Producer incentives in electricity markets with green quotas and tradable certificates

Utilities Policy 55 (2018) 59–68

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Producer incentives in electricity markets with green quotas and tradable certificates

T

Kevin M. Curriera,∗, Susanne Rassouli-Currierb a b

Department of Economics, Oklahoma State University, Stillwater, OK, 74078, USA Department of Economics, University of Central Oklahoma, Edmond, OK, 73034, USA

A B S T R A C T

We study both intended and unintended consequences of cost reductions by green producers in a competitive electricity market operated under a green quota enforced via a green certificate system. We show that green producers may not have an incentive to exploit the full cost reduction potential of their technology and can in general be expected to engage in strategic cost padding. We propose a method of incentivizing RE producers to exploit the full cost reduction potential of the green technology. The method allows for strategic cost padding, but only at the expense of profit reducing changes in the RE quota.

1. Introduction The European Union's 2030 Framework for Climate and Energy Policy calls for an increase in the share of renewable energy (RE) to a minimum (a “green quota”) of 27% by the year 2030 (European Commission, 2014). Similar RE objectives exist around the world. Two of the most common mechanisms for the promotion of RE in electricity markets are a system of tradable green certificates (a quantity-based scheme), and the feed-in tariff (a price-based scheme).1 Under a green certificate system, a green quota (i.e., the percentage of total electricity generated that must originate from renewable sources) is stipulated and RE (“green”) electricity producers are allowed to issue one green certificate for each unit of electricity generated. A designated party of the electricity supply-chain is then obliged to purchase certificates in a market separate from the electricity market. Penalties are typically imposed for non-compliance. Revenue from green certificate sales effectively subsidizes green producers, and equilibrium in the green certificate market implies satisfaction of the green quota. Green certificate systems are now employed in the United States, India, South Korea, China and Australia. In the EU, green certificate systems are employed in Belgium, Norway, Romania, and Sweden (European Commission. 2018). Under a feed-in tariff system, green producers are guaranteed a price or a premium over the market price of electricity. Subsidies are typically differentiated by technology type (wind, solar, etc.) and may be financed by the government or an end-user tax on

electricity consumption. The use of feed-in tariffs is widespread and currently employed by many EU members including France, Germany, The Czech Republic, Greece, and Italy, among others (European Commission. 2018). For a comprehensive discussion of the anticipated advantages and disadvantages of the green certificate and feed-in tariff schemes in Sweden, see Bergek and Jacobsson (2010). RE and emissions reduction goals should be achieved efficiently. A number of recent papers have demonstrated some important unintended consequences of the simultaneous use of various combinations of emissions control techniques (i.e., emissions trading) and/or RE promotion methods. For example, Bӧhringer et al. (2008) demonstrated the existence of excess costs from the simultaneous use of emissions taxes and the EU emissions trading system (ETS). In addition, Bӧhringer and Rosendahl (2010) demonstrated that the strengthening of a green quota in the presence of an ETS will increase the output level of the most emissions intensive producer. Currier (2014) demonstrated that intensification of RE investment cost reduction policies in electricity markets employing green certificate systems will lead to higher carbon emissions by carbon-based producers. Morey and Kirsch (2014) provided a comprehensive discussion of numerous unintended consequences of Germany's RE promotion initiatives (see also Bӧhringer and Behrens, 2015; Eichner and Pethig, 2010). In this paper, we provide an analysis of potential unintended consequences of simultaneous cost reduction and green certificate trading. Regardless of the details of the RE support mechanism,

∗

Corresponding author. E-mail addresses: [email protected] (K.M. Currier), [email protected] (S. Rassouli-Currier). In the USA, Tradable Green Certificates are typically called Renewable Energy Credits or Renewable Energy Certificates. Other RE support mechanisms include, loan guarantees, investment grants, tax incentives and tendering schemes. 1

https://doi.org/10.1016/j.jup.2018.09.004 Received 4 October 2017; Received in revised form 10 September 2018; Accepted 11 September 2018 0957-1787/ © 2018 Elsevier Ltd. All rights reserved.

Utilities Policy 55 (2018) 59–68

K.M. Currier, S. Rassouli-Currier

reduction potential of green technology, implying that green producers can be expected to seek rents through cost padding. We also demonstrate, however, that side payments between the carbon-based and green producers can mitigate against this behavior, but only to a limited extent. Finally, we propose a method of incentivizing RE producers to exploit the full cost-reduction potential of green technology. This mechanism works by linking the level of the green quota to the realized value of a cost parameter in a manner to ensure that RE producers maximize profits if and only if they fully exploit all potential cost efficiencies.

