How Consumers Choose the Green Electricity Product Instead of Conventional Electricity? A Welfare Analysis Approach

Abstract

The aim of this article is to analyze theoretically whether changes in an access charge pricing policy can promote green electricity use. The model considers two hypothetical firms: One firm offers green electricity product, and the other firm provides conventional electricity. Each firm pays an access charge to the natural monopoly in order to have access to the transportation network. Through using a vertical differentiation model, we try to analyze the link between the access charges paid by the two firms and the qualities offered. We also attempt to explain why the consumers do not often choose green electricity. Finally, we suggest a new policy that can lead the consumers to choose the green electricity product instead of conventional electricity. Our model shows that changes in the access charge pricing policies can constitute a relevant component in the reforms of the electricity sector and can have impacts on the consumption of the green electricity. A differentiating access charge policy could allow a better penetration of the green electricity product and an increase in the social welfare when consumers have greater preferences in environmental qualities. Otherwise, their preservation at a uniform level is desirable in order to maintain the competition.

JEL Classifications: B21, C72, L13, Q21, P28

Keywords

Access charge Competition Sustainability Environmental quality Green electricity

Introduction

The world’s electricity market has undergone two major changes over the last two decades. First, many countries experienced liberalization and deregulation (Glachant, 2002; Joskow, 1996). The typical electricity market is characterized by the coexistence of an essential facility which is a natural monopoly, and final services providers which are competitive. In this case, the final services-providing firms use the essential facilities as an input and pay in return an access charge to the natural monopoly and in here where the interest of this study lies. The access conditions are a very important factor for fair competition in electricity markets (Green, 1997; Laffont et al., 1994; Laffont et al., 1997). In order to avoid a strategic behaviour of the incumbent monopoly, the regulator requires that this cost (access charge) need to be uniform for all of the competitors. Controlling this network by imposing high access charges can exclude new firms from entering the typical electricity market. Indeed, the dominant position of the natural monopoly can exclude competition by imposing high charges. The imposition of a uniform access charge is thought of as the best solution in order to strengthen competition.

Second, the strong passion for undoing the harmful effects of climate change has led most OECD countries to adopt and promote renewable energy as an alternative and viable solution to the use of conventional fossil fuel sources. The European Union for example has set a target of 20% of its energy use to be satisfied from renewable energies in 2020 (COM, 2019). More recently, the United States and China have reached an agreement to reduce their carbon emissions by more than 25% by 2030. Countries like Denmark have set a target to have 100% of their energy use coming from renewable energy sources in 2050. Technological changes can also help alleviate the toxic effects of climate change and foster a greater movement toward more competitive use of the renewable. It seems obvious in the literature that the consumer in many parts of the world is willing to combat the damaging effect of the climate change (Batley et al., 2001; Roe et al., 2001) but is not able to buy the green energy products. For example, in Finland, 30% of the households consider that green electricity is good but in 2004 only 0.2% of those households used it (Salmela & Varho, 2006). Furthermore, in Australia, according to data from the first quarter of 2014, the actual behaviour in terms of subscription to green electricity is reflected only in a small percentage of the overall number of Australian households nationwide (GreenPower, 2014). Finally, there is still a strong need on part of the consumers and the policymakers to find alternative solutions. Thus, we need a paradigm shift in order to foster the use of renewable energy, particularly a move towards more use of green electricity.

Our purpose in this study is to analyze whether special changes in access charge pricing policy can promote the green electricity product. We propose a novel paradigm to explore the particular structure of the electricity market and to help government regulators promote the use of green electricity among consumers.

The previous literature linked to the green electricity has tried to come up with some explanations for the weak consumption of green electricity, in spite of a high ecological consciousness and consumers’ willingness to pay in several OECD countries. A different strand of the literature has paid attention to consumers’ psychological indicators of willingness to pay more for green electricity (Clark et al., 2003; Hansla et al., 2008; Hartmann & Apaolaza-Ibanez, 2012; Sang et al., 2020; Welsch & Kuhling, 2009). A large part of this literature concludes that a lot of people possess a favourable attitude and a willingness to pay more for green electricity (Ashworth, 2011; Ashworth et al., 2006; Salmela & Varho, 2006; Truffer et al., 2001; Wilson & Dowlatabadi, 2007). Nevertheless, consumers do not buy green electricity.

The second strand has tried to give reasons to explain the lack of strong green electricity consumption and also suggests some strategies to increase it. The weak demand for green electricity has been explained by the information and option overload (Youssef & Abderrazak, 2009; Brécard, 2015). Indeed, when consumers have too much information on the green side of a product, they maybe muddled and will not take it into account. In fact, when consumers are facing one label with a clear information message, they can behave accordingly and choose the product given their tastes and revenues. If they are facing a situation where several firms setting different labels or environmental signals, they may become confused and may not take into account the different labels in making choices (Youssef & Abderrazak, 2009; Brécard, 2015). Moreover, Conte and Jacobsen (2014) conclude that in the USA, green electricity can reach a good penetration if it is sold at relatively low costs and when it is sold to more educated consumers. Hobmann and Fredericks (2014) conclude that the main reasons for non-subscription to green electricity are relative costs and the associated unaffordability. Some authors propose intensive strategies (e.g., promotional materials and education campaigns, action on prices, labelling, etc.) in order to increase consumers’ green electricity knowledge (Rundle-Thiele et al., 2008; Zarnikau, 2003).

The third strand has been interested in the necessary changes in the regulations of this sector in order to allow a better green electricity penetration. Several renewable energy programmes have large initial costs and need long time for generating revenues and profits (Menz, 2005; Gan et al., 2007; Güney, 2019; Verbruggen et al., 2011). Therefore, government policies such as feed-in-tariffs, tax credits, tradable certificates and investment incentives are considered very important tools to reduce costs and accelerate market penetration of the green electricity product. However, the efficiency of renewable energy sources policies varies by policy instruments and renewable energy sources together (Saidi & Omri, 2020; Zaho et al., 2013).

Our article attempts to contribute to this strand of the literature. Indeed, despite the presence of several regulatory instruments that helps to promote the green electricity product, there is always a weak demand for this clean product. The introduction of an appropriate governmental policy of renewable energy promotion linked to the access charges could lead to a socially efficient solution. Furthermore, if there is a link between the access charges and the green electricity demand, we can propose a governmental policy that aims at promoting renewable energy uses. To our knowledge, the regulation through access charges has not been studied in the literature.

