natural gas) available for use in _n_ sectors (e.g., electricity, consumer goods). The electricity sector is central to the problem we analyze, 7
and is disaggregated into _m_ generation technologies (e.g., thermal power plants, solar photovoltaics).

The extraction of exhaustible primary resources, _x_ , is described by the following equation: where _x_<sup>_ij_</sup> _t_<sup>denotesthestockofaprimaryexhaustibleresource</sup><sup>_i_ofgrade</sup><sup>_j_in</sup> period _t_ , and ∆ shows the net ow of the extracted resource (i.e., the dierence between extracted and newly discovered or recycled resources).

We assume that some of these primary resources (e.g., other minerals) are embodied in electricity-producing capital stock in form of semi-conducting materials (see the middle part of Figure 1). The accumulation of a primary exhaustible resource _i_ of grade _j_ used in sector _m_ and technology _n_ in period _t_ is given by where _x_<sup>_ijmn_</sup> _t_ denotes the accumulated amount of a primary exhaustible resource _i_ of grade _j_ used in sector _m_ and technology _n_ in period _t_ , ∆ shows the net addition to that resource stock, and _δt_<sup>_mn_</sup> is the depreciation rate of capital based on generation technology _m_ in sector _n_ .

Finally, the accumulation of capital, _k_ , used in sector _m_ and technology _n_ follows the standard rule where _kt_<sup>_mn_</sup> denotes the capital stock employed in sector _m_ and technology _n_ in period _t_ , ∆ shows the net addition to the capital stock.

# 2.2 Supply Relations

The middle part of Figure 1 illustrates key interactions on the supply side. The production of most types of electricity considered in the model as well as the production of consumer goods, combines capital, fossil fuels and other 8
minerals (the latter either used as intermediate inputs directly in the production process or indirectly embodied in capital stocks). The production technology of emerging renewable electricity (both intermittent and non intermittent) employs only capital, as renewable energy, e.g., solar radiation, is assumed to be available in an innitely elastic supply. The production of low carbon electricity combines thermal and intermittent renewable generation technologies. The production of electricity combines high-, low-, and zero carbon generation technologies. These production processes can all be characterized by the constant elasticity of substitution (CES) production function: where _yt_<sup>_mn_</sup> denotes the output of a good or service in sector _m_ and technology _n_ in period _t_ , _θ_<sup>_mn_</sup> and _θ_<sup>_ij_</sup> are Hicks neutral and input-specic conversion technology parameters, _α_<sup>_mn_</sup> is the value share of inputs, and _ρmn_ = ( _σmn −_ 1) _/σmn_ is the constant elasticity of substitution (CES) function parameter proportional to the elasticity of substitution between inputs, _σmn._<sup>6</sup> Specic equations for each production process are shown in the technical appendix.

# 2.3 Preferences and Welfare

The consumers place value on consumption of consumer goods, electricity, other minerals, and other goods and services. The supply of other goods and services is predetermined in our partial equilibrium model aimed at the analysis of renewable electricity. The reason we include other goods and services in the model is for a complete representation of the demand system. The consumer utility is described by the Stone - Geary preferences, with corresponding utility function given by where _yt_<sup>_p_denotestheconsumptionofgoodorservice</sup><sup>_p_inperiod</sup><sup>_t_,andthepa-</sup> rameters _β_<sup>_p_</sup> and _γ_<sup>_p_</sup> correspond to consumer expenditure shares and subsistence parameters for nal consumption goods and services.

> 6In special cases where only one input is used, CES collapses to a linear production function.

