Toward an optimal household solar subsidy: A social-technical approach

Energy 147 (2018) 377e387

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Toward an optimal household solar subsidy: A social-technical approach Shen Liu a, Gregory Colson a, Na Hao b, Michael Wetzstein c, * a

Department of Agricultural and Applied Economics, University of Georgia, Athens, GA, 30602, USA School of Economics, Beijing Technology and Business University, Beijing, China c Department of Agricultural Economics, Purdue University, West Lafayette, IN, 47907, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 7 July 2017 Received in revised form 16 October 2017 Accepted 5 January 2018

An analytical framework is developed for integrating the social science into a socio-technical approach for assessing the optimal solar energy subsidy. Estimating the optimal solar subsidy based on the analytical framework takes into account technical environment, health, employment, and electricity accessibility benefits as well as household's prosocial behavior. Results indicate that an optimal subsidy is positively affected by the marginal external benefit; however, this effect is mitigated by the rebound effect based on motivational-crowding theory. Calibrating the model using published elasticities yields estimates of the optimal solar energy subsidy equal to approximately $0.02 per kilowatthour when prosocial behavior is omitted. The estimated optimal subsidy is in line with many current state feed-in-tariff rates, which may be the upper bound when social science is not considered in policy analysis. © 2018 Elsevier Ltd. All rights reserved.

JEL classification: Q2 Q4 Q5 Keywords: Marginal external benefit Motivational crowding Optimal subsidy Prosocial evaluation Solar photovoltaic (PV)

1. Introduction Despite economic returns from the adoption of many energyefficient technologies and a wide array of government policies to foster adoption, uptake rates are slow and not aligned with policymakers' expectations. This “efficiency paradox” indicates an assortment of factors beyond simple cost-benefit economics influences adoption decisions. For the case of residential solar photovoltaic (PV) technologies, Sommerfeld et al. [42] indicate there are a number of motivations and energy use behaviors, including prosocial, associated with adoption. Understanding how consumers view solar technologies and their interaction with policies aimed to foster PV adoption is critical for unlocking the potential of solar PV [41].
nabou and Tirole [7]; providing government As addressed by Be

* Corresponding author. E-mail addresses: [email protected] (S. Liu), [email protected] (G. Colson), [email protected] (N. Hao), [email protected] (M. Wetzstein). https://doi.org/10.1016/j.energy.2018.01.038 0360-5442/© 2018 Elsevier Ltd. All rights reserved.

incentives for households taking a certain action can have perverse effects, when considering households' social reputations. The classic illustration is paying for human blood could actually reduce supply [44], with recent applications by Ackermann et al. [1]; Clot et al. [10]; and Dwenger et al. [13]. Household prosocial behavior is the intrinsic motivation to take actions, which are in the community's best interest. In accordance with motivational-crowding theory, external motivation in the form of government incentives can result in a loss (crowding out or rebound effect) of intrinsic motivation [23]. A subsidy for PV adoption could mitigate, crowd out, intrinsic prosocial behavior of adoption. Households' reputation for being pro-environment may not be as strong with a PV subsidy. Moving beyond simple economic calculations to consider prosocial behaviors has been raised not only for PV policies, but energy policy in general. Cooper [11] offers a diagnosis for why the social sciences have limited impact on energy policymaking and advocates a new socio-technical approach to the study of energy. In terms of PV policy, the idea is to integrate the prosocial behavior

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S. Liu et al. / Energy 147 (2018) 377e387

efforts of Sommerfeld et al. [42] into actual PV policy. Economics is the natural bridge for such integration. What is missing in general energy policy, PV policy in particular, is household prosocial behavior. Against this backdrop, the objective of this study is to employ economic theory for integrating prosocial behavior into a socio-technical approach for PV government policy. This will direct the development of empirical efforts within both social and natural sciences toward aligning households' adoption of renewable energy with policymakers' expectations. As a foundation, in the past decade an array of government policies, programs, and financial assistance have supported PV as the fastest rising renewable power technology [29]. PV generation expanded from 1.5 GW in 2000 [29] to just over 100 GW in 2012 [39]. In the United States, a range of government programs drives this expansion of residential-renewable energy systems. At the federal level, taxpayers may claim a 30% personal tax credit for residential PV systems and installation costs [12]. State and municipal authorities also employ various supporting policies in the form of cash rebates, net metering, renewable-portfolio standards (RPS), solar set-asides, and solar renewable-energy credits [8,43]. Recently, states have enacted Feed-in-Tariff (FIT) systems (California, Hawaii, Oregon, Vermont, and Rhode Island) [39]. Goldberg [25] estimates when considering cumulative subsidies and electricity generation, from 1947 to 1999, solar energy received subsidies worth $0.51/kWh (in 1999 dollars). Badcock and Lenzen [6] estimate that in 2007 the global total subsidy for solar PV was $0.64/kWh (in 2007 dollars). More recent studies by the EIA [14,18] estimate that the direct federal financial interventions and subsidies in U.S. solar energy markets grew from $179 million in 2007 to $1134 million in 2010 (2010 dollars). Despite the long history of subsidizing solar energy in the U.S., previous research has not determined the optimal level of a PV subsidy with consideration of possible motivational crowding. In contrast, a research vein is directed toward determining the engineering-economic efficient feed-in-tariff (FIT) [4], the design of regulatory incentives [5,24], and the influence of a carbon tax or cap-and-trade [37] for attracting renewable-energy investments. Similarly, Burr [9] and Hughes and Podolefsky [27] estimate the effects of policies on residential solar installations. A related effort by Lobel and Perakis [33] develops a model which determines the optimal solar subsidies required to achieve a desired adoption target at minimum cost. Supporting this effort is determining the desired adoption target, based on internalizing external environmental effects through a solar subsidy. Previous research efforts have integrated the physical science of PV with economics in their development of engineeringeconomic models. Missing from these efforts is further integration with the prosocial behavior of PV. As developed in the following section, failure to integrate prosocial behavior into the calculus of determining the optimal subsidy can lead to the Sommerfeld et al. [42] comment: past policy impacts have missed policymakers' expected targets.