policymakers have the presumption that support will be withdrawn as cost efficiencies and technological advances in the RE production chain permit green producers to eventually compete on an equal footing with carbon-based producers (Couture and Gagnon, 2010; Choi et al., 2015).2 Hence, the study of cost-reduction incentives facing green producers is an important research question.3 Cost reductions may be attributable to experiential learning by doing or learning by waiting (Thompson, 2010), as well as improvements in RE equipment production and installation.4 Within the context of electricity markets employing an emissions tax and a green quota, Currier (2016a) showed that green producers have incentives to engage in rent seeking behavior and even collusion. This may include “cost padding” in the form expense exaggeration, deliberate waste, and managerial perquisites, as well as political lobbying designed to increase or prolong subsidization (Sappington, 1980). Currier (2016b) showed that in an electricity market employing an emissions trading system (ETS) and a green quota, there will always be one green producer with an incentive to pad its own costs and attempt to disadvantage its rival green producers. In addition, Currier and Rassouli-Currier (2018) found cost padding incentives for green producers operating under a green quota with an authorized target rate-of-return to ensure investor confidence. Some recent research has focused on green producer incentives for strategic behavior. Gawel et al. (2016) provided a comprehensive overview of the interests of the various stakeholders in RE in Germany and the EU, noting in particular RE producers desire for rents stemming from generous subsidies. Delmas et al. (2016) found strong empirical evidence that across production sectors, producers at the extremes of the environmental performance spectrum (i.e., greenhouse gas emissions) have the highest lobbying expenditures. Bergek and Jacobsson (2010) assessed the performance of the Swedish green certificate system between 2003 and 2008. They found evidence of very large rents accruing to green producers and only minimal technical change (cost efficiencies). Kwon (2015) studies South Korean RE markets and found evidence of rent seeking and rent generation under both green certificate systems and feed-in tariffs, attributable primarily to information asymmetries between policymakers and RE producers. Schmitz et al. (2013) assert that rent management is a key ingredient in RE industrial policy and discussed the factors that are necessary for it to succeed. Stokes (2013) noted that the feed-in tariff for solar PV in Ontario Canada doubled between 2006 and 2009 in spite of significant experiential learning. This finding illustrates the tension between ensuring investor confidence (with generous subsidies) and adaptively managing the RE policy as new information (e.g., learning induced cost reductions) becomes available. In this paper, we model some consequences (both intended and unintended) of cost reductions by green producers in a competitive electricity market with a green quota implemented by a tradable certificate system. Using a stylized model of a generic competitive electricity market, we first establish that the green certificate system is an efficient policy instrument for implementing a green quota. We then demonstrate inter alia that cost reductions by green producers decrease the equilibrium green certificate price over time but increase emissions from carbon-based production, thus supporting the argument that a green certificate system may not be an efficient policy instrument for emissions reduction (Vogstad et al., 2003). In addition, we show that RE producers may not have an incentive to exploit the full cost-

2. The model We consider a closed competitive electricity market where q denotes total consumption of electricity. There are n identical “green” (renewable) producers producing output x and m identical carbon-based (fossil fuel) producers producing output y. Thus, q = nx + my. Green producers' parameterized cost functions are Cx(c, x) where reductions in the parameter c reflect experiential learning in RE generation as well as reduced manufacturing and installation costs of RE equipment. These costs are increasing and strictly convex in output: ∂Cx ∂x

> 0 and

∂2Cx ∂x 2

> 0 .5 ∂C (c, x )

∂2C

> 0 and ∂c ∂xx > 0 . Thus, Furthermore, we assume that x ∂c reductions in the cost parameter c imply reduced total and marginal cost. For notational ease, we shall henceforth denote ∂Cx (c, x ) by MCx(c, ∂x

∂MC

∂MC

x). Thus, ∂x x > 0 and ∂c x > 0 . In view of the intermittent (i.e., non-dispatchable) nature of many RE sources, any meaningful notion of green producer cost must also account for the need for back-up generation, such as battery storage in solar PV. We assume that green producers internalize power-balancing costs stemming from intermittency.6 Thus, in the present setting the cost function Cx(c, x) indicates the minimum cost of generating x units of green electricity with certainty when the cost parameter is c. See also footnote 17. Carbon-based producers' cost functions are denoted by Cy(y) with C′ y, C″ y > 0 . Furthermore, firm-level emissions are proportional to carbon-based output: e = λy, λ > 0. Aggregate emissions are then E = mλy. Green producers generate zero emissions.7 Consumer demand is formed by the maximization of consumer surplus V = U(q) – pq where U ′ > 0, U ″ < 0 , and p denotes the market price of electricity. The inverse demand function is p (q) ≡ U ′ (q) where p′ (q) < 0 . In our setting, the renewables target is implemented through the use of a green certificate system. Specifically, the policy mandate is that the proportion of green output to total output be α ∈ (0, 1) , i.e., nx = α[nx + my]. Green producers can issue one certificate at price ρ for each unit of x produced. Thus, green producer profits are πx = (p + ρ)x – Cx(c, x). Furthermore, carbon-based producers are obliged to purchase (at price ρ) β certificates for each unit of y produced.8 Therefore, carbon-based producers profits are πy = ( p – βρ)y – Cy(y). Assuming all producers maximize profit, a renewables target of α is met α in equilibrium when β ≡ 1 − α .9 5 See Requate (2015) for a rigorous justification of the assumption of convex costs in RE production. 6 Alternatively, these costs could be borne by the system itself. 7 While green electricity production does not generate GHG emissions, external effects may be present. For example, wind power generation may include effects on landscapes and bird life. See Stokes (2013) for concerned citizens' reaction to wind turbines in Ontario. 8 In general, purchase obligations may be imposed on generators, wholesalers, retailers or consumers. Following Tamas et al. (2010) and Requate (2015) we assume fossil-fuel producer obligations. It should be noted however that in our model producer obligations are formally equivalent to consumer obligations. See also footnote 9. 9 As noted earlier, in a “compliance market”, penalties are assessed for non-