9
The objective of the planner is to maximize the welfare function, Ω _,_ dened as the sum of net aggregate surplus discounted for _T_ periods at the constant rate _d >_ 0 . Net surplus is computed by integrating the marginal valuation of each product, less the exogenous (e.g., land and labor) costs of extracting primary resources and producing consumer goods and electricity, as well as capital rental and adjustment costs. The planner thus allocates scarce primary resources across the extractives, consumer electronics, and power generation sectors to solve the following problem: where _Cij_<sup>_x_</sup> � _x_<sup>_ij_</sup> _t_ � _, Cmn_<sup>_k_(</sup><sup>_k_</sup> _t_<sup>_mn_</sup> ) and _Cmn_<sup>_y_(</sup><sup>_y_</sup> _t_<sup>_mn_</sup> ) denote, correspondingly, the primary resource extraction, capital rental and adjustment, and production cost functions. Specic functional forms of these costs are presented in the technical appendix.

# 3 Empirical Implementation of the Model with an Application to Solar Electricity

The model we develop is applicable to a broad range of mineral stock-dependent renewable electricity generation technologies, such as biomass, solar, and wind. For example, the output of biomass depends critically on inorganic fertilizer inputs (Heller et al. 2003), which are, in turn, produced of fossil fuels and inorganic minerals. The generation technology of both conventional solar photovoltaics and wind turbines employs dierent extractives, including scarce precious metals and rare earth elements (Fthenakis, Wang and Kim 2009, Feltrin and Freundlich 2008, Kleijn and Van der Voet 2010, Alonso et al. 2012). For the sake of concreteness, this paper focuses on solar electricity. Though currently solar electricity contributes only a fraction of the global energy supply, its potential deployment scenarios range from a marginal role to one of the major sources of energy supply in 2050 (IPCC 2011).

Specically, we consider four solar electricity generation technologies: conventional rst- and second-generation solar photovoltaics (PVs), emerging organic PVs, and concentrated solar power (CSP) with storage. Conventional PVs are both intermittent and depend on extractives. Organic PVs are also 10
intermittent but do not employ any scarce minerals in electricity generation.<sup>7</sup> However, their conversion eciency is smaller and their manufacturing cost is larger as compared to conventional PVs. The CSP with storage technology neither depends on scarce minerals nor is intermittent, however its manufacturing cost, which includes highly expensive electricity storage facilities, is larger compared to organic PVs. Other electricity generation technologies include coaland natural gas red plants. As explained earlier, we do not include large-scale hydro and nuclear generation plants, which are not assumed to compete with solar electricity in the nal dispatch.

The key exhaustible primary resources employed in these electricity generation sectors are coal, natural gas, silver and indium. While the reasons for including fossil fuels are straightforward, our choice of metals requires additional explanation. Silver is commonly used as an electrode material the rst-generation crystalline Si-based PV cells, which currently take the largest market share of solar electricity. According to a recent study by the Silver Institute (2011), since the expansion of PV technology in the early 2000s, silver otake for production of solar panels has expanded dramatically, from around 3 million ounces (Moz) in 2004 to nearly 50Moz in 2010. Currently, silver end use for thick-lm PV accounts for nearly 10 percent of the total industrial demand for silver. Feltrin and Freundlich (2008) argue that if the decit of silver is not addressed, crystalline Si solar cells will hardly surpass the few terawatt range in the coming century. Similarly, indium is a critical input in indium tin oxide (ITO) transparent conductor lms, which constitute the base for the second-generation thin lm PVs. Indium has very scarce reserves, and the its price reached a high of $1,000/kg in 2008 and continues to grow. Fthenakis (2009) argues that even in the optimistic scenarios, thin lm PVs would not be sustainable if the price of indium increases by more than about 10 times above its current maximum price.

To quantify the signicance of market mediated responses to potential deployment of solar photovoltaics, we focus on the consumer electronics segment of consumer goods. The Silver Institute (2011) estimates that the electrical and electronic industry accounted for 243 Moz of silver, or 50 percent of total industrial silver demand in 2010, of which 41Moz of silver were used in the pro7This assumption requires additional clarication. While organic PV cells themselves do not contain any scarce materials, the metal back electrodes and the transparent conductive front electrodes both do. However, as mineral requirements for organic PVs are considerably lower than for conventional PVs (and are likely to be even lower in the future), we treat them as not dependent on scarce minerals.