2. Model Building upon previous work in the optimal tax/subsidy literature, including gasoline taxes [36], ethanol subsidies [46], and biodiesel subsidies [50], a theoretical model for the optimal residential PV subsidy is developed. In particular, households' PV prosocial valuations are integrated into this optimal tax/subsidy
nabou and Tirole [7]; households may literature. As addressed by Be receive pro-environmental and social self-esteem benefits from generating solar electricity. Letting q represent the household

benefit, a household's level of PV will influence this benefit,

q ¼ (PV), where it is assumed vq/vPV > 0 and v2 q=vPV 2 < 0. The adoption of PV provides a household a positive reputation or mystique of being prosocial in terms of pro-environmental concerns. In contrast, any PV subsidies may decrease these prosocial benefits. 2.1. Agent decision problem For integrating prosocial valuation into determining the optimal PV subsidy, consider a household PV decision based on utility maximization. The main objective is to provide an intuitive treatment of household PV economics in a universal setting considering prosocial valuation. It is assumed solar energy, PV, is determined by peak hours of sunlight per year z (hours) and quantity of solar panels purchased by the household (watts or kW). Let h denote peak hours of sunlight per day, z ¼ 365h. In general, a household receives utility from electricity consumption and from generating solar energy (personal satisfaction, independent security from generating energy, and prosocial valuation) [48]. A household also receives satisfaction from non-interference of electrical power, A. Specifically, access to electricity, A, is assumed to depend on a household's solar energy production

A ¼ AðPVÞ with

vA > 0: vPV

(1)

Assume a household also receives satisfaction from a conventional utility plant (coal, natural gas, and petroleum), F, and a composite consumption good, X, with associated numeraire price pX ¼ 1. A utility function may then be represented as

u½X; F; PV; AðPVÞ; qðPV Þ;

(2)

where all the determinants positively influence utility. Fig. 1 illustrates this household problem where a household's choice variables directly influence its level of satisfaction. These choice variables are arguments in (2): composite consumption good, X, fossil fuel, F, solar energy, PV, electricity access, A, and prosocial valuation, q. Electricity access and prosocial valuation are influenced by solar energy. As indicated in Fig. 1, associated with this utility function are external environmental effects along with “green” and high-tech job opportunities and/or rural development effects (externalities).1 Let the environmental effect of consuming power-plant electricity, D, be decomposed into greenhouse gas emissions, Dg , and localized air pollution, Da , (e.g., SO2;  NOX ;  PM2:5 ;  and PM10 ) which have a more localized negative impact on the environment, health, and infrastructure. It is assumed greenhouse gas emissions and localized air pollution depend on aggregate conventional electricity, F. Specifically,



 vDg vDa > 0; > 0: D ¼ Dg F þ Da F ; vF vF

(3)

In addition to these environmental effects, there may be “green”

1 The choice of external effects is subject to empirical investigation determining their individual magnitudes. The objective is to present a set of possible external effects and determine how such effects in general will affect the optimal subsidy. There are other external effects including environmental damage from transportation and extraction of fossil fuels (oil, coal, and natural gas). Including these externalities does not enrich the theoretical model, but will positively affect the optimal subsidy. Also, it is assumed the U.S. economy is closed in terms of no leakages from the United States' attempts to reduce negative external effects, influencing another country's efforts [21].

S. Liu et al. / Energy 147 (2018) 377e387

379

Externalities

Choice Variables

Commodity, X

Greenhouse,

Budget Constraint

Conventional Power, F

Indirect Utility Function: Maximize Household Satisfaction

Photovoltaic, PV

Access, A

Local Emissions,

Green Jobs, J

Subsidy, s

Photovoltaic, PV

Marginal Benefit of Solar Energy equals Marginal Cost minus the Subsidy

Prosocial Valuation,

Indirect Utility Function

Fig. 1. Agent (household) decision.

and high-tech job opportunities, J, effects associated with the PV industry. Employment can be a macroeconomic benefit of renewable-energy deployment [30]. Subsidies for renewableelectricity generation will change the composition of domestic employment. Job opportunities, J, then depends on aggregate solar energy, PV.


 J ¼ J PV ;

vJ > 0: vPV

(4)

Associated with green job opportunities is potential poverty mitigation in rural areas with the instillation of residential solar PV systems. Subsidies for rural PV systems will provide direct incentives for rural development. Considering this possible rural development would augment this employment effect (4). Additively attaching these external effects to the household utility function (2) yields

U ¼ u½X; F; S; A; q  dðDÞ þ fðJÞ:

(5)

The external effects D and J are features of the household's environment, so they are perceived as exogenous. The functions u and f are quasi-concave, whereas d is weakly convex representing the disutility from environmental damages. The external benefits of reduced environmental damages (both greenhouse gas emissions and localized air pollution) along with increased “green” and high-

tech job opportunities and possible rural development are embedded in (5). Given the presence of externalities, households ignore the effect of their own electricity consumption on environmental damages from consuming and generating electricity along with job opportunities and rural development. In Fig. 1, this is represented by the dash lines connecting the externalities with the household utility maximizing problem. Government subsidy programs in the form of a solar panel subsidy sI , subsidy of the amount of PV generated, sPV , and a feed-in-tariff (FIT) subsidy, sF , are developed with the objective of internalizing the externalities within households' decisions. A household's expenditures are on X, the composite good, E, its consumption of electricity (kWh), and PV z , the purchases of solar panels (kW), with associated per-unit prices, 1, pE , and pPV . The price of solar panels is pPV ¼ rðI  sI Þ, where r is the interest rate and I and sI are the cost of the panels and installation subsidy per sunlight hour. With income W, a household then attempts to maximize utility (2), subject to the budget constraint

X þ pE E þ rðI  sI ÞPV ¼ W þ sPV PV þ ðpE þ sF ÞPV; X þ pE F  ½rI  ðrsI þ sPV þ sF ÞPV ¼ W; where F ¼ E e PV denotes household consumption of non-solar electricity. Denote s ¼ ðrsI þ sPV þ sF Þ, then

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S. Liu et al. / Energy 147 (2018) 377e387

X þ pE F þ ðpz  sÞPV ¼ W;