2 The RE maturity threshold is often referred to as “grid parity”. For a discussion of the difficulties associated with the determination of grid parity, see Olsen and Jones (2012) and Choi et al. (2015). In most jurisdictions, RE support contracts typically last 15–20 years. 3 The RE technologies with the greatest cost reduction potential are Solar PV, Concentrating Solar Power and Wind (IRENA, 2015). 4 Learning by waiting refers to RE spillover effects from other industries, technologies or countries.

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It is straightforward to show that when ρ = μ(1 – α) and , equations 8–10 are identical to (11) – (13). We thus have Proposition 1.11

In view of the above, market equilibrium is described by the following equations.

U ′ (nx + my ) = p

(1)

p + ρ = MCx(c, x)

(2)

p − βρ = C′ y (y )

(3)

nx = α[nx + my]

(4)

Proposition 1. When the electricity market and the green certificate market both clear and β is set equal to α , the policymaker’s constrained welfare 1 − α maximization objective is met. Having provided rigorous justification for the use of the green certificate system as a policy instrument to enforce a renewables target, we now turn to an analysis of some implications of improved cost efficiency by green producers.12

Equation (1) is consumer surplus maximization. Equations (2) and (3) are green and carbon-based producer profit maximization respectively. Equation (4) is the renewables target whose satisfaction is α equivalent to green certificate market clearance when β = 1 − α .10 0 0 Fig. 1 provides an illustration where ( p , q ) denotes the market equilibrium prior to the introduction of the green quota and ( p1 , q1) denotes the equilibrium after the imposition of the green quota.

4. Implications of increased green producer cost efficiency Recall now that green producer costs are Cx(c, x) where reductions in c are assumed to represent ongoing experiential learning by RE project developers, equipment manufacturers and installers, site operators, etc. Using (1) – (4) for fixed n, m, and α, the long-run equilibrium values of the variables are parameterized by c and using the Implicit Function Theorem we may write: p ≡ p(c), x ≡ x(c), y ≡ y(c), and ρ ≡ ρ(c). These solutions satisfy the equilibrium identities:

3. Equilibrium and welfare Prior to studying the implications of reductions in the green producers' cost parameter, it is instructive to examine the rationale for using the green certificate system. We begin by defining social welfare W = U(nx + my) – nCx(c, x) – mCy(y). Suppose that the policymaker's objective is to choose production levels to maximize welfare subject to the policy mandate nx = α[nx + my]. Forming the Lagrangian function L(x, y, λ) = U (nx + my) – nCx(c, x) – mCy (y) + μ[nx – αnx – αmy], the first-order necessary conditions for a constrained welfare maximum are:

p (nx (c ) + my (c )) + ρ (c ) ≡ MCx (c, x (c )),

(14)

α ⎞ ρ (c ) ≡ C′ y (y (c )), p (nx (c ) + my (c )) − ⎛ 1 − α⎠ ⎝

(15)

nx(c) ‒ αnx(c) ‒ αmy(c) ≡ 0.

(16)

Using the fact that p′ (q) ≡ U ″ (q) and differentiating (14) ‒ (16) with respect to c yields (in matrix form): ∂MC

L x = U ′ (q) n − nMCx (c, x ) + μ (n − αn) = 0,

(5)

L y = U ′ (q) m − mC′ y (y ) + μ (− αm) = 0,

(6)

Lλ = nx − αnx − αmy = 0,

(7)

mU ″ ⎛ nU ″ − ∂x x ⎜ nU ″ mU ″ − C″ y ⎜ − αm ⎝ n − αn

(8)

p − C′ y (y ) + μ (−α ) = 0

(9)

nx = α(nx + my)

x ′ (c ) =

y′ (c ) =

ρ′ (c ) =

Recall now that using the profit maximization conditions and green certificate market clearance, we have: (11)

p − βρ = C′ y (y ),

(12)

nx = mβy.