11
duction of cell phones, personal computers, laptops, and plasma display panels. The main use of indium today is in liquid crystal displays (LCDs), accounting for 65% of its current consumption (Fthenakis 2009, p. 2749). The consumer electronics industry is the most signicant end user of both silver and indium, and thus a key competitor for input materials to both types of conventional PVs. Additionally, silver itself is a nal consumer good. The Silver Institute (2011) estimates that about 30 percent of all silver is consumed directly in the form of silverware, coins and jewelry, although its non-industrial share constantly is declining constantly.

The technological parameters are taken externally from a number of sources, including earlier relevant studies in material and environmental sciences, international agencies, and life-cycle assessments. This is a common practice, which is widely employed in small- and large-scale computational economic-energyenvironmental models (e.g., GCam, DICE, GTAP-E, MIT-EPPA, and many others; for a survey of these models applied to the analysis of solar energy, see Baker et al. (2013)). The parameters related to costs and preferences are either estimated econometrically (based on data availability) or calibrated to match the recent extraction paths of indium, silver and fossil fuels, as well as recent deployment dynamics of solar PV capacity. The model parameters and data sources are summarized in the technical appendix.

We simulate the model over the 200 year period 2010 - 2209, focusing analysis on the next century to minimize the terminal eects.

# 3.1 Model Baseline

Figures 2 - 4 show the key results for our model baseline simulations. While these simulations are by no means intended to be accurately predictive, they are a useful point of reference for understanding the signicance of depletable resource constraints and market mediated responses along the socially optimal deployment path of solar electricity.

Figure 2 shows the optimal production path of solar electricity, broken down by dierent generation technologies, and the reserves of silver and indium, which, as explained above, are the key primary inputs to deployment of conventional PVs. The output of electricity from conventional PVs expands drastically in the rst half of the coming century, reaching its maximum of 800 TWh around 2050 (panel a).

12
<!-- Start of picture text --> Stock of Silver: Model Baseline<br>600<br>500<br>400 \NN<br>2 NN<br>& 300 _—<br>Br SN<br>200 NN aoe———<br>100 —<br>0 2020 2040 2060 2080 2100<br>. | . Year<br><!-- End of picture text -->

<!-- Start of picture text --> Stock of Indium:Model Baseline<br>16<br>14 XY<br>12 N\<br>10 NNONNS<br>n _~<br>& 8 oS<br>Br —<br>6 NN——<br>4 ———<br>2<br>0<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->
<!-- Start of picture text --> 2 x 10° Stock ofNatural Gas: Model Baseline<br>NN<br>8 oN<br>_ ee<br>0.5<br>0 2020 2040 2060 2080 2100<br>2 | 7 Year<br><!-- End of picture text -->

<!-- Start of picture text --> 5 Stock of Coal: Model Baseline<br>7X 10<br>6p —<br>———<br>—~ee<br>5 ne——ae<br>ot<br>g5<br>3<br>2<br>1<br>0<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->
<!-- Start of picture text --> Consumption of Consumer Electronics:<br>Model Baseline<br>1200<br>1000<br>»<br>2800<br>a<br>g<br>5< 600<br>z<br>= 400<br>200<br>0<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text --> <!-- Start of picture text --> Consumption of Silver as End<br>Product: Model Baseline<br>8<br>6<br>Ss7<br>g<br>a4<br>z°<br>2<br>0<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->
in silver reserves at the end of the coming century (panel b).