(6)

vL ¼ uX  l ¼ 0; vX

where pz is the price of solar panels, (rI). As illustrated in Fig. 1, (6) directly influences the level of household satisfaction with the subsidy, s, influencing both (6) and (5). The three subsidies collapse into a single component s for internalizing household externalities and in practice differ across countries. As an example, if a FIT subsidy is consistently higher than the market price of electricity, it represents a continuous subsidy, as is the case in Germany [6,22]. However, in Spain, FITs are set at a level 80%e90% of the average market electricity price [6], which does not provide a continuous subsidy. Only during periods of fluctuating electricity prices does the subsidy effectively exist [6,26]. In general, FIT rates leading to significant renewable-energy investments are set above the retail cost of electricity [20]. Aggregate household consumption of electricity E consists of aggregate conventional electricity from the power plant F and aggregate solar energy generated by the households, PV. The power plant sells E at a price pE , and buys PV at a price of (pE þ s). It is assumed the power plant produces F ¼ E  PV at a marginal constant cost c. Electricity price pE depends on aggregate household electricity consumption, E, aggregate solar energy generation PV, and subsidy s. In terms of the United States, approximately 75% of its population is served by investor-owned utilities, which are private companies but subject to state regulation [38]. The remaining 25% of the population is served by consumer-owned utilities, which are established as nonprofit utilities. However, even the investorowned utilities are regulated to only earn a normal return on investments with revenue equaling costs.

Equation (9a) states that the household's marginal monetary benefit of consuming an additional kWh of energy from a power plant is equal to the price of energy purchased from the electrical plant. Equation (9b) states that the agent's marginal monetary benefit of producing an additional kWh of solar energy is equal to the cost of producing an additional kWh pz , less the subsidy s. The marginal benefit is the sum of the direct benefits from using solar, uPV ; plus the indirect benefit of increasing access, uA APV , and prosocial valuation, uq qPV . Failure to consider possible prosocial valuation will yield a non-optimal solution.

pE E ¼ ðpE þ sÞPV þ cF

2.3. Welfare effects

Solving for pE yields the price of electricity as a function of the subsidy and aggregate conventional and solar electricity,

 PV
s þ c: pE s; F; PV ¼ F

(7)

vL ¼ uF  lpE ¼ 0; vF vL ¼ uPV þ uA APV þ uq qPV  lðpz  sÞ ¼ 0; vPV vL ¼ W  X  pE F  ðpz  sÞPV ¼ 0: vl The marginal utility of PV, uPV , is augmented by the benefits of PV in non-interference of electrical power, uA APV , along with the marginal prosocial valuation benefits of PV, uq qPV . Taking the ratios and rearranging

uF

l

¼ pE ;

(9a)

ðuPV þ uA APV þ uq qPV Þ

l

(9b)

As illustrated in Fig. 2, the welfare effects of an incremental change in the solar energy subsidy may be determined by totally differentiating the indirect utility function (8) with respect to the subsidy level s. With the aid of the envelope theorem vV=vs ¼ uq qs þ lPV, and vV=vpE ¼ lF < 0, vV=vðpz Þ ¼ lPV < 0; 0

The utility sets the electricity price as the solar-to-fossil energy ratio times the subsidy plus marginal cost. Given the nonprofit status of the utility, the subsidy is paid by the utility customers in the form of an increase in the price of electricity pE .

¼ pz  s:

0

vV=vD ¼ d < 0, vV=vJ ¼ f > 0, vV=vA ¼ uA > 0, yields 0 dD 0 dJ dV dp dðpz Þ dA ¼ uq qs þ lPV  lF E  lPV d þ f þ uA : ds ds ds ds ds ds (10)

From the definition of pE , D, J, and A in (7), (3), (4), and (1), respectively, 2.2. Agent's choice As illustrated in Fig. 1, the optimal subsidy is determined from the indirect utility function

Vðs; pE ; pz ; D; J; R; A; qÞ ¼ maxfuðX; F; PV; A; qÞ  dðDÞ þ fðJÞ þl½W  X  pE F  ðpz  sÞPVg;

(8)

obtained by maximizing (5) subject to (6), where l is the Lagrange multiplier. The terms s;  pE ; pz ;  D; J; and A become the model's parameters. The F.O.C.s for (8) are

dpE PV PV vF 1 vPV s 2 þs ; ¼ F F vs ds F vs

(11a)

dD vDa vF vDg vF ¼ þ ; ds vF vs vF vs

(11b)

dJ vJ vPV ¼ ; ds vPV vs

(11c)

dA vA vPV ¼ : ds vPV vs

(11d)

In determining (11), aggregate electricity from power plant, F,

S. Liu et al. / Energy 147 (2018) 377e387

381

0     1 dV uq PV PV vF 1 vPV dðpz Þ d vDg vF vDa vF ¼ qs þ PV  F s 2 þs  PV  þ F F vs ds l ds l l vF vs vF vs F vs 0

þ

f vJ vPV uA vA vPV þ l vPV vs l vPV vs 0

0

u PV vF vPV dðpz Þ d vDa d vDg  ¼ q qs þ s s  PV þ ds F vs vs l l vF l vF  0 f vJ u vA vPV þ þ A : l vPV l vPV vs

!

and aggregate solar energy generated by a household, PV, are no longer constant, so their partials with respect to s are partials of F and S. Substituting (11) into (10) and dividing by l results in the marginal monetary welfare effect of the solar energy subsidy s: Equation (12a) may be simplified by defining the externality, 0

access, EDg F

and

development

effects

as

EDa F ¼ dl

vDa vF

(12a)

vF vs

>0 ;

0 0 vD vJ vA > 0; yielding: ¼ dl vFg > 0 ; EJPV ¼ fl vPV > 0; APV ¼ ulA vPV

 vF 1 dV uq PV vF vPV dðpz Þ  Da F ¼ qs þ s s  PV  E þ E Dg F F vs vs ds vs l ds l   JPV PV vPV : þ E þ A vs (12b)

electricity consumption, EDg F  atPVF .2 Fig. 2 illustrates how the welfare effects of a change in the subsidy are summarized in the following two propositions and associated corollaries. First, given public concern with CO2 emissions, fossil energies are becoming an inferior good where households with higher incomes will tend to spend proportionally less of their income on carbon-based fuels. This leads directly to Proposition 1. vF < 0, fossil energy is an inferior good, then vF < 0. Proposition 1. If vW vs An increase in the subsidy yields less fossil-energy consumption. Proof: The Marshallian demand function for F is F ¼ Fðpz  s; pE ; WÞ; the Hicksian demand function is FV ¼ FV ðpz  s; pE ; VÞ, and the expenditure function is W ¼ Wðpz  s; pE ; VÞ. The consumption of fossil-energy identity is then