(13)

0

(17)

−α2m (1 − α )

∂MCx ∂c

M −nα

∂MCx ∂c

M

,

(18)

,

(19)

(−αnmU ″ − (mU ″ − C″ y ) (n) (1 − α ) M

(20)

where |M | denotes the determinant of the coefficient matrix on the left side of (17). It is straightforward to show that |M | > 0, this fact being equivalent to the condition |D | > 0 in the constrained welfare maximization problem discussed in Section 3. U ″ < 0, α ∈ (0, 1), C″ y > 0, Recall now that

(10)

p + ρ = MCx (c, x),

∂MC ⎞ ⎛ x ′ (c ) ⎞ ⎛ ∂c x ⎞ ⋅ ⎜ y′ (c ) ⎟ = ⎜ 0 ⎟ ⎜ ⎟ ⎜ ρ′ (c ) ⎟ ⎝ 0 ⎠ ⎠ ⎠ ⎝

Solving for x ′ (c ), y′ (c ), and ρ′ (c ) yields the following.

where μ denotes the Lagrange multiplier associated with the renewables target. Letting D denote the 3 × 3 bordered Hessian matrix associated with (5)–(7), it is straightforward to show that |D| > 0 since ∂MC U ″ < 0, ∂x x > 0, and C″ y > 0. Thus, any solution to (5)–(7) yields a constrained welfare maximum. Note that (5)–(7) may be rewritten as follows. p – MCx(c, x) + μ(1 – α) = 0

1

−α ⎟ 1 − α⎟

and

∂MCx (c, x ) ∂c

> 0 . We may now state Proposition 2.

Proposition 2. A reduction in the green producers’ cost parameter c will: (1) (2) (3) (4)

(footnote continued) compliance with the purchase obligation. We assume that penalties for noncompliance are sufficiently high that the green quota is satisfied. For a green certificate model where the non-compliance penalty is explicitly modeled, see Ciarreta et al. (2017). 10 Regardless of whether the obligation to purchase green certificates is placed on consumers or producers, the market equilibrium conditions reduce to U ′ (nx + my ) = αMCx (c, x ) + (1 − α ) Cy′ (y ) and nx = α (nx + my ) implying that the methods are equivalent.

increase green output, reduce the green certificate price, and increase emissions. reduce the end-user price of electricity.

11 Note that (8)–(10) imply that the green certificate system is equivalent to a uniform feed-in tariff s financed by end-user tax t where s = μ and t = αμ. This observation has been made previously by Böhringer and Rosendahl (2010). 12 It is important to note however that while the green certificate systems enforces the green quota efficiently, the green quota itself does not directly address a specific market failure. Moreover, cost efficiency is not achieved (i.e., the equimarginal conditions do not hold) unless the certificate price is zero.

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Fig. 1. Market equilibrium before and after the introduction of the green quota. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

by green producers.

We observe that green-producer cost reductions increase green production and reduce the certificate price. This is consistent with the presumption that as green producers become cost competitive with carbon-based producers over time, the certificate market will be phased out as green and carbon-based producers compete on an equal footing at the first-best welfare maximum with p = MCx (c, x ) = C′ y (y ) in equilibrium.13 Moreover, the end user price of electricity falls as costs fall since total electricity production increases. An apparent expectation is that green output will displace carbonbased output as green production will become cost competitive (i.e., achieves grid parity) and thus realize emission reductions consistent with policy goals. Our results demonstrate, however, that under a green quota, as c falls, emissions increase since E = λmy. This is a consequence of the binding policy mandate that green production constitute a fixed proportion of total production. Recall now that πx = (p + ρ) x ‒ Cx(c, x). In equilibrium, we thus have πx (c ) ≡ (p (c ) + ρ (c )) x (c ) − Cx (c, x (c )) . Differentiating with respect to c we obtain

π ′ x (c ) = (p + ρ) x ′ (c ) + x·(p′ (c ) + ρ′ (c )) − ∂Cx / ∂c − MCx ·x ′ (c )

5. Incentivizing green producer efficiency Green producers can be incentivized to adopt all potential cost efficiencies by exploiting the fact that the policymaker has control over the stipulated value of the green quota α. We begin by assuming that the green producer profit function πx (α, c ) is pseudoconcave15 and that the policymaker has identified a desired RE penetration level α and an attainable value of the green producer cost parameter c for which the green certificate price ρ(α , c )= 0 . Furthermore, let the current (initial) value of the cost parameter be c > c and let the initial value of the green quota be α < α for which πx ( α , c ) < πx (α , c ) . The procedure is applied as follows: Step 1: The policymaker computes

u=

∂πx ∂α

α

(21a)

∂πx ∂α

(α , c ) ∂π

(α , c ) + c ∂cx (α , c )

and Using (14), this simplifies to π ′ x (c ) = x·(p′ (c ) + ρ′ (c )) − ∂Cx / ∂c . We observe then that the sign of the comparative statics derivative π ′ x (c ) is indeterminate since p′ (c ) > 0, ρ′ (c ) > 0 and ∂Cx / ∂c > 0.14 Green producers may be expected to anticipate the long-run market impacts of cost reductions and thus behave non-myopically. Since the long-run effect of reductions in c on green producer profits has potential implications for rent seeking behaviors, such as cost padding, we next discuss a method for incentivizing the full potential for cost reduction

v=

∂πx ∂c

α

∂πx ∂α

(α , c ) ∂π

(α , c ) + c ∂cx (α , c )