# 3.2 Counterfactual Simulations

Private and public investment decisions in solar electricity generation technologies must be made despite signicant uncertainty about their future costs and eciencies, evolution of energy demand, as well as the future valuation of energy services from solar electricity, including its GHG abatement potential. Though we do not explicitly incorporate uncertainty at the optimization stage of the model, we examine the ways in which global solar electricity production responds to changes in factors corresponding to the most important sources of uncertainty associated with this problem. Specically, we consider the comparative dynamic eects of changes in consumer preferences, global GHG emissions regulations, and cost reduction in solar electricity generation technologies. Below, we present three counterfactual scenarios, which capture the following changes:

- Scenario A: Permanent increase in electricity demand. Evolution of global electricity demand is the key driver aecting deployment of dierent renewable electricity generation technologies in the long run (Neuho 2005). Our model does not incorporate the key drivers shaping global electricity demand in the long run, such as population increases, economic growth, changes in industrial structure, urbanization, and improved electricity access and reliability. Instead, we attempt to quantify the signicance of these drivers by conducting sensitivity analysis with respect to exogenous changes in electricity demand, measured by a 20 percent increase in the expenditure share on electricity services and a comparable decline in expenditures on predetermined other goods and services. As the expenditures on goods and services from competing industries (i.e., silver and consumer electronics) do not change, this sensitivity analysis also allows for quantifying the signicance of market-mediated responses.

- Scenario B: The GHG emissions constraint is introduced. The scenario is illustrative of the range of regulatory uncertainty surrounding global GHG emissions based on the projections of the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC 2014). Meeting the targets aimed at tackling the climate change challenge requires major reductions in carbon emissions from the electricity sector, and expansion

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of low carbon electricity generation technologies (Grubb et al. 2008), including solar electricity. In this scenario, we introduce a maximum target, amounting to a 50 percent reduction in baseline GHG emissions from coal and natural gas by 2100. This corresponds to the least amount of regulation aimed at achieving CO2 equivalent concentration (including GHGs and aerosols) at stabilization of 580 650ppm, which is consistent with the Representative Concentration Pathways 4.5 (RCP4.5) GHG forcing scenario.<sup>8</sup> The target is introduced in 2010 and its stringency is linearized over the next 100 years.

_•_ Scenario C: Permanent decline in the costs of the Concentrated Solar Power generation technology. CSP has important advantages over other solar electricity generation technologies, such as less dependency on primary materials and the option for non-intermittent electricity supply. The high cost of capital is considered one of the key barriers for CSP deployment, however the potential for cost reductions in CSP appears to be quite large (Ummel and Wheeler 2008). Some recent studies have argued that if these cost reductions are realized, CSP could become a viable backstop technology to replace coal-red generation globally (Williges et al. 2010, Viebahn et al. 2011). This scenario envisions a hypothetical case of a 50 percent reduction in CSP capital costs realized in 2010, which corresponds to the maximum feasible range of the near term cost reduction for that technology (IEA-ETSAP and IRENA 2013).

We also consider combinations of scenarios A and B (scenario A+B) and scenarios A, B, and C (scenario A+B+C). For all scenarios we report changes that are incremental to the model baseline.

Figures 5 and 6 describe the results of simulations of changes in the optimal consumption of consumer electronics, electricity, and silver, as well as changes

> 8RCPs constitute a new set of scenarios that replace the Special Report on Emissions Scenarios (SRES) standards for the Intergovernmental Panel on Climate Change (IPCC ) Fifth Assessment Report (AR5). RCPs are referred to as pathways to emphasize that their primary purpose is to provide time-dependent projections of atmospheric GHG concentrations (Moss et al. 2008). There are four pathways: RCP8.5, RCP6, RCP4.5 and RCP2.6, whereby each number post RCP refers to the projected radiative forcing by the end of the coming century. RCP 4.5 is the second optimistic stabilization scenario in which total radiative forcing is stabilized shortly after 2100, without overshooting the long-run radiative forcing target level (Clarke et al. 2007, Wise et al. 2009). Introducing regulation consistent with the most optimistic stabilization scenario, the RCP2.6, would require additional modeling changes, such as options for sequestering carbon, which are beyond the scope of the research question addressed in this study.

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in the electricity generation portfolios for scenarios A, A+B, and A+B+C. The results for scenarios B and C alone are available in the technical appendix.