FV ðpz  s; pE ; VÞ≡F½pz  s; pE ; Wðpz  s; pE ; VÞ:

2.3.1. Marginal external effects For further analysis and interpretation, it is convenient to express the marginal welfare effects (12b) in terms of elasticities. This is accomplished by first defining MEB as the net marginal external benefit of solar energy generation



MEB ¼ EJPV  EDa F þ EDg F



t  aPVF

;

(13)

where the parameters t and aPVF are defined as ðvFvs ÞPV εDFs PV D S t ¼ ðvPV ÞF ¼ εS ; aPVF ¼ F ; and εFs and εPVs denote elasticity of dePVs vs mand for conventional electricity with respect to the subsidy and elasticity of supply for solar electricity with respect to the subsidy, respectively. The ratio of solar electricity to conventional electricity is denoted by aPVF . MEB is composed of the direct benefits of solar-energy generation, EJS , and the indirect net external marginal benefits from a perunit change in energy consumption. The direct marginal benefits are the effect of solar-energy generation on job opportunities and possible rural development, EJPV . The indirect marginal benefits are changes in greenhouse gas emissions from conventional electricity consumption, EDa F  atSF , and air quality pollution from conventional 2 If the conventional utility is producing electricity with a mix of renewables (solar and/or wind farms) and nonrenewables (coal and/or natural gas), the greater this renewable mix, the less of a negative effect on local air quality and greenhouse gas emissions. The marginal external benefit (MEB) of employing noncentralized household-solar systems would then be less, leading to a reduction in the optimal household subsidy. The associated Renewable Portfolio Standard (RPS) then results in a lower optimal household-solar subsidy.

With two commodities, fossil energy F and solar energy PV, the Slutsky equation for a change in the price of solar energy is,

vF vFV vF PV : ¼  vðpz  sÞ vðpz  sÞ vW If PV is a net substitute for F, then

vFV vðpz sÞ > 0;

and

vFV vs

< 0. For a

constant pz , the Slutsky equation can then be written as

vF vFV vF ¼ PV: þ vs vW vs ðÞ If

vF vW

< 0, an inferior good, then

(14) vF < 0. vs

,

With households' preferences to reduce their proportion of income spent on fossil fuels as incomes rise, policies favoring solar PV will not only increase solar PV, but also reduce fossil-energy consumption. In general, if fossil energy is an inferior good, so vF/vs < 0, then a subsidy will both enhance solar adoption, εPVs > 0, and retard fossil energy use, εFs < 0. The reduction in fossil energy from an increase in the solar-energy subsidy will reinforce the positive effect the subsidy has on solar adoption. The more responsive these elasticities are the lower is the optimal subsidy. A lower optimal subsidy is also associated a very responsive prosocial valuation to the subsidy. Motivation crowding theory indicates the importance to consider the prosocial valuation characteristic of solar energy and its negative association with subsidies. As listed in Table 1, an increase in a solar subsidy will lead to less fossil-fuel consumption, lower environmental damage, but higher cost of electricity unless the income effect completely offsets the negative substitution effect. However, as in the general case of a Giffen good, this is a paradox, which is unlikely to occur. It would

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S. Liu et al. / Energy 147 (2018) 377e387

Indirect Utility Function

Totally Differentiate with respect to the Subsidy, s

Proposition 1

Proposition 2

Corollaries 1.1, 1.2, 1.3, 1.4

Corollaries 2.1, 2.2

Theorem 1: Optimal Solar Subsidy

Proposition 3

Proposition 4

Corollary 4.1

Fig. 2. Welfare effects.

require a relatively large proportion of income spent on solar PV and a small Hicksian elasticity of substitution between solar and fossil energy. The propositions and corollaries supporting the results in Table 1 are: dpE Corollary 1.1. From Proposition 1, vF vs < 0, then ds > 0. An increase in the subsidy will increase the fossil-fuel price. Proof: From (11a)

dpE PV PV vF 1 vPV s 2 þs : ¼ F F vs ds F vs dpE vPV Given vF vs < 0 and vs > 0, then ds > 0.

,

If the utility incurs the cost of a solar PV subsidy, it will pass a portion of this cost unto consumers of fossil energy through higher fuel prices. dD Corollary 1.2. From Proposition 1, vF vs < 0, then ds < 0. An increase in

S. Liu et al. / Energy 147 (2018) 377e387

383

Table 1 Welfare effect results. Fossil-Energy Condition Inferior good,

Normal good,

vF vW

vF vW

Proposition/Corollary

Result

Proposition 1 Corollaries 1.1 1.2 1.3 1.4

Increased subsidy, s, reduces fossil-fuel consumption.

<0

Increased subsidy, s, increases fossil-fuel price. Increased subsidy, s, reduces environmental damage. The more responsive fossil energy is to the subsidy, s, the higher the marginal external benefits of solar. The more responsive solar is to its subsidy, s, the lower is its marginal external benefits.

>0 Proposition 2 Corollaries 2.1 2.2

Response of subsidy, s, on fossil-energy consumption is indeterminant. Response of subsidy, s, on fossil-price is indeterminant. Response of subsidy, s, on environmental damage is indeterminant.

the subsidy will decrease environmental damage. Proof: dD ¼ vDg vF vF vs ds then dD < 0. ds

From (11b)

a þ vD vF

vF , vs

and from (3)

dDg dF

> 0;

dDa dF

> 0:

, Given vF vs < 0, Corollary 1.2 states if the objective of a solar PV subsidy is to reduce fossil-energy consumption, then given fossil energy is an inferior good the objective will be realized. Corollary 1.3. From Proposition 1, εFs < 0, then the more responsive fossil energy, F, is to a solar-energy subsidy, s, the higher is the MEB, vMEB < 0. vεFs Proof: Taking the partial derivative of (13) with respect to the elasticity εFs yields