Step 2: Green producers are offered the “menu” M = {(α, c ) |α ε [ α , α ], c ε [ c, c ] and u·α + v·c ≤ 1} where c is the realized value of the cost parameter. We demonstrate in Proposition A1 in the Appendix that if green producers are profit maximizers, they will choose the green quota to be α and will employ the most efficient technology available (c = c) thereby foregoing cost padding. The procedure works by exploiting the fact that green producer profits are increasing in α over a subset of

13

Similarly, the process of reducing a feed-in tariff over time as RE costs decline is referred to as “tariff degression”. The feed-in tariff can be degressed by the policymaker, whereas the certificate price is subject to market forces. 14 While it is true that the derivative of green profits with respect to the cost parameter is negative ceteris paribus, (myopic behavior), our model duly accounts for the induced changes in the market clearing output and certificate price, in which case the sign of the total derivative πx′ (c ) is indeterminant For a discussion of this important point within the context of the effect of input price changes on long-run equilibrium in a competitive industry, see Meyer (1967), Ferguson and Saving (1969) and Silberberg (1974).

15 Let U ⊂ Rn be open and convex. A continuously differentiable function f : U → R is pseudoconcave at x ′ ε U if ∇f (x ′)·(x − x ′) ≤ 0 implies f (x ) ≤ f (x ′) for all x U . The function f is pseudoconcave on U if the preceding condition holds for all x ′ ε U .

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[0, 1]. Green producers are offered a menu of (α, c ) pairs and are - in principle - allowed to pad costs or deliberately incur waste etc. However, green producers may engage in such behavior only at the “expense” of a reduced value of the green quota α. The menu, which exploits the global properties of the green profit function, is designed in such a way as to ensure that profits are maximized if and only if green producers fully exploit all possible efficiencies. Implementation of the procedure requires the policymaker to know the green producers' cost reduction potential c ex ante and to be able to observe the realized value of c ex post.16 In the following section, we provide a numerical example that illustrates our results and provides additional insights.

πy =

(p

− 2 3ρ

)y

− y2

(28)

Equations (21) and (22) are market demand. Equations (23) and (24) are profit maximization by green and carbon-based producers, α respectively, where β = 1 − α = 2 3 . Equation (25) is the policy mandate, and (26) is total emissions. Equations (27) and (28) are green and carbon-based profits, respectively. Equilibrium solutions are as follows.

p (c ) =

50(9 + 2c ) 17 + c

(29)

x (c ) =

125 17 + c

(30)

6. Numerical example

y (c ) =

375 17 + c

(31)

In this section, we obtain some additional insights from a numerical example. We begin by assuming that consumer utility is

E (c ) =

2,250 17 + c

(32)

ρ (c ) =

150(−3 + c ) 17 + c

(33)

q (c ) =

1,250 17 + c

(34)

q2

U (q) = 100q − 2 in which case market demand is q(p) = 100 – p. There are two competitive carbon-based producers with cost function Cy(y) = y2. In addition, there are four green producers with parameterized cost function Cx(c, x) = cx2. The initial (current) value of c is assumed to be 35, but the policymaker believes that through experiential learning etc., the cost parameter can be reduced over time to c = 3.17 Total production is q = 4x + 2y. Assuming the emissions coefficient λ = 3, total emissions from carbon-based production is E = 2(3)y = 6y. Finally, we assume that the policy mandate is that 40% of all electricity produced originates from green sources. A remark about the specification for the green producers' cost function is in order. While some RE sources such as wind power might superficially appear to have very low variable costs, the costs stemming from generation uncertainty due to intermittency is a substantial operating cost (Rao et al., 2015). Thus, consistent with their mission, policymakers will want producers to reduce this uncertainty and its associated cost. Experiential learning in wind forecasting, aggregation of diverse wind sources, and co-located energy storage (currently very expensive) can all reduce the additional costs stemming from intermittency, reflected in the green cost parameter c. (See also footnote 5.) Market equilibrium is described by the following system of equations. p = 100 – q

(21b)

q = 4x + 2y

(22)

p + ρ – 2cx = 0

(23)

p −

2ρ − 2y = 0 3

(25)

E = 6y

(26)

πx = (p + ρ)x – cx2

(27)

14,625 (17 + c )2

(35)

πx (c ) =

15,625(c ) (17 + c )2

(36)