This study addresses the above issues by aiming to analyze how a change in the policy towards access charges can promote green electricity. We know that this practice to have fair competition is in theory prohibited. But if the environmental goals are as important as the competition goals, one must examine the foundation of the policies of those goals.¹ In the early stage of liberalization, policymakers imposed a uniform access charge to transform energy markets into competitive markets. Competition policy thus was set prior to any other objectives. Nowadays, the electricity markets are competitive, and environmental policies have come to the top of the goals of decision-makers. Indeed, given the size and the scope of the climate change effects, public policies may value more future environmental goals than competition policies, especially in the energy sector. The aim of this article is to show that if there is a change in the valuation of these policies, then this change may induce a stronger adoption of green electricity. In particular, we will discuss whether a change in the access charge policy can improve the green electricity demand or not.

This paper contains four novelties compared to the previous literature. Firstly, in the current paper, we attempt to show how the promotion of the renewable energy market through labelling could be supported by a reform in the policy of access charge pricing (i.e., changes in the competition policy in order to achieve an environmental goal). Secondly, most of the studies have focused on the reasons behind the modest penetration of green electricity and on the necessary regulations to promote it, but without linking the regulations of the sector to the low performance of green electricity consumption in the market. A modelling of this precise case would help one understand whether a reform in this direction is possible and at which price. Thirdly, we propose in the current paper a theoretical model to help understand the link between the reforms in electricity market and low subscription to green electricity. We should note here that the majority of the papers on this topic present only case studies. Fourthly, we show that the changes in the policies of the access charge pricing can constitute, in some cases, a relevant variable in the reforms of the electricity sector and can also have impacts on the consumption of the green electricity. This case may also raise the question of access charge prices in network industries.

Our paper shows that changes in the access charge pricing policy can constitute a relevant component in the reforms of the electricity sector and can have impact on the consumption of the green electricity. A differentiated access charge policy could allow a better penetration of the green electricity product and an increase in the social welfare when consumers have great preferences in environmental qualities.

The remainder of this paper is organized as follows. The second section presents our model and the main hypotheses. The third section examines the price competition and its link with the access charges. The fourth section discusses the link between the access charges and the qualities offered. The fifth section presents the social welfare analysis. Finally, the sixth section presents recommendations regarding the state’s interventions in the market to promote the green electricity.

The Structure of the Model

In this section, we present the main assumptions of a vertical differentiation model where the environmental quality is the element of discrimination. We begin by giving a short description of the electricity supply industry before moving to the analysis of the firms’ behaviour and the consumers’ behaviour.

Electricity Supply Industry

The electricity supply industry can be illustrated by four vertically successive stages. The generation of electric power which is competitive, the transmission network which is a natural monopoly with a substantial market power, the distribution network which is also natural monopoly and the retailing of electric power to the end users which is highly competitive. The vertical complementarities between competitive and monopolistic networks are crucial for competition in generation and retail stages. Indeed, access to monopoly networks is important for competition in the generation and retail networks. In order to transmit their electricity to consumers, the producers need to access the transportation network. They have to pay an access charge to the owner of the transportation network, that is, to the natural monopoly. This access charge is proportional to their use of the network² (Yun et al., 2016).

Firms’ Behaviour

In this study, we observe two different electricity providers in the generation network. The first one offers the green electricity product (good H) and the second provides the conventional electricity product (good L). The dominant operator, that is, the network natural monopoly, controls the bottleneck facility required for the interconnection with entrants competing in the generation segment. Therefore, the provision of good H by the competing green electricity firm requires access to the local network in order to reach the final consumers. Thus, this firm needs to pay an access charge³ noted a′ to the natural monopoly in order to use the bottleneck facility. The conventional electricity firm L has also to pay an access charge noted a to the natural monopoly to reach the final consumers.

We assume that green electricity (good H) is offered by a green label⁴ $(L_{H})$ with high environmental quality $q^{H}$ and price $p^{H}$ and that the conventional electricity product (good L) is offered with environmental quality $q^{L}$ and price $p^{L}$ We also assume that $q^{H} > q^{L}$ . We assume that the quality levels should follow the following condition: $q^{i} \in [0, + \infty [where i = H,L.$ Following Zhou et al. (2001), we assume that firm H has a fixed investment cost⁴ $F (q^{H}) = β^{H} q^{H^{2}}$ to have the eco-label $(L_{H})$ where $β^{H} > 0$ . This cost is due to the use of green electricity (construction, installation, etc.). On the other hand, we assume that firm L has the fixed investment cost⁵ $F (q^{L}) = β^{L} q^{L^{2}}$ . This cost is due to the use of conventional electricity (maintenance, installation, etc.). We further assume that $β^{H} > β^{L}$ . This assumption implies that firm H requires an investment cost that is higher than the conventional electricity one.

In order to focus on investment decisions in environmental quality, we assume that the marginal cost of quality is constant and for simplicity we let this cost be zero: $c_{H} = c_{L} = 0$ .

Consumers’ Behaviour

We assume that the consumers are aware of the importance of the environment for the benefits of the current and future generations, in the sense that they all prefer the most environment-friendly product if they have the choice between several ‘environmental qualities’ when the products are sold at same price. Thus, a vertical differentiation model seems to correspond to our situation. In this model, all consumers buy almost one unit of the product. The consumers are identified by a taste parameter $θ$ for the environmental quality. We assume that $θ$ is uniformly distributed on [c,d] where c,d > 1. For more simplicity, we suppose that d – c = 1.

Each consumer buys at most one unit of good i and derives utility $θ q^{i}$ from the consumption of the good with quality $q^{i}$ (i = H,L). The consumers pay $p^{i}$ for environmental quality $q^{i} (i = H,L)$ . We consider, as Mussa and Rosen (1978), that the indirect utility of a consumer of type $θ$ buying from firm i (i = H,L) a unit good of environmental quality $q^{i}$ at price $p^{i}$ is given by:

U (q^{i}, p^{i}; θ) = θ q^{i} - p^{i} where i = H, L

We let the taste parameter be $\tilde{θ}$ , which presumes that the consumer is indifferent between the high or low environmental quality. We have $\tilde{θ} = \frac{p^{H} - p^{L}}{q^{H} - q^{L}}$ .