DF  E a þ E Dg F vMEB ¼ <0 vεFs εPVs aPVF

,


DF  E a þ EDg F εFs vMEB ¼ <0 vεPVs ε2PVs aPVF

Similar to Corollary 1.3, in terms of PV, a large increase in PV from s will lead to a large impact on reducing negative externalities. Prior to CO2 emission concerns, fossil energies were generally thought of as normal goods. In this case, as demonstrated in Proposition 2, the direction of fossil-energy consumption from favorable solar PV policies is unclear. vF > 0, fossil energy is a normal good, then the sign Proposition 2. If vW vF of vs is indeterminant. An increase in the subsidy can result in reduced, an increase, or no change in fossil-energy consumption. Proof: The proof follows directly from (14) in the proof of Proposition 1.

vF vF If vsV > vW PV, then vF vs < 0, which is consistent with Proposition 1.

vF V

Instead, if vF vs < vW PV, then From Corollary 1.3, the more responsive F is to s, the higher will be the MEB. A large reduction in F from a change in s will lead to a large impact on reducing negative externalities. Corollary 1.4. From Proposition 1, εFs < 0, then the more responsive solar energy, PV, is to a solar-energy subsidy, s, the lower is the MEB, vMEB < 0. vεPVs Proof: Taking the partial derivative of (13) with respect to the elasticity εPVs yields

,

vF vs

> 0. The income effect,

completely offsets the negative net substitution effect vF > 0: vs

vFV vs ;

vF vW

PV,

leading to ,

Given Proposition 2, an increase in a solar subsidy may result in more fossil energy consumption. Corollary 2.1. From Proposition 2, if also indeterminant.

vF vs

Corollary 2.2. From Proposition 2, if also indeterminant.

vF vs

is indeterminant, then is indeterminant, then

dpE ds

is

dD ds

is

Table 2 Optimal solar subsidy results. Statement

Results

Theorem 1 Proposition 3

Optimal solar subsidy If PV is more responsive to a subsidy, s, relative to fossil fuel, F, then:

Proposition 4 Corollary 4.1

1. The more responsive prosocial valuation is to the subsidy, s, the lower will be the subsidy, s. 2. The subsidy is positively related to marginal external benefits. 3. The subsidy is positively related to the marginal benefits of access from PV. For a positive optimal subsidy, s* > 0, there cannot be a strong motivational-crowding effect leading to a large reduction in prosocial valuation for a subsidy increase. Optimal zero solar subsidy. A large motivational-crowding effect can lead to inefficiency of any positive subsidy. If the response of solar panels to a subsidy, s, is negative, εpz s < 0, then a larger prosocial valuation response to a subsidy is required for a zero optimal subsidy.

384

S. Liu et al. / Energy 147 (2018) 377e387 Table 3 Benchmark values and parameter ranges. Parameter

Symbol

a

Range Lower

Upper

Peak Hours of Sunlight per Day (hr) Household Solar Electricityb (kWh) Retail Price of Electricityc ($/kWh) Price of Solar Panelsd ($/kW)

h PV pE pz

4.5 6315 0.119 3.282

3.0 2526 0.118 1.935

6.5 14,596 0.122 5.854

Ratio Solar Electricity/Fossil Electricitye

aPVF

0.036

0.026

0.037

hF

0.05 2.714

0.02 1.516

0.05 3.912

εD IW εpz s

2.69

1.88

3.50

0

0.1

0.1

Externality and Access Effects Environmental Costsi ð102 $=kWhÞ

EDa F þ EDg F

2.24

1.75

3.12

Job Opportunitiesj ð102 $=kWhÞ

EJPV

5.66

1.30

9.30

Access to Electricityk ð102 $=kWhÞ

APV

0.092

0.065

0.118

Marginal External Benefits ð102 $=kWhÞ

MEB

7.87

Optimal Solar PV Subsidy ð102 $=kWhÞ

s*

7.69

Elasticities Income elasticity of Demand for Conventional Electricityf Solar Electricity Elasticity of Supply with respect to the Subsidyg

εSPVs

Income Elasticity of Demand for Solar Panelsh Elasticity for price of solar panels with respect to the subsidy

a b c d e f g h i j k

[35]. [40] and NREL. [19]. [40]. [15e17]. [2]. [31]. [3]. [34]. [47] and [49]. [45].

The proofs follow directly from the proofs of Corollaries 1.1 and 1.2.

2.4. Optimal solar energy subsidy

Theorem 1. The optimal solar-energy subsidy is


 uq εqs q þ MEB þ APV εPVs  εpz s pz s* ¼ l PV ð1  tÞεPVs

(15)

Proof: Setting first-order condition (12b) to zero and dividing by vPV vs yields

εp s u ε q þ ts  s  z pz þ MEB þ APV : 0 ¼ q qs l εPVs PV εPVs Solving for s then yields the optimal solar-energy subsidy. Recalling t ¼

s* ¼

Benchmark

εDFs εSSs

Proposition 1 implies Proposition 3, so if vF/vW < 0, fossil energy is an inferior good, then vs*/vεqs > 0, vs*/vMEB > 0, and vs*/vAAPV > 0. However, even given Proposition 2, where the sign of vF/vs is indeterminant, as long as solar energy is more subsidy responsive than fossil energy, the optimal subsidy is positively influenced by the elasticity of prosocial valuation, marginal external benefits and accessibility, and negatively by the price of solar panels. In terms of the prosocial valuation effect, the less responsive prosocial valuation is to the subsidy, then the higher will be the subsidy. If prosocial valuation is not considered, then the subsidy will be set higher than the optimal. Integrating prosocial behavior measures into the calculus of household decisions will reduce the optimal subsidy. The sign of s* depends on the responsiveness of the solar-panel price to the subsidy as developed in Proposition 4. uq

ε

q

Proposition 4. If εðrIÞs  l pqzs PV < ðMEBþpAz ÞεPVs , then s* > 0. Proof: In (15), given the denominator ð1  tÞεPVs > 0, the sign of s*

; (15) may be rewritten as


 þ MEB þ APV εpz s pz    : εFs ε PVs  εFs 1  εPVs

uq εqs q l εPVs PV

,

The proof follows directly from the denominators in (16). If  εPVs > εFs , then 1  εεSsFs > 0 and εSs  εFs > 0. ,

PV

q þ ðMEB þ APV Þε depends directly on the numerator, ulq εqs PV PVs  εpz s pz .

(16)

The results from Theorem 1 are outlined in Table 2 with two propositions and a corollary. Proposition 3. If εPVs > εFs , then vs*/vεqs > 0, vs*/vMEB > 0, and vs*/ vAPV > 0.