At the initial value of the cost parameter (c = 35), the green sector issues and sells 9.62 green certificates at a certificate price of 92.31 with certificate revenue equal to 887.57. In addition, with the market price of electricity equal to 75.96, revenue from green electricity sales is 730.40. As the cost parameter is reduced from 35 to 3 over time, Equations (29), (30) and (33) imply that the market price of electricity falls from p = 75.96 to 37.50; green production increases from 2.40 to 6.25; and the certificate price falls from 92.31 to 0, consistent with the expectation that the green certificate market will be phased out as green producers achieve parity with carbon-based producers. As predicted by Proposition 2, total emissions increase in this scenario. To study cost-efficiency incentives, we utilize Equations (35) and (36) and Fig. 2 below showing πx (c ) , πy (c ) and industry profit 31,250(9 + 2c )

π (c ) = 4πx (c ) + 2πy (c ) = . As the diagram illus(17 + c )2 trates, green producer profits are monotonically increasing in c for c < 17 and monotonically decreasing for c > 17 with πx(17) = 229.78. In addition, industry profits are monotonically increasing in c for c < 8 and monotonically decreasing for c > 8 with π(8) = 1250. In the absence of side payments, green producers will have little incentive to adopt any technology for which the associated cost parameter is below 17. Initially (i.e., in the early phases of deployment), as c decreases from 35, green producer profits increase. However, if the true value of c falls below 17, green producers have no incentive to fully exploit this new cost reduction potential. Indeed, below c = 17, reductions in c reduce profits and green producers thus have incentives to seek rents via cost padding and political lobbying. Note, however, that for values of c between 8 and 17, industry profits rise as c falls, even though green profits fall. This implies that if side payments from carbon-based producers to green producers are permitted, carbon-based producers could induce green producers to fully exploit any cost reduction potential to the threshold value of c = 8.18 The foregoing

(24)

4x = .4(4x + 2y)

πy (c ) =

16

For an application of a similar technique, see Currier and Rassouli-Currier (2018). 17 As a justification for the RE cost function, suppose that the green producer production function is x = (νK )1/4 (θL)1/4 where labor augmenting technical progress via experiential learning increases ?? and capital augmenting intermittency reduces ν. Letting w and r denote the prices of labor and capital respectively, it is straight forward to show that the cost function is C = cx 2 where 2w1/2r 1/2 c = 1/2 1/2 . Thus, learning and/or reduced intermittency reduce c . For a stoν θ chastic programming approach to the power-balancing and intermittency problem, see Morales and Pineda (2017).

18 Side payments are in fact a feature of some international environmental agreements, such as the Montreal Protocol The Montreal Protocol is widely regarded as a success, due to the efficacy of side payments in settings with

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Fig. 2. Green, carbon-based, and industry profit under a mandated green quota. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

still c = 4 . Cost padding of various forms could provide “evidence” of this behavior. Finally, it is also important to observe that cost padding by green producers will increase the market price of electricity (Equation (29)) but reduce emissions (Equation (32)). To restore cost efficiency incentives, we apply the procedure described in section 5 with green producer profits20

discussion is summarized in Proposition 3. Proposition 3. Exploitation of the full cost reduction potential (to c = 3) in the RE market will never occur, even if side payments are permitted between green and carbon-based producers. If side payments are permitted, green producers will engage in strategic cost padding when the true value of the cost parameter falls below 8. If side payments are not permitted, green producers will engage in cost padding when the true value of the cost parameter falls below 17.

πx (α, c ) =

Proposition 3 states that adoption of cost efficiencies that reduce c to 3 can never be incentivized, although the possibility of side payments enlarges the range of c values over which they can be incentivized.19 It should be noted that in our model, rents can be gained by either cost padding or political lobbying. To illustrate, suppose that the true value of the cost parameter has fallen from c = 4 to c = 3. Using equation (33), this implies that the equilibrium certificate price will fall from $7.14 to zero. If green producers lobby for extension of the green certificate program with the subsidy maintained at $7.14 (or, equivalently, for a uniform feed-in tariff to be maintained at $7.14), this is formally equivalent to insisting that the current value of the cost parameter is

2500α 2c (4 − 4α + 2α 2 + α 2c )2

(37)

c = 3, α = .1, c = 35 and α = 0.4 and M = {(α, c ) |α ε [.1, .4], 7c c ε [3, 35] and 50α + 81 ≤ 1}.21 Fig. 3 below provides an illustration 27 showing M and several green producer isoprofit curves. With α restricted to 0.4, green profits increase as c is reduced from 35 to 17. However, if the true value of c falls below 17, green producers have no incentive to fully exploit this new cost reduction potential since profits are reduced. Hence, as noted earlier, simply mandating that α = .4 will not induce full-cost efficiency. However, when offered the menu of options M, profits are maximum when the full cost-reduction potential of the technology is exploited (i.e., c = 3).

(footnote continued) highly asymmetric participants (countries). See Barrett, 2005. 19 In the general case, cost efficiencies can be incentivized over the interval [cˆ , c ], where cˆ is the global maximum of industry profit π (c ). In the example, cˆ = 8.