# 3.2.1 Changes in the Electricity Generation Portfolio

Figure 5 shows changes in the electricity generation portfolios for scenarios A, A+B, and A+B+C. Beginning with scenario A, we observe that the permanent increase in electricity demand results in an expansion of all electricity generation technologies. Production of electricity from coal and natural gas red power plants increases, respectively, by 2,350 and 3,700 TWh per year by 2050, which is 22.4 and 12.8 percent larger compared to the model baseline (panels a and b). Production of electricity from conventional and organic PVs continues to increase throughout the coming century, adding 131.6 TWh per year by 2100, which is 16 percent larger compared to the model baseline (panel c). Production of electricity from CSP increases by a small amount, adding 5 TWh per year by 2100 (panel d).

Now consider scenario A+B, whereby the permanent increase in energy demand is accompanied by the introduction of the GHG emissions constraint. As the GHG emissions constraint becomes more stringent, production of electricity from coal and natural gas red power plants declines around 2040 (panels a and b), osetting the expansion in electricity output from increased demand for electricity. At the end of the coming century, production of electricity from coal and natural gas red power plants declines by 3,700 and 9,400 TWh per year, which is 36 and 33 percent smaller compared to the model baseline. Contrary to our expectations, the GHG emissions constraint results in a decline in electricity generation from both conventional and organic PVs, although this decline takes place much later in the coming century, around 2075 (panel c). The reason for this, somewhat paradoxical, decline is that solar photovoltaics are an intermittent source of electric power generation, and thus need to be complemented by electricity from coal or natural gas red power plants. As electricity generation from both coal and natural gas red power plants declines with the increased stringency of the GHG emissions constraint, so eventually does the electricity generation from PVs. Electricity generation from CSP technology, which we assume is non-intermittent and zero carbon, benets from the GHG emission constraint and adds 12 TWh per year by the end of the century (panel d).

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<!-- Start of picture text --> Coal-based Electricity Generation:<br>Deviation from Model Baseline<br>4000<br>2000<br>=<br>E -2000 ——<br>-4000}| ~—— ScenarioBase A :<br>—— Scenario A+B<br>-6000<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->

<!-- Start of picture text --> Natural Gas-based Electricity Generation:<br>Deviation from Model Baseline<br>5000<br>0 we<br>= -5000 ~<br>E NN<br>;<br>-10000}| ——— ScenarioBase A TM<br>—— Scenario A+B<br>-15000<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->

<!-- Start of picture text --> Conventional and Organic Solar PV<br>Generation: Deviation from Model Baseline<br>150<br>100 —<br>50} / _<br>§ / ~<br>Ss gl<br>= N<br>=<br>°50<br>—Base<br>-100 —— Scenario A<br>—— Scenario A+B<br>-150<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text --> <!-- Start of picture text --> CSP Solar Generation:<br>Deviation from Model Baseline<br>100<br>80<br>§ 60<br>= —— Base<br>= ~~ Scenario A<br>e 40 —— Scenario A+B<br>20 eeScenario A+B+C7 _<br>_ ee<br>ol<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->
<!-- Start of picture text --> Consumption of Consumer Electronics:<br>0 Deviation from Model Baseline<br>—— Base<br>3.<br>2-150 —— Scenario A+B<br>5<br>& -200<br>Z|= -250 _<br>ee<br>300, OO<br>-33 5 0<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->

<!-- Start of picture text --> Total Electricity Generation:<br>1 x10! Deviation from Model Baseline<br>——<br>8<br>= -0.5<br>Ee<br>-1<br>~— Base<br>Ls —— Scenario A<br>>!) Scenario A+B ]<br>Scenario A+B+C<br>“5 tt<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text --> <!-- Start of picture text --> Total Emissions:<br>Deviation from Model Baseline<br>2000<br>1000<br>a<br>8 0<br>& : .<br>>§ -1000 /<br>~<br>6 — Base ~<br>-3000||~ Scenario A .<br>—— Scenario A+B :<br>-4000<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->

<!-- Start of picture text --> Consumption of Silver as End Product:<br>Deviation from Model Baseline<br>0.4<br>_<br>03 —— Base<br>Scenario A<br>7g —— Scenario: A+B<br>B 0.2<br>[o} ‘<br>0.1), LL<br>HS<br>oN<br>0<br>2020 2040 2060 2080 2100<br>Year<br><!-- End of picture text -->
natural gas red power plants, GHG emissions increase, adding 1,400 billion tons of CO2 by 2100 (panel c). The consumption of silver in nal demand is little changed (panel d).