Since all consumers use electricity, we assume that the demand is totally covered in this market. Thus, consumers of taste $θ \in [\tilde{θ}, d]$ buy the good of environmental quality $q^{H}$ . Consumers with $θ \in [c, \tilde{θ}]$ buy the good of quality $q^{L}$ . Demand functions of low and high environmental qualities are thus given by:

D^{L} (p^{L}, p^{H}, q^{L}, q^{H}) = \tilde{θ} - c = \frac{p^{H} - p^{L}}{q^{H} - q^{L}} - c

(2.1)

D^{H} (p^{H}, p^{L}, q^{H}, q^{L}) = d - \tilde{θ} = d - \frac{p^{H} - p^{L}}{q^{H} - q^{L}}

(2.2)

In the next sections, we will develop a two-stage game. The game is as follows: In the first step, firms H and L compete in qualities, and in the second stage, the two firms compete in prices. Our aim is to analyze the link between access charges and the equilibrium in qualities and price equilibrium.

Price Competition and Access Charges

The aim of this section is to analyze the link between the access charges and the equilibrium prices.

Equilibrium Prices

To have access to the network, the green electricity and the conventional electricity firms must pay a unit access charge noted a′ and a, respectively, to the natural monopoly. Firms L and H’s profits are then respectively:

π^{L} (p^{L}, p^{H}, q^{L}, q^{H}) = (p^{L} - a) D^{L} (p^{L}, p^{H}, q^{L}, q^{H}) - β^{L} q^{L^{2}}

(3.1)

π^{H} (p^{H}, p^{L}, q^{H}, q^{L}) = (p^{H} - a') D^{H} (p^{H}, p^{L}, q^{H}, q^{L}) - β^{H} q^{H^{2}}

(3.2)

By calculating the Nash equilibrium, we find the following equilibrium prices⁶:

p^{H *} = \frac{1}{3} [(1 + d) (q^{H} - q^{L}) + a + 2 a']

(3.3)

p^{L *} = \frac{1}{3} [(2 - d) (q^{H} - q^{L}) + 2 a + a']

(3.4)

\begin{array}{l} p^{H *} - p^{L *} = \frac{1}{3} [(2 d - 1) (q^{H} - q^{L}) + (a' - a)] \end{array}

(3.5)

The results are given in Equations (3.3)–(3.5) imply that the difference in equilibrium prices of

firms H and L depends on:

The parameter d which represents consumers’ environmental taste heterogeneity.

The environmental quality differentiation $(q^{H} - q^{L})$ ; and

The difference in access charges $(a^{'} - a)$ .

Equilibrium Prices, Access Charges and Consumers’ Environmental Taste heterogeneity

Equilibrium Prices and Access Charges

The price difference results in Equation (3.5) implies that on the one hand, given $a^{'} < a$ , the difference in prices is positive if and only if $(2 d - 1) (q^{H} - q^{L}) > (a' - a)$ On the other hand, if $a^{'} > a$ , the difference in prices is always positive, or green electricity is priced more than conventional electricity. We suppose here that the regulator will impose the access charge a′ that is inferior to a $(a^{'} < a)$ but will let the difference in prices be positive. We note that when $a = a^{'}$ , the difference in prices is positive but higher than the one where $a^{'} < a$ .

In the case $a^{'} < a$ , we can derive three different situations to promote green electricity through access charges:

The regulator decreases a′ and lets a be unchanged. That is, the green electricity firm has to pay a new access charge called a1′ to the natural monopoly.

The regulator decreases a′ to a1′ and increases a to a1, where a1′ is the new access charge payed by the green electricity firm to the natural monopoly and a1 the new access charge payed by the conventional electricity one to the natural monopoly.

The regulator increases a to a1 and keeps a′ unchanged.

Under these three conditions, we can establish the following conclusions.

In this First Situation: The natural monopoly decreases a′ to a1′ but keeps a unchanged.

Under these conditions, the changes in the equilibrium prices of firms H and L are given respectively by Equations (3.6) and (3.7):

Δ p^{H *} = p_{a_{1}'}^{H *} - p_{a'}^{H *} = \frac{2}{3} (a'_{1} - a')

(3.6)

Δ p^{L *} = p_{a_{1}'}^{L *} - p_{a'}^{L *} = \frac{1}{3} (a'_{1} - a')

(3.7)

In the same manner, the changes in the profits of firms H and firm L are respectively given by Equations (3.8) and (3.9):

Δ π^{H} = π_{a'_{1}}^{H} - π_{a'}^{H} = \frac{1}{3} (a' - a'_{1}) D^{H} (p^{H *}, p^{L *}, q^{H}, q^{L})

(3.8)

Δ π^{L} = π_{a'_{1}}^{L} - π_{a'}^{L} = \frac{1}{3} (a_{1}' - a') D^{L} (p^{H *}, p^{L *}, q^{H}, q^{L})

(3.9)

Equations (3.6) and (3.7) show that the differences in prices will decrease for the two firms since the regulator decreases a′ to a1′ but keeps a unchanged. We can also see that the equilibrium price of the green electricity product decreases twice more than that of the conventional electricity product. On the other hand, Equations (3.8) and (3.9) show that the profit of the firm offering the green electricity product will increase, whereas that of the conventional electricity product will decrease. Indeed, by reducing the access charge of firm H, the natural monopoly will indirectly raise the costs of the conventional electricity, which makes its profit drop.

Furthermore, under this situation, the price of the green electricity product decreases more than that of the conventional electricity, and the demand for the green electricity product is going to rise, whereas that of the conventional electricity will drop.

Finally, we can conclude that decreasing the access charge of the labelled green electricity product can promote the renewable energy and can lead consumers to choose this product instead of conventional electricity.

In this Second Situation: The natural monopoly decreases a′ to a1′ and increases a to a1.