20 It is straight forward to show that πx (α, c ) is pseudoconcave over the set [.1, .4] x [3, 35]. Calculations available from the author upon request. 21 Note that when α = 0.4, the green profit function (37) reduces to (36) which is monotonically increasing in c on.[3, 17].

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Fig. 3. Profit maximization under the “menu” M.

producer profits are monotonically increasing in c, implying the wellknown incentive to attempt to raise rivals' costs via economic or political disadvantaging. Moreover, green producer profits decline monotonically in c, implying that green producers will always fully exploit any cost-reduction potential. Thus, the introduction of a policy mandate in the form of a binding green quota can substantially weaken green producers' incentives to exploit cost-reduction potential but eliminates carbon-based producer incentives to raise their green rivals' costs.

Several points regarding the application of the menu procedure should be noted. First, the application of the procedure requires only that the green producer profit function πx (α, c ) be pseudoconcave over the set [ α , α ] x [ c, c ]. When πx (α, c ) is twice continuously differentiable, a sufficient condition for pseudoconcavity is that the determinant of the 3 × 3 bordered Hessian of πx (α, c ) be strictly positive.22 More importantly, practical application of the procedure will typically require that the point (α , c ) be approached incrementally over time, because of the lack of global information (on the part of the policymaker) regarding the green profit function and/or the fact that the full cost-reduction potential (grid parity) of the green technology will typically only be realized gradually over time. Under such circumstances, the procedure can be applied with intermediate cost reduction targets as follows. Without loss of generality, suppose that the initial value of the cost parameter is c and that true cost parameter reductions occur at the beginning of time periods 2 through n with c > c2 > c3 > … > cn ≡ c. If the policymaker identifies a corresponding sequence of green quotas α < α2 < α3 < … < αn ≡ α for which πx (αt + 1, ct + 1) > πx (αt , ct ) , the menu procedure can be applied in each time period, thereby incentivizing each subsequent cost reduction. Within the context of Fig. 3, the procedure would incentivize a sequence of points beginning at the upper left hand corner of the diagram and proceeding to the lower right hand corner, bounded on the left by the isoprofit curve πx (α, c )= 55.517 and on the right by the isoprofit curve πx (α, c )=117.188.23 Finally, it is instructive to consider the equivalent parameterized model absent the policy mandated green quota (implemented via a certificate market) where equilibrium is determined by the usual equimarginal conditions p = MCy(y) = MCx(x). Fig. 4 shows the carbon-based and green producer profits for our example. Carbon-based

7. Conclusions and policy implications Worldwide concern about carbon emissions has led to a number of policies that attack the problem both directly by reducing emissions as well as indirectly by attempting to displace carbon-based energy production with renewable-based energy production. A frequently employed RE promotion mechanism is a policy mandated green quota, which stipulates that a certain percentage of total electricity generation must originate from renewable sources. A common method of implementing a green quota is a system of so-called green certificates, which are financial assets sold to carbon-based producers by green producers (and thus effectively subsidize them) at a market-determined price independent of the electricity market. In RE markets, there is an expectation that over time green producers will become cost competitive with carbon-based producers as experiential learning in RE generation and improvements in equipment manufacturing and installation reduce costs in the production chain. It is therefore important to examine all implications of increased cost efficiency in RE production under common RE promotion mechanisms, such as the green quota and certificate system described here. Our analysis demonstrates that when both the electricity market and the certificate market are in equilibrium, output levels that maximize welfare (defined as consumer utility net of production costs) subject to the policy-mandated green quota are obtained. While this argument may be used to rationalize the use of the certificate market in the presence of a green quota, it should be noted that this welfare formulation ignores environmental damages from carbon-based production and does not address the corresponding market failure directly. Within the context of a stylized competitive electricity market, our

22 It should be noted that πx (α, c ) is not monotonically increasing on the set.[ α, α ] x [ c, c ]. 23 Our analysis provides an additional justification for the common practice of stipulating a sequence of increasing binding RE targets, such as is the current policy in the EU under the Renewable Energy Directive (European Commission, 2014).

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Fig. 4. Green and carbon-based profit in the absence of the green quota. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

