Environmental and Resource Economics

, Volume 67, Issue 4, pp 925–940 | Cite as

Feed-in Subsidies, Taxation, and Inefficient Entry

  • Fabio Antoniou
  • Roland Strausz


We study (energy) markets with dirty production and lumpy entry costs of clean production (renewables). For intermediate entry costs, markets yield inefficient production and inefficient entry. A mix of three popular regulatory instruments—polluter taxation, feed-in subsidies for renewables, and consumption taxation—cannot correct these market failures for larger entry costs. The instruments are imperfect because they affect marginal incentives, whereas entry is a lumpy fixed cost problem. Whenever the first best is implementable, feed-in subsidies and consumption taxes are redundant. The second best requires feed-in subsidies or