Under these conditions, the changes in the equilibrium prices of firms H and L are given respectively by Equations (3.10) and (3.11):

Δ p^{H *} = (p_{a_{1}'}^{H *} - p_{a'}^{H *}) + (p_{a_{1}}^{H *} - p_{a}^{H *}) = \frac{2}{3} (a'_{1} - a') + \frac{1}{3} (a_{1} - a)

(3.10)

Δ p^{L *} = (p_{a_{1}}^{L *} - p_{a}^{L *}) + (p_{a'_{1}}^{L *} - p_{a'}^{L *}) = \frac{2}{3} (a_{1} - a) + \frac{1}{3} (a'_{1} - a')

(3.11)

In the same manner, the changes in the profits of firm H and firm L are respectively given by Equations (3.12) and (3.13):

Δ π^{H} = (π_{a'_{1}}^{H} - π_{a'}^{H}) + (π_{a_{1}}^{H} - π_{a}^{H}) = \frac{1}{3} [(a_{1} - a) + (a' - a'_{1})] D^{H} (p^{H *}, p^{L *}, q^{H}, q^{L})

(3.12)

Δ π^{L} = (π_{a'_{1}}^{L} - π_{a'}^{L}) + (π_{a_{1}}^{L} - π_{a}^{L}) = \frac{1}{3} [(a - a_{1}) + (a'_{1} - a')] D^{L} (p^{H *}, p^{L *}, q^{H}, q^{L})

(3.13)

Equations (3.10) and (3.11) show that the difference in prices of firm H decreases, whereas that of the conventional electricity firm L increases. On the other hand, Equations (3.12) and (3.13) show that the profit of the firm offering the green electricity product will increase, whereas that of the conventional electricity product will decrease. Under this situation, a part of the consumers will prefer to choose the labelled product instead of the conventional electricity. Indeed, by reducing the access charge of firm H and increasing that of the conventional electricity L, the natural monopoly will indirectly raise the costs of the conventional electricity, which makes its profit fall and its price increase.

Finally, we can conclude that by decreasing the access charge on the labelled green electricity producer and increasing the one on the conventional electricity, we can promote the renewable energy and can cause a part of the consumers to choose this product instead of the conventional electricity. This situation can thus contribute to the promotion of the renewable electricity products.

In the Third Situation: The natural monopoly keeps a′ unchanged but increases a to a₁.

Under these conditions, the changes in the equilibrium prices of firms H and L are given respectively by Equations (3.14) and (3.15):

Δ p^{H *} = p_{a_{1}}^{H *} - p_{a}^{H *} = \frac{1}{3} (a_{1} - a)

(3.14)

Δ p^{L *} = p_{a_{1}}^{L *} - p_{a}^{L *} = \frac{2}{3} (a_{1} - a)

(3.15)

In the same vein, the changes in the profits of firm H and firm L are respectively given by (3.16) and (3.17):

Δ π^{H} = (π_{a_{1}}^{H} - π_{a}^{H}) = \frac{1}{3} (a_{1} - a) D^{H} (p^{H *}, p^{L *}, q^{H}, q^{L})

(3.16)

Δ π^{L} = (π_{a_{1}}^{L} - π_{a}^{L}) = \frac{1}{3} (a - a_{1}) D^{L} (p^{H *}, p^{L *}, q^{H}, q^{L})

(3.17)

Equations (3.14) and (3.15) show that the differences in prices will increase for the two firms. We can also see that the equilibrium price of the conventional electricity product increases twice more than that of the green electricity firm. On the other hand, Equations (3.16) and (3.17) show that the profit of the firm offering the green electricity product will increase, whereas that of the conventional electricity product will decrease. Indeed, by increasing the access charge of firm L, the natural monopoly will indirectly reduce the costs of the green electricity, which makes its profit rise.

We can thus conclude that these three situations entice the green electricity firm to obtain a competitive advantage compared to the conventional electricity one. The cooperation between the network monopoly and the green electricity firm has influenced the market by reducing the conventional electricity firm’s profit and by raising its costs through paying higher access charges. In all of these cases, cooperation raises the conventional electricity costs, which causes part of the consumption to be transferred in favour of the labelled product. This strategy can promote the renewable energy by pushing the producers to invest in green electricity in order to obtain greater advantage in terms of lower access charges.

Equilibrium Prices and Consumers’ Environmental Taste heterogeneity

Here we now examine the relationship between equilibrium prices and consumers’ heterogeneity d.

The equilibrium price of the green electricity firm depends positively on parameter d. The higher d is, the more the consumers are aware of the environmental quality and the higher the price the green electricity firm will charge. In the same vein, the conventional electricity price depends negatively on parameter d. The more the consumers prefer environmental quality, the more the conventional electricity price will fall.

The market share of the conventional electricity firm is given by:

\frac{p^{H *} - p^{L *}}{q^{H} - q^{L}} - (d - 1) = \frac{2 - d}{3} + \frac{a' - a}{3 (q^{H} - q^{L})}

The market share of this electricity firm depends on the degree of the consumer’s heterogeneity (d), the difference in the access charges $(a^{'} - a)$ and the difference in qualities $(q^{H} - q^{L})$ . We note that the share of the conventional electricity market share falls with the increase in the difference in the access charges $(a^{'} - a)$ since $a^{'} < a$ . This assumption permits the green electricity firm to take greater advantage of the market share space. Furthermore, the higher d is, the more the consumers prefer environmental qualities and the more the conventional electricity market share will fall. Finally, the covered market configuration implies that the more consumers prefer environmental quality (d is high), the more the market share of the conventional electricity firm will fall and that of the green electricity firm will increase and vice versa.

Equilibrium Prices and Quality Difference

Regarding results Equations (3.3) and (3.4), we can conclude that the greater the quality difference is, the higher the equilibrium price of the green electricity firm and the lower that of the conventional electricity firm. But this effect is dominated by the consumers’ heterogeneity degree d. Thus, if d is too low, the quality difference will have a small impact on the equilibrium prices. Indeed, in this case, the consumers will not have strong preferences towards environmental quality, and then the quality difference will not play an important role. However, if d is high, the difference in qualities will necessarily be high and the difference in equilibrium prices will be high.

Finally, differences in access charges $(a^{'} < a)$ allow to increase the green electricity firm’s market share, thereby helping promote renewable energy. But, the market shares of the two firms and the Nash equilibrium prices depend equally on the consumers’ heterogeneity regarding environmental quality and on the quality difference.

In the next section, we are interested in quality competition and in the link between quality equilibrium and access charges.