Solving for εpz 

uq

q l εqs PV

pz

yields the proposition.

,

Proposition 4 states for s* > 0, the benefits of solar ðMEB þ APV Þ per-unit price of solar panels, weighted by how responsive solar power is to the subsidy, εPVs , must be greater than the responsiveness of the price of solar panels to the subsidy, εðrIÞs , plus the responsiveness of marginal monetary benefits from prosocial

S. Liu et al. / Energy 147 (2018) 377e387

greater this responsiveness, the lower will be the optimal subsidy. This would when reinforce the lower optimal subsidy when considering prosocial valuation motivational crowding. The magnitude of this responsiveness is an empirical question requiring the parameterization of (15).

Table 4 Monte Carlo results for optimal solar PV subsidy. Level, x ðdollar=kWhÞ

Probability s* < x

0.05 0.04 0.03 0.02 0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15

0.059 0.074 0.094 0.117 0.146 0.173 0.207 0.246 0.288 0.329 0.373 0.422 0.473 0.522 0.569 0.612 0.654 0.699 0.736 0.780 0.816

uq

ε

2.5. Application The optimal solar subsidy (15) is generally true for any region or country, although the parameters and elasticities will likely vary. As an application, parameter and elasticity values, obtained from published sources, are employed for determining the optimal U.S. solar subsidy. Unfortunately, at this stage no parameter values exist for the PV prosocial valuation effect uq

l

q

valuation to the subsidy,  l pqzs PV . There cannot be a strong motivational-crowding effect leading to a large reduction in prosocial valuation for a subsidy increase. Corollary

4.1. Optimal

zero

ðMEBþ APV ÞεPVs pz

 εpz s , then s* ¼ 0.

solar

subsidy.

If

385

uq

ε

q

 l pqzs PV

¼

Proof follows directly from Theorem 1. Corollary 4.1 indicates the possibility of any positive subsidy leading such a large motivational-crowding effect that the subsidy is inefficient. This illustrates how prosocial efforts in identifying the responsiveness of prosocial valuation to a PV subsidy is just as important as the natural sciences in determining the magnitudes of MEB. For policy analysis, economics in the form of Theorem 1 provides the bridge linking these two sciences. Economics also plays a role in determining the direction and magnitude for the elasticities of PV and panel price, pz , to the subsidy, s. Assuming the Law of Demand, εPVs > 0 and empirical economic analysis has determined the magnitude of this response [31]. The effect of a solar subsidy on panel prices is generally unknown. In the long run, a solar subsidy may stimulate demand for panels leading to a supply response and if the panel industry is characterized by economies to scale, then panel prices would fall. This scenario implies εpz s < 0, which requires a larger prosocial valuation response to a subsidy for an optimal zero subsidy, Corollary 4.1. However, in the short run the sign could be reversed, εpz s > 0. In this case, the sign is similar to the share of a commodity tax being borne by both the seller and buyer. It is the result of a portion of the subsidy being received by the sellers of solar panels in the form higher panel prices, pz . The numerator in (15) indicates MEB plus APV multiplied by εPVs, is mitigated by the any positive response of pz to a change in the subsidy. The more elastic pz is to a change in the subsidy, the larger will be the response of pz and the less effective will be the subsidy. This slippage in the effects of the subsidy yields a lower optimal subsidy. The subsidy is being absorbed into higher prices for solar panels, which mitigates its effectiveness. Depending on the magnitude of the elasticities, this slippage can affect intended policy results. The denominator in (15) can be rewritten as ðεPVs  εFs Þ, which weights the MEB mitigated by the solar panel cost effect by the responsiveness of generating solar energy and use of conventional energy by the subsidy. The

q εqs PV pz

Instead, the optimal subsidy is calculated assuming this effect is zero, so it represents an upward bound on the subsidy. Based on this result, the optimal subsidy may be discounted depending on any current subjective valuation of PV motivational crowding. These values also reflect just one possible scenario. Alternative subsidy levels will occur for different regions with modifications to these values. For the numerical analysis of determining the optimal solar PV subsidy (15), benchmark values and parameter ranges are summarized in Table 3. A summary outlining the determination of these estimated values are in Liu [32]. Based on Table 3, the optimal solar PV subsidy for a median income household is s* ¼ 7:69 cents/ kWh with associated MEB ¼ 7:87 cents/kWh. If excluding the external effect of employment, the optimal solar PV subsidy for median income household reduces to s* ¼ 2:24 cents/kWh with associated MEB ¼ 2:23 cents/kWh. These results provide the natural science side of PV government policies. Without consideration of prosocial behavior in a social-technical approach, this only represents at best an upper bound. For comparison, the PV subsidy for Virginia residential participants is approximately 3.75 cents/kWh, which is between the two estimates of optimal PV subsidies [20]. 2.5.1. Sensitivity analysis The wide range of parameter values in Table 3 suggests the benchmark optimal subsidy has an associated rather large variance. In order to investigate the sensitivity of the optimal solar PV subsidy, s* , to ranges of these parameter values, both individual parameter variation and Monte Carlo analysis were implemented. In terms of the individual parameter variations, results indicate the optimal solar PV subsidy is mainly influenced by the elasticity of solar-panel price with respect to the subsidy, εpz s , environmental effects, EDa F þ EDg F , job opportunities effects, EJPV , and access to electricity effects, APV . All the other parameters have a relatively small impact on the optimal subsidy. In particular, the optimal subsidy is not sensitive to household income. For investigating the macro effect of simultaneously changing all the parameters, Monte-Carlo analysis on the optimal subsidy is performed. In particular, 5000 random draws of parameters in Table 3 were generated using a uniform probability distribution over respective ranges of the parameters. The drawn parameters were then employed to calculate the optimal solar PV subsidy in (15), and to create an empirical CDF for the optimal subsidy. Table 4 lists the probabilities of the optimal subsidy being below specific thresholds. As indicated in the table, the probability of the optimal subsidy being non-positive is only 17.3%. Thus, the likelihood of a positive subsidy is reinforced by the Monte-Carlo analysis. There is also over an 80% probability that the optimal subsidy is less than