As we have shown earlier, the introduction of the GHG emissions constraint results in lower production of electricity from all generation technologies, except for the inframarginal CSP. As the higher cost of energy adversely aects total welfare, there is an additional small decline in the consumption of consumer electronics (panel a). Electricity consumption is substantially aected with the positive eect of higher energy demand reversed around 2040 (panel b). At the end of the coming century, total electricity generation declines by 13,200 TWh per year, which is 33 percent smaller compared to the model baseline. As most of the electricity generation comes from coal and natural gas red power plants, GHG emissions follow a very similar path, coming into net decline after 2040, and decreasing by 2,900 billion tons of CO2 by 2100 (panel c). As the GHG emissions target results in long-term reduction in deployment of conventional PVs, it indirectly increases the availability of silver, more of which is consumed in nal demand. Compared to the model baseline, consumption of silver as an end use product increases by 350 tons per annum in 2010, however this increase disappears by the end of the coming century (panel d).

The addition of a drastic reduction in costs of CSP generation technology (scenario A+B+C) has a very small impact on the consumption of nal goods and services and GHG emissions. As shown above, the increase in electricity generation from CSP is drastic relative to its baseline level; however, this increase has a very small impact on total electricity generation (panel b), and does not aect the consumption of other goods and GHG emissions from fossil fuel plants.

# 4 Conclusions

This study demonstrates that materials scarcity and competition from their alternative end uses has a signicant eect on the potential for widespread deployment of solar electricity in the long run. Our analysis is based on a computable partial equilibrium model, which provides the basis for the quantitative analysis of potential interactions between solar electricity generation technologies and other relevant industries, underpinning the options for solar and other renewable energy policies. It is a dynamic, long-run, perfect foresight framework, 21
which chooses optimal scarce resource extraction policies that maximize the discounted net present value of the services from electricity (generated from coal and natural gas red power plants, and solar electricity), consumer electronics, silver products, and other goods and services.

Though our results are not supposed to be accurately predictive, they serve as an important point of reference for understanding the signicance of depletable resource constraints and market mediated responses along the socially optimal deployment path of solar electricity. We also examine the ways in which global solar electricity generation responds to changes in factors corresponding to the most important sources of uncertainty associated with this problem. Specically, we consider the comparative dynamic eects of higher demand for energy services, GHG emissions regulations, and cost reduction in solar electricity generation technologies.

Our model baseline suggests that global solar electricity production will continue to expand rapidly in the near decades, fostered by improved generation technologies and falling production costs. However, later throughout the coming century, materials scarcities become a signicant constraint for further expansion of solar generation. Policies aimed at boosting demand for solar electricity will adversely aect other industries, such as consumer electronics, which compete with solar photovoltaics for scarce materials. Introduction of the GHG emissions constraint hampers further deployment of intermittent solar photovoltaics backed by fossil fuel electric plants, but leads to a small increase in nonintermittent concentrated solar power technology. This result demonstrates the signicance of policies aimed at decoupling intermittent electricity generation from back-up generation based on carbon-intensive power plants. While drastic cost reductions in CSP generation technology lead to a further boost of solar electricity, they are not sucient for making signicant changes in the global electricity generation portfolio. Solar electricity remains a marginal source of global electricity generation even in the world of higher energy demand, strict GHG emissions regulations, and generation eciency improvements. These ndings suggest that even with major technological breakthroughs solar electricity alone will not be sucient to address the growing concerns about climate change mitigation in the coming century.

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