Quality Competition and Access Charges

We let ${\tilde{R}}^{H} (q^{H}, q^{L})$ and ${\tilde{R}}^{L} (q^{L}, q^{H})$ be the revenues of firms H and L, respectively. We have:

{\tilde{R}}^{H} (q^{H}, q^{L}) = p^{H^{*}} D^{H^{*}} and {\tilde{R}}^{L} (q^{L}, q^{H}) = p^{L^{*}} D^{L^{*}}

This leads to:

{\tilde{R}}^{H} (q^{H}, q^{L}) = \frac{1}{9} [{(d + 1)}^{2} (q^{H} - q^{L}) + 3 a' (d + 1) + \frac{(a + 2 a') (a' - a)}{q^{H} - q^{L}}]

(3.18)

{\tilde{R}}^{L} (q^{L}, q^{H}) = \frac{1}{9} [{(2 - d)}^{2} (q^{H} - q^{L}) + (2 - d) (2 a' + a) + \frac{(2 a + a') (a' - a)}{q^{H} - q^{L}}]

(3.19)

By taking the derivative of ${\tilde{R}}^{H} (q^{H}, q^{L})$ and ${\tilde{R}}^{L} (q^{L}, q^{H})$ with $q^{H}$ and $q^{L}$ , respectively, we obtain:

\frac{\partial {\tilde{R}}^{H}}{\partial q^{H}} = \frac{1}{9} [{(d + 1)}^{2} - \frac{(a + 2 a') (a' - a)}{{(q^{H} - q^{L})}^{2}}] > 0

(3.20)

\frac{\partial {\tilde{R}}^{H}}{\partial q^{L}} = \frac{1}{9} [- {(d + 1)}^{2} + \frac{(a + 2 a') (a' - a)}{{(q^{H} - q^{L})}^{2}}] < 0

(3.21)

\frac{\partial {\tilde{R}}^{L}}{\partial q^{L}} = \frac{1}{9} [- {(2 - d)}^{2} + \frac{(2 a + a') (a' - a)}{{(q^{H} - q^{L})}^{2}}] < 0

(3.22)

\frac{\partial {\tilde{R}}^{L}}{\partial q^{H}} = \frac{1}{9} [{(2 - d)}^{2} - \frac{(2 a + a') (a' - a)}{{(q^{H} - q^{L})}^{2}}] > 0

(3.23)

The results in Equations (3.19)–(3.23) imply that an increase in $q^{H}$ and a decrease in $q^{L}$ increase simultaneously firms H and L’s revenues. We can thus conclude that the more the products are differentiated in qualities, the more price competition is relaxed and the more firms’ revenues will increase. This is a very important result since it shows that the green electricity firm has to increase its environmental quality in order to relax price competition. In the same manner, the conventional electricity firm has to diminish its quality to relax price competition.

In the following subsection, we will examine the equilibrium in qualities.

Quality Equilibrium

The aim of this subsection is to study the relationship between the access charges and the equilibrium in qualities in order to discern if the access charges have an impact on quality levels. We turn now to the first step of the game where firms compete in quality. We have the firms’ profits:

\begin{array}{l} {\tilde{π}}^{H} (q^{H}, q^{L}) = {\tilde{R}}^{H} (q^{H}, q^{L}) - {\tilde{C}}^{H} (q^{H}, q^{L}) where {\tilde{C}}^{H} (q^{H}, q^{L}) = a' D^{H *} + β^{H} q^{H^{2}} . \\ {\tilde{π}}^{L} (q^{L}, q^{H}) = {\tilde{R}}^{L} (q^{L}, q^{H}) - {\tilde{C}}^{L} (q^{L}, q^{H}) where {\tilde{C}}^{L} (q^{L}, q^{H}) = a D^{L *} + β^{L} q^{L^{2}} . \end{array}

The Nash equilibrium gives the following results:

\frac{\partial {\tilde{R}}^{H} (q^{H}, q^{L})}{\partial q^{H}} = \frac{\partial {\tilde{C}}^{H} (q^{H}, q^{L})}{\partial q^{H}}

(3.24)

\frac{\partial {\tilde{R}}^{L} (q^{L}, q^{H})}{\partial q^{L}} = \frac{\partial {\tilde{C}}^{L} (q^{L}, q^{H})}{\partial q^{L}}

(3.25)

The optimal qualities equalize marginal costs of investments and marginal revenues. The stability and concavity conditions are satisfied⁷. The quality equilibrium is unique.

Effect of the Access Charge Choice on Qualities

The costs of firms H and L are given by:

{\tilde{C}}^{H} (q^{H}, q^{L}) = a' D^{H} + β^{H} q^{H^{2}} = \frac{1}{3} a' [(d + 1) - \frac{(a' - a)}{(q^{H} - q^{L})}] + β^{H} q^{H^{2}}

(3.26)

{\tilde{C}}^{L} (q^{L}, q^{H}) = a D^{L} + β^{L} q^{L^{2}} = \frac{1}{3} a [(2 - d) + \frac{(a' - a)}{(q^{H} - q^{L})}] + β^{L} q^{L^{2}}

(3.27)

Equations (3.24) and (3.25) become:

\frac{\partial {\tilde{R}}^{H} (q^{H}, q^{L})}{\partial q^{H}} = \frac{\partial {\tilde{C}}^{H} (q^{H}, q^{L})}{\partial q^{H}} = \frac{1}{3} a' \frac{\partial D^{H *}}{\partial q^{H}} + 2 β^{H} q^{H}

(3.28)

\frac{\partial {\tilde{R}}^{L} (q^{L}, q^{H})}{\partial q^{L}} = \frac{\partial {\tilde{C}}^{L}}{\partial q^{L}} = \frac{1}{3} a \frac{\partial D^{L *}}{\partial q^{L}} + 2 β^{L} q^{L}

(3.29)

Equations (3.26)–(3.29) induce several remarks. In deciding on quality, the firms face three basic considerations. The first is the profitability of the location in the quality space based on revenues and the cost of investment in quality for a given distance from the rival’s quality. The second is the effect of a change in the difference between the two qualities proposed on the associated price competition. Indeed, a reduction in the gap between qualities would increase the associated price competition, and therefore limits the gains of the two firms. The conventional electricity firm will not be enticed to increase its quality level, $q^{L}$ , while the green electricity firm is driven to increase its quality $q^{H}$ but it must be aware of its fixed cost $β^{H} q^{H^{2}}$ . Indeed, even if the green electricity firm has an important fixed cost, it cannot significantly decrease its environmental quality in order to maintain competition and keep its environmental label. Conversely, one can decrease conventional electricity’s quality in order to decrease its fixed cost. Products are thus differentiated in quality.