sector (c = 3 in our example) will never materialize. Thus, while strong asymmetries between green and carbon-based producers suggest that a system of side payments may be effective at incentivizing cost reductions, our results establish that the green quota is a policy mandate that may be inimical to full cost efficiency on the part of green producers in competitive electricity markets. To help restore cost-efficiency incentives, we propose offering green producers a “menu” of options in which the green quota is tied to the realized value of the cost parameter. Cost padding would be at the expense of a lower allowed value of the green quota α. Using the finding that green producer profits increase in α over a subset of [0, 1], we demonstrate that green producers can be incentivized to exploit the full cost-reduction potential of the green technology. The mechanism requires the policymaker to know the cost reduction potential of the green technology ex ante, have at least local (i.e, current) information regarding green producer profits, and be able to observe the realized value of the cost parameter at any point during implementation. In practice, it is unlikely that the policymaker would have precise knowledge of a green producer's cost-reduction potential. To the extent that these exacting informational requirements are not satisfied (Kwon, 2015), our analysis demonstrates that ensuring full exploitation of the RE cost reduction potential when a green quota is in force is likely to be challenging.25 Whether less information-intensive measures can mitigate these perverse cost-reduction incentives is an open question. Future research should focus on RE market design with manageable information requirements and good incentive properties. Our results suggest that even under perfectly competitive conditions in both the electricity and certificate market, the RE support mechanism can create perverse long-run (non-myopic) incentives for green producer cost efficiency. Thus, future empirical testing of our model is warranted. In reality, many electricity markets are not yet fully liberalized. Future research should also study green producer cost efficiency

model demonstrates that as the costs of green production fall, the equilibrium price of green certificates is driven to zero. This is consistent with the expectation that as cost efficiencies in RE production are achieved, subsidies to green producers will be gradually be eliminated, in which case green producers will compete with carbon-based producers on an equal footing. Moreover, as green costs fall, green output rises as expected. However, we also demonstrate that in this case emissions from carbon-based production will increase as well. Thus, achievement of cost efficiencies in RE production is inconsistent with an emissions reduction objective under a fixed green quota. With regard to efficiency incentives of green producers, we also show that after the green quota and certificate system are introduced, cost reductions in the RE sector can lower equilibrium profits of green producers via induced changes in the output and certificate market. Our findings imply that the anticipated cost efficiencies (i.e., the RE cost reductions necessary to drive the certificate price to zero) may never be realized.24 An additional implication is that green producers will engage in rent-seeking behavior, including cost padding in the form of expense exaggeration, deliberate waste, and managerial perquisites as well as political lobbying. These observations suggest that policymakers must be vigilant about performance benchmarking and auditing and might even consider retrospective prudence reviews as employed by public utility regulators. Stokes (2013) suggests a requirement to solicit multiple cost estimates or requiring cost documentation of each RE project prior to implementation. In addition, we showed that when side payments between the green sector and the carbon-based sector are permitted, the range of cost parameter reductions that are incentive compatible is expanded although exploitation of the full cost-reduction potential in the green

24 It should be noted that in our model, cost reductions are assumed to reflect experiential learning by doing and learning by waiting, with the implication of a passive role toward RE costs efficiencies on the part of the policymaker. In reality, policymakers often undertake various R&D support policies in RE, particularly in the early stages of technology development. Within the context of our model, reductions in the cost parameter could also be a consequence of the introduction or intensification of such a policy.

25 Nevertheless, our proposed procedure will in principle incentivize any attainable cost reduction. If the policymaker overestimates the cost reduction potential of the green technology, the “menu” process will terminate before the certificate price is driven to zero.

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hinges on the assumption of non-myopic behavior of green producers. That is, green producers are assumed to be able to anticipate the longrun implications of the market adjustments made in response to learning-induced cost reductions. It is plausible that this change of investor sentiment could induce strategic behavior designed to affect when and how the support scheme would be terminated.

incentives in oligopoly settings where green and/or carbon-based producers may exert market power in both the electricity market and the green certificate market. See for example Von der Fehr and Ropenus (2017), Amundsen and Bergman (2012) and Linares et al. (2008). Finally, it would be useful to directly explore green energy producers' perceptions of the short-run and long-run incentives provided by the green certificate market.26 Focusing on RE investor incentives, Linnerud and Simonsen (2017) observed that immediately after the green certificate scheme was introduced in Norway, investors were eager to lock in future subsidies, but as the certificate phase-out deadline approached, investors became increasingly skeptical of success and pessimistic about the effects of withdrawing subsidies. Our analysis

Acknowledgement We are deeply indebted to Janice Beecher and four anonymous referees for numerous useful comments and suggestions on an earlier version of this paper.

Appendix Proposition A1. The point (α , c ) is the solution to the green producers’ constrained profit maximization problem: Maximize πx (α, c ) subject to (α, c ) ∈ M . Proof: Since the firm must choose (α, c ) ∈ M , (α, c ) will satisfy u·α + v·c ≤ 1 which implies that ∂πx ∂α

α

∂πx ∂α

(α , c )·α

(α , c ) +

∂π c ∂cx

(α , c )

+

∂πx ∂c

α

∂πx ∂α

(α , c )·c ∂π

(α , c ) + c ∂cx (α , c )

≤1

for all (α, c ) ∈ M . Using the definition of the gradient of π (α, c ) , the above inequality implies that ∇πx (α , c )·(c − c, α − α ) ≤ 0 for all (α, c ) ∈ M . Since πx (α, c ) is pseudoconcave (see footnote 15), it follows that πx (α , c ) ≥ π (α, c ) for all (α, c ) ∈ M and the conclusion follows. Appendix B. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jup.2018.09.004.

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