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$0.15/kWh. 3. Conclusions and policy implications The theoretical development provides the basic determinants of how households' response to policies designed for internalizing the households' external electricity costs. With this theoretical understanding, policymakers will have an improved understanding, based on sound economic theory, of how households will likely respond to policymakers' choices. This alone provides new insights into our understanding of how to move forward toward renewable energies. Specifically, the results outlined in Table 1 indicate unless the income effect completely offsets the substitution effect, an increase in a solar subsidy will lead to less fossil-fuel consumption, lower environmental damage, but higher cost of electricity. The value of these results is in realizing these generally accepted results by policymakers do not universally hold. If fossil fuel is an inferior good with rising incomes decreasing its consumption, then yes policymakers are correct in their acceptance. If fossil fuel is a normal good with rising incomes increasing its consumption, then acceptance of a solar subsidy leading to less fossil-fuel consumption, lower environmental damage, but higher electricity costs may not hold. The value in these results is the importance of economic theory in developing the possible market consequences of a solar subsidy. Without economic theory, policymakers may rely on assumptions that do not hold when making decisions. As outlined in Table 2, the optimal solar subsidy is directly influenced by prosocial behavior and the motivational-crowding effect. The value of these results is indicating theoretically how the optimal solar subsidy is influenced. Policymakers in determining the optimal subsidy may want to consider prosocial behavior and the effect their policies have crowding out this behavior. It's of value to policymakers to consider the relative responsiveness of solar photovoltaic and fossil fuel to a subsidy. There is value in policy determination of knowing if solar photovoltaic is more responsive to a subsidy relative to fossil fuel, then the more responsive prosocial valuation is to the subsidy the lower will be the subsidy. The results indicate policymakers should consider the degree of motivational crowding when setting a solar subsidy. Realizing a large motivational-crowding effect can lead to inefficiency of any positive subsidy. In tandem with a solar subsidy, potentially crowding prosocial valuation is the possibility of slippage in the form of higher prices for renewable-energy inputs. As the results indicate, for solar energy, a solar subsidy may drive up the price of solar panels. If so, then the effectiveness of the subsidy is further compromised. The theoretical results indicate it would be of value for policymakers to know the responsiveness of solar panel prices to a subsidy. In addition to no information on the degree of possible prosocial valuation, little information exists on the degree of price slippage. The results indicate value in furthering this research inquiry. The results transcend determining the optimal solar subsidy. Energy policy in general is greatly enriched when the whole spectrum of science is applied to policy. Results demonstrate how economics can integrate prosocial behavior with the natural science of environmental impacts associated with the adoption of solar photovoltaic. With such integration, socio-technical approach, the true impact of solar policies can be assessed for deriving optimal government policies. As indicated by the results, a portion of prosocial behavioral efforts in articulating motivations and energy use behavior should be directed toward results that can be integrated into economic analysis. The value of prosocial behavior to policymakers is greatly

enhanced then mated with natural science in an economic framework. This is congruent with natural science providing measures of environmental effects for economic analysis. Without some bending of science efforts toward integration, a socio-technical approach will be hampered. The optimal household solar subsidy depends on how responsive households are to the subsidy. This theoretical household solar inquiry is valuable in providing a framework for future empirical analysis. With this framework, empirical efforts will determine the magnitudes of household responsiveness to solar subsidies. Specifically, future effects can be directed toward revealing households' solar prosocial valuations and degree of motivational crowding by solar subsidies. With economic theory providing a bridge linking the prosocial valuation with the natural science of assessing environment costs, future empirical efforts will have theory as a basis for their models instead of ad-hoc modelling. With this framework, sound energy policies based on a comprehensive science approach will emerge. References [1] Ackermann K, Fleiß J, Murphy R. Reciprocity as an individual difference. J Conflict Resolut 2016;60(2):340e67. [2] Alberini A, Gans W, Velez-Lopez D. Residential consumption of gas and electricity in the U.S.: the role of prices and income. Energy Econ 2011;33: 870e81. https://doi.org/10.1016/j.eneco.2011.01.015. [3] Algieri B, Aquino A, Succurro M. Going "green": trade specialization dynamics in the solar photovoltaic sector. Energy Pol 2011;39:7275e83. https://doi.org/ 10.1016/j.enpol.2011.08.049.
ricourt, Sun P. Efficient feed-in-tariff policies for renewable [4] Alizamir S, de Ve energy technologies. Oper Res 2016;64(1):52e66. [5] Ambec S, Crampes C. Electricity provision with intermittent sources of energy. Resour Energy Econ 2012;34:319e36. https://doi.org/10.1016/ j.reseneeco.2012.01.001. [6] Badcock J, Lenzen M. Subsidies for electricity-generating technologies: a review. Energy Pol 2010;38:5038e47. https://doi.org/10.1016/ j.enpol.2010.04.031.
nabou R, Tirole J. Incentives and prosocial behavior. Am Econ Rev [7] Be 2006;96(5):1652e78. [8] Burns J, Kang J. Comparative economic analysis of supporting policies for residential solar PV in the United States: solar renewable energy credit (SREC) potential. Energy Pol 2012;44:217e25. https://doi.org/10.1016/ j.enpol.2012.01.045. [9] Burr C. Subsidies, tariffs and investments in the solar power market. Working paper. Boulder, Boulder, CO: University of Colorado; 2014. [10] Clot S, Grolleau G, Ibanez L. Do good deeds make bad people? Eur J Law Econ 2016;42(3):491e513. [11] Cooper A. Building physics into the social: enhancing the policy impact of energy studies and energy social science research. Energy Res Soc Sci 2017;26:80e6. [12] DSIRE. Residential renewable energy tax credit. 2012. Retrieved April 16, 2014, from, http://www.dsireusa.org/library/includes/incentive2.cfm?Incenti ve_Code¼US37F&State¼federal%C2%A4tpageid¼1&ee¼1&re¼1. [13] Dwenger N, Kleven H, Rasul I, Rincke J. Extrinsic and intrinsic motivations for tax compliance: evidence from a field experiment in Germany. Am Econ J Econ Pol 2016;8(3):203e32. [14] EIA. Federal financial interventions and subsidies in energy markets 2007. 2007. Retrieved June 16, 2014, from, http://www.eia.gov/oiaf/servicerpt/subsi dy2/. [15] EIA. Electricity power monthly. 2014. Retrieved September 22, 2014, from, http://www.eia.gov/electricity/monthly/. [16] EIA. Residential sector energy consumption. 2014. Retrieved from, http:// www.eia.gov/totalenergy/data/monthly/pdf/sec2_5.pdf. [17] EIA. What is U.S. electricity generation by energy source?. 2014. Retrieved April 16, 2014, from, http://www.eia.gov/tools/faqs/faq.cfm?id¼427&t¼3. [18] EIA. Direct federal financial interventions and subsidies in energy in fiscal year 2010. 2010. Retrieved from, http://www.eia.gov/analysis/requests/subsidy/ pdf/subsidy.pdf. [19] EIA. Energy consumption by sector. 2012. Retrieved from, http://www.eia.go v/totalenergy/data/monthly/pdf/sec2_3.pdf. [20] EIA. Feed-in tariff: a policy tool encouraging deployment of renewable electricity technologies. 2013. Retrieved June 16, 2014, from, http://www.eia.gov/ todayinenergy/detail.cfm?id¼11471. [21] Elliott J, Fullerton D. Can a unilateral carbon tax reduce emissions elsewhere? Resour Energy Econ 2014;36:6e21. https://doi.org/10.1016/ j.reseneeco.2013.11.003. [22] Eurelectric. A quantitative assessment of direct support schemes for renewables. 2004. Retrieved from, http://gasunie.eldoc.ub.rug.nl/FILES/root/2004/