The third consideration is the level of the access charges paid by the two firms to the network monopoly in order to access the transmission network. We have:

\frac{\partial {\tilde{C}}^{H}}{\partial a'} = \frac{1}{3} [(d + 1) - \frac{2 a' - a}{q^{H} - q^{L}}]

(3.30)

\frac{\partial {\tilde{R}}^{H}}{\partial a'} = \frac{1}{3} [(d + 1) + \frac{1}{3} \frac{(4 a' - a)}{(q^{H} - q^{L})}]

(3.31)

\frac{\partial {\tilde{C}}^{L}}{\partial a} = \frac{1}{3} [(2 - d) + \frac{a' - 2 a}{q^{H} - q^{L}}]

(3.32)

\frac{\partial {\tilde{R}}^{L}}{\partial a} = \frac{1}{9} [(2 - d) + \frac{(a' - 4 a)}{(q^{H} - q^{L})}]

(3.33)

By examining Equations (3.30)–(3.33), we note that the quantities $\frac{\partial {\tilde{C}}^{H}}{\partial a'}, \frac{\partial {\tilde{R}}^{H}}{\partial a'}, \frac{\partial {\tilde{C}}^{L}}{\partial a} and \frac{\partial {\tilde{R}}^{L}}{\partial a}$ depend on the quality differentiation, the access charges a and a′, and the consumers’ heterogeneity parameter d.

At this point, we can make three different remarks.

Remark 1: We notice that $\frac{\partial {\tilde{R}}^{H}}{\partial a'} < 0 if a' > \frac{1}{4} (a - 3 (d + 1) (q^{H} - q^{L}))$ .

Under this condition, the lower $\frac{\partial {\tilde{R}}^{H}}{\partial a'}$ is, the greater a decrease in a′ leads to a higher increase in ${\tilde{R}}^{H}$ . This situation implies that the green electricity firm must diminish $\frac{\partial {\tilde{R}}^{H}}{\partial a'}$ in order to increase its revenue. This firm will then increase its environmental quality in order to maintain the effect of a′ on its revenue. The decrease in the access charge of the green electricity firm favours the production of a higher environmental quality and is in favour of the promotion of renewable energy.

Remark 2: We have $\frac{\partial {\tilde{R}}^{L}}{\partial a} < 0 if a' < 4 a + (d - 2) (q^{H} - q^{L})$ .

By supposing that $\frac{\partial {\tilde{R}}^{L}}{\partial a} < 0$ , we can conclude that the lower $\frac{\partial {\tilde{R}}^{L}}{\partial a}$ is, the greater an increase in the access charge a leads to a higher decrease in the revenue ${\tilde{R}}^{L}$ . The conventional electricity firm must then increase $\frac{\partial {\tilde{R}}^{L}}{\partial a}$ by diminishing its quality $q^{L}$ . The increase in the conventional electricity access charge leads to a decrease in its quality, which can push it to invest in quality in order to obtain an advantage in terms of access charges.

Remark 3: We can see that $\frac{\partial {\tilde{R}}^{H}}{\partial a'}$ depends positively on the parameter d, whereas $\frac{\partial {\tilde{R}}^{L}}{\partial a}$ depends negatively on d.

We can thus distinguish between two different cases.

The first case where d is low. In this case, consumers do not have great preferences for the environmental quality. We observe a decrease in $\frac{\partial {\tilde{R}}^{H}}{\partial a'}$ and an increase in $\frac{\partial {\tilde{R}}^{L}}{\partial a}$ . This situation implies that the introduction of the green electricity product will have no impact on the consumption. In this case, a policy of pricing towards differentiated access charges does not favour the promotion of the renewable energies when consumers are heterogeneous and do not prefer the environmental quality. Indeed, in this case, consumers are not aware of the importance of environmental impacts of the green electricity and will not buy it even if it exists in the market.

The second case is where d is high (consumers are homogeneous and have strong preferences for environmental quality). We observe an increase in $\frac{\partial {\tilde{R}}^{H}}{\partial a'}$ and a decrease in $\frac{\partial {\tilde{R}}^{L}}{\partial a}$ . This situation implies that the difference in qualities is necessarily high. A policy of pricing towards differentiated access charges favours the promotion of the renewable energy when the consumers prefer environmental qualities. The introduction of differentiated access charges diminishes the prices and the green electricity product becomes more attractive to consumers.

The main results of this section can be summarized as follows. First, we can conclude that the decrease in the access charge of the green electricity firm favours the production of a higher environmental quality. Second, the increase in the conventional electricity access charge leads to a decrease in its quality, which can push the conventional electricity producer to invest in environmental quality in order to have an advantage in terms of access charges. Furthermore, we can conclude that the higher d is, the greater the part of consumers who initially buy the conventional electricity product will buy the green electricity product, and vice versa. Therefore, a policy of differentiated access charges diminishes the difference in prices, but this policy can promote renewable energy. It cannot promote green electricity when consumers are heterogeneous towards environmental quality (d is low).

Welfare Analysis

We turn now to the study of the effect of the introduction of different access charges on social welfare. We define social welfare as the sum of the consumer surplus and the producer surplus. We let W be the social welfare function. We have:

W = \int_{c}^{\tilde{θ}} θ q^{L} d θ + \int_{\tilde{θ}}^{d} θ q^{H} d θ - β^{L} q^{L^{2}} - β^{H} q^{H^{2}}

where $\tilde{θ} = \frac{p^{H} - p^{L}}{q^{H} - q^{L}}$ and c = d – 1 due to the full coverage of the market. By calculating t social welfare, we obtain the following expression:

W = \frac{- 5 d^{2} q^{L} + 14 d q^{L} - 8 q^{L} + 5 d^{2} q^{H} + 4 d q^{H} - q^{H}}{18} + \frac{(2 d - 1) (a - a')}{9} - \frac{{(a' - a)}^{2}}{18 (q^{H} - q^{L})}

We let W₁ be the social welfare when a = a′. We have:

W = \frac{- 5 d^{2} q^{L} + 14 d q^{L} - 8 q^{L} + 5 d^{2} q^{H} + 4 d q^{H} - q^{H}}{18} + \frac{(2 d - 1) (a - a')}{9} - \frac{{(a' - a)}^{2}}{18 (q^{H} - q^{L})}

In order to examine the effect of the promotion of the green electricity toward different access charges, we compare the social welfare W1 when $a = a^{'},$ with W which represents the social welfare when $a^{'} \neq a$ . We thus study the difference between W1 and W and obtain that:

W - W_{1} = \frac{(a - a')}{9} [(2 d - 1) + \frac{(a' - a)}{2 (q^{H} - q^{L})}]

When $a^{'} < a$ , the difference W – W1 is positive if $d > \frac{1}{2} [\frac{a' - a}{q^{H} - q^{L}} + 1]$ .

At this point of the analysis, we can derive two different situations.

First case ⁸: If $\frac{1}{2} [\frac{a' - a}{q^{H} - q^{L}} + 1] < d < 2 + [\frac{a' - a}{q^{H} - q^{L}}]$ then W > W₁.

This situation means that if the consumers are aware of the environmental quality, then a promotion policy of the green electricity product towards different access charges leads to an increase in the social welfare, compared to the case where the access charges are equal. In this case, the differentiated access charges policy could permit a better penetration of the green electricity product and an increase in social welfare.

Second case: If $1 < d < \frac{1}{2} [\frac{a' - a}{q^{H} - q^{L}} + 1]$ then W < W₁.

In this case, consumers’ heterogeneity is low which means that the consumers are not aware of the environmental quality. Under this condition, we can see a decrease in the social welfare, compared to the case when we have the same access charges. In this situation, the maintenance of the access charges at a uniform level is desirable in order to increase the social welfare.

Promoting Green Electricity by Authority

Promoting green electricity by an Authority needs to address several problems at the same time. First, as can be seen, the access charges represent an important part of the price functions and have a direct effect on the low penetration of the green electricity product. Second, there is a lack of consumer confidence in the green electricity product. These problems lead to an underinvestment in green electricity.

The Authority must play an important part in promoting the green electricity product. If the network monopoly invests in renewable energy using public funds, this policymaker can regulate the access charge. We suggest returning to differentiated access prices in countries where consumers are heterogeneous in their preferences of environmental qualities. The Authority can also impose ‘eco-taxes’ to encourage the consumers to choose green electricity and to make them confident about using the green electricity product. Consumers who use green electricity do not pay these eco-taxes, while those who do not subscribe to green electricity pay it.

Furthermore, the Authority can promote green electricity by offering a lower access charge to the green electricity producer, compared to the charge levied by conventional electricity firms. But, as we have seen in our paper, this situation favours the labelled product and can be a barrier to entry for the conventional electricity firm. Indeed, for the conventional electricity firm, the very high costs of labelled products are a real constraint. The authority should impose an environmental quality norm in order to minimize this problem and not allow the green electricity firm to take advantage of this situation.

Finally, a segmented green electricity market where there are different green electricity products with different renewable energy sources (solar, hydroelectric, biomass), with different levels of access charges depending on the energy source, can make the consumers more confident in the green electricity product.

Conclusion

The objective of this article is to analyze theoretically whether a change in the access pricing policy can promote green electricity. We consider two firms competing in the generation network. One firm offers green electricity, while the other supplies the conventional electricity to consumers. Each firm pays an access charge to the natural monopoly in order to have access to its transportation network. Through a vertical differentiation model, we have attempted to analyze the link between the access charges paid by the two firms and the qualities offered to the consumer. We have also attempted to understand why the consumer does not choose the green electricity product. Finally, we have examined the resulting impact on social welfare, and also suggested some policies that may lead the consumer to choose the green electricity product over the conventional electricity.

We have obtained the following main results. In deciding on quality, the firms face three basic considerations. The first consideration is the profitability of the location in the quality space based on the accrued revenues and the incurred cost of investment in quality for a given distance from the rival’s quality. The second consideration is the effect of a change in the difference between the two proposed qualities on the market share. Indeed, a reduction in the gap between qualities increases the associated price competition, and therefore limits the gains of the two firms. In this case, a conventional electricity firm will not be encouraged to increase its quality level. The third consideration is the level of the access charges paid by the two firms to the network monopoly in order to have access to the transportation network.

Our model shows that changes in the pricing of the access charge policies can constitute a relevant variable in the reforms of the electricity sector and can have impact on the consumption of the green electricity. A differentiated access charge policy could allow a better penetration of the green electricity product and an increase in social welfare when consumers have great preferences for environmental qualities. Otherwise, the preservation of the access charges at a uniform level for both firms is desirable in order to maintain competition.

Appendices

Appendix A1: Price Equilibrium

Part 1: First Order Conditions

The Nash Equilibrium must satisfy the following first order conditions:

\frac{\partial π^{H} (p^{H}, p^{L}, q^{H}, q^{L})}{\partial p^{H}} = 0

(1)

\frac{\partial π^{L} (p^{L}, p^{H}, q^{L}, q^{H})}{\partial p^{L}} = 0

(2)

By resolving Equations (1) and (2), we obtain the following reaction functions:

p^{H} (p^{L}) = \frac{1}{2} [d (q^{H} - q^{L}) + p^{L} + a']

p^{L} (p^{H}) = \frac{1}{2} [p^{H} + a - c (q^{H} - q^{L})]

The equilibrium prices are thus given by:

\begin{array}{l} p^{H *} = \frac{1}{3} [(2 + c) (q^{H} - q^{L}) + a + 2 a'] \\ p^{L *} = \frac{1}{3} [(1 - c) (q^{H} - q^{L}) + 2 a + a'] \end{array}

Given that d – c = 1, the equilibrium prices become:

p^{H *} = \frac{1}{3} [(1 + d) (q^{H} - q^{L}) + a + 2 a']

p^{L *} = \frac{1}{3} [(2 - d) (q^{H} - q^{L}) + 2 a + a']

\begin{array}{l} p^{H *} - p^{L *} = \frac{1}{3} [(2 d - 1) (q^{H} - q^{L}) + (a' - a)] \end{array}

Part 2: Concavity and Stability Conditions

Concavity

For the concavity conditions to be satisfied, we need to have:

\frac{\partial^{2} π^{H} (p^{H}, p^{L}, q^{H}, q^{L})}{\partial p^{H^{2}}} < 0 and \frac{\partial^{2} π^{L} (p^{L}, p^{H}, q^{L}, q^{H})}{\partial p^{L^{2}}} < 0

We have:

\frac{\partial^{2} π^{H} (p^{H}, p^{L}, q^{H}, q^{L})}{\partial p^{H^{2}}} = - \frac{2}{q^{H} - q^{L}} < 0

and

\frac{\partial^{2} π^{L} (p^{L}, p^{H}, q^{L}, q^{H})}{\partial p^{L^{2}}} = - \frac{2}{q^{H} - q^{L}} < 0

Concavity conditions are satisfied. 2.

Stability Conditions

For the stability conditions to be satisfied, we need to have:

\frac{\partial^{2} π^{H} (p^{H}, p^{L}, q^{H}, q^{L})}{\partial p^{H^{2}}} \frac{\partial^{2} π^{L} (p^{L}, p^{H}, q^{L}, q^{H})}{\partial p^{L^{2}}} - \frac{\partial^{2} π^{H} (p^{H}, p^{L}, q^{H}, q^{L})}{\partial p^{H} \partial p^{L}} \frac{\partial^{2} π^{L} (p^{L}, p^{H}, q^{L}, q^{L})}{\partial p^{L} \partial p^{H}} > 0

(- \frac{2}{q^{H} - q^{L}}) (- \frac{2}{q^{H} - q^{L}}) - (- \frac{1}{q^{H} - q^{L}}) (- \frac{1}{q^{H} - q^{L}}) = \frac{3}{{(q^{H} - q^{L})}^{2}}

The stability conditions are satisfied.

Appendix B: Interior Solutions

$p^{H *}$ and $p^{L *}$ are interior solutions if:

$p^{H *} > a'$ and $p^{L *} > a$ .

$(1 + d) (q^{H} - q^{L}) + 2 a' + a - 3 a' > 0$ if and only if $d > \frac{a' - a}{q^{H} - q^{L}} - 1$ .

$(2 - d) (q^{H} - q^{L}) + 2 a + a' - 3 a > 0$ if and only if $d < 2 + \frac{a' - a}{q^{H} - q^{L}}$

But we have d > 1, $p^{H *}$ and $p^{L *}$ represent interior solutions if:

1 < d < 2 + \frac{a' - a}{q^{H} - q^{L}}

Appendix C: Equilibrium in Qualities

Part 1: First Order Conditions

We have:

${\tilde{π}}^{H} (q^{H}, q^{L}) = {\tilde{R}}^{H} (q^{H}, q^{L}) - {\tilde{C}}^{H} (q^{H}, q^{L})$ where ${\tilde{C}}^{H} (q^{H}, q^{L}) = a' D^{H *} - β^{H} q^{H^{2}} .$

${\tilde{π}}^{L} (q^{L}, q^{H}) = {\tilde{R}}^{L} (q^{L}, q^{H}) - {\tilde{C}}^{L} (q^{L}, q^{H})$ where ${\tilde{C}}^{L} (q^{L}, q^{H}) = a D^{L *} - β^{L} q^{L^{2}} .$

The Nash equilibrium must satisfy the following first order conditions:

\frac{\partial {\tilde{π}}^{H} (q^{H}, q^{L})}{\partial q^{H}} = 0

(1)

\frac{\partial {\tilde{π}}^{L} (q^{L}, q^{H})}{\partial q^{L}} = 0

(2)

By resolving (1) and (2), we obtain the two following equations:

\frac{\partial {\tilde{R}}^{H} (q^{H}, q^{L})}{\partial q^{H}} = \frac{\partial {\tilde{C}}^{H} (q^{H}, q^{L})}{\partial q^{H}}

(3)

\frac{\partial {\tilde{R}}^{L} (q^{L}, q^{H})}{\partial q^{L}} = \frac{\partial {\tilde{C}}^{L} (q^{L}, q^{H})}{\partial q^{L}}

(4)

Part 2: Concavity and Stability Conditions

Concavity Conditions

We have:

\frac{\partial^{2} {\tilde{π}}^{H} (q^{H}, q^{L})}{\partial q^{H^{2}}} = \frac{(a' - a)}{{(q^{H} - q^{L})}^{3}} [\frac{2}{9} (2 a' + a) + \frac{a'}{3}] - 2 β^{H} < 0

\frac{\partial^{2} {\tilde{π}}^{H} (q^{L}, q^{H})}{\partial q^{L^{2}}} = \frac{2}{9} \frac{{(a' - a)}^{2}}{{(q^{H} - q^{L})}^{3}} - 2 β^{L} < 0 if and only if β^{L} > \frac{2}{9} \frac{{(a' - a)}^{2}}{{(q^{H} - q^{L})}^{3}} .

Concavity conditions are satisfied. 2.

Stability Conditions

We must have:

\frac{\partial^{2} {\tilde{π}}^{H} (q^{H}, q^{L})}{\partial q^{H^{2}}} \frac{\partial^{2} {\tilde{π}}^{L} (q^{L}, q^{H})}{\partial q^{L^{2}}} - \frac{\partial^{2} {\tilde{π}}^{H} (q^{H}, q^{L})}{\partial q^{H} \partial q^{L}} \frac{\partial^{2} {\tilde{π}}^{L} (q^{L}, q^{L})}{\partial q^{L} \partial q^{H}} > 0

[\frac{2}{9} \frac{{(a' - a)}^{2}}{{(q^{H} - q^{L})}^{3}} - 2 β^{L}] [\frac{{(a' - a)}^{2}}{{(q^{H} - q^{L})}^{3}} (\frac{2}{9} (2 a' + a) + \frac{a'}{3}) - 2 β^{H}] - [\frac{4}{81} \frac{{(a' - a)}^{2} (5 a' + a) (a' + a)}{{(q^{H} - q^{L})}^{6}}] > 0

The system is globally stable and concave if $β^{L} > \frac{2}{9} \frac{{(a' - a)}^{2}}{{(q^{H} - q^{L})}^{3}}$ . There is a unique equilibrium in qualities $(q^{L *}, q^{H *})$ .

Footnotes

Notes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Walid Hadhri

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