S. Liu et al. / Energy 147 (2018) 377e387 2913948/2913948.pdf. [23] Frey B, Jegen R. Motivation crowding theory. J Econ Surv 2001;15(5): 589e611. [24] Garcia A, Balzate J, Barrera J. Regulatory design and incentives for renewable energy. J Regul Econ 2012;41(3):315e36. [25] Goldberg M. Federal energy subsidies: not all technologies are created equal. 2000. Retrieved from, http://www.earthtrack.net/files/repp-subsidies.pdf. [26] Hoffman W. PV solar electricity industry: market growth and perspective. Sol Energy Mater Sol Cell 2006;90:3285e311. https://doi.org/10.1016/ j.solmat.2005.09.022. [27] Hughes J, Podolefsky M. Getting green with solar subsidies: evidence from the California solar initiative. J Assoc Environ Res Econ 2015;2(2):235e75. [29] IEA. Solar (PV and CSP). 2014. Retrieved June 16, 2014, from, http://www.iea.o rg/topics/solarpvandcsp/. [30] IRENA. The socio-economic benefits of solar and wind energy. 2014. Retrieved from, http://www.irena.org/DocumentDownloads/Publications/Socioeconomi c_benefits_solar_wind.pdf. [31] Johnson E. The price elasticity of supply of renewable electricity generation: evidence from state renewable portfolio. Georgia Tech, School of Economics; 2011. https://www.econ.gatech.edu/research/workingpapers. [32] Liu S. Three essays on U.S. Renewable energy policies, Ph.D. Dissertation, department of agricultural and applied economics. University of Georgia; 2016. http://purl.galileo.usg.edu/uga_etd/liu_shen_201605_phd. [33] Lobel R, Perakis G. Consumer choice model for forecasting demand and designing incentives for solar technology. MIT Sloan research; 2011. paper number 4872e11. [34] Muller NZ, Mendelsohn R, Nordhaus W. Environmental accounting for pollution in the United States economy. Am Econ Rev 2011;101:1649e75. https://doi.org/10.1257/aer.101.5.1649. [35] NREL. Solar maps. 2012. Retrieved June 16, 2014, from, http://www.nrel.gov/ gis/solar.html. [36] Parry IH, Small KA. Does britain or the United States have the right gasoline tax? Am Econ Rev 2005;95:1276e89. https://doi.org/10.1257/ 0002828054825510. [37] Plambeck E, Taylor T. On the value of input efficiency, capacity efficiency, and the flexibility to rebalance them. Manuf Serv Oper Manag 2013;15(4):630e9.

387

[38] RAP. Electricity regulation in the U.S.: a guide. 2011. Retrieved from, http:// www.raponline.org/document/download/id/645. [39] REN21. Renewables 2013 global status report. 2013. Retrieved from, http:// www.ren21.net/portals/0/documents/resources/gsr/2013/gsr2013_lowres. pdf. [40] SEIA. U.S. Solar market insight. 2011-2013. Retrieved June 17, 2014, from, http://www.seia.org/research-resources/us-solar-market-insight. [41] Singh G. Solar power generation by PV (photovoltaic) technology: a review. Energy 2013;53(1):1e13. [42] Sommerfeld J, Buys L, Desley V. Residential consumers' experiences in the adoption and use of solar PV. Energy Pol 2017;105:10e6. [43] Timilsina GR, Kurdgelashvili L, Narbel PA. Solar energy: markets, economics and policies. Renew Sustain Energy Rev 2012;16:449e65. https://doi.org/ 10.1016/j.rser.2011.08.009. [44] Titmuss R. The gift relationship: from human blood to social policy. London: Allen and Unwin; 1970. [45] U.S. Department of Energy. White house council of economic advisors and energy department release new report on resiliency of electric grid during natural disasters. 2013. Retrieved June 17, 2014, from, http://energy.gov/arti cles/white-house-council-economic-advisers-and-energy-department-relea se-new-report-resiliency. [46] Vedenov D, Wetzstein M. Toward an optimal U.S. ethanol fuel subsidy. Energy Econ 2008;30:2073e90. https://doi.org/10.1016/j.eneco.2007.02.004. [47] Wei M, Patadia S, Kammen DM. Putting renewables and energy efficiency to work: how many jobs can the clean energy industry generate in the US? Energy Pol 2010;38:919e31. https://doi.org/10.1016/j.enpol.2009.10.044. [48] Welsch H, Biermann P. Electricity supply preferences in Europe: evidence from subjective well-being data. Resour Energy Econ 2014;38:38e60. https:// doi.org/10.1016/j.reseneeco.2014.05.003. [49] World Economic Forum. Energy for economic growth energy vision update 2012. 2012. Retrieved from, http://www3.weforum.org/docs/WEF_EN_Ene rgyEconomicGrowth_IndustryAgenda_2012.pdf. [50] Wu H, Colson G, Escalante C, Wetzstein M. An optimal U.S. biodiesel fuel subsidy. Energy Pol 2012;48:601e10. https://doi.org/10.1016/ j.enpol.2012.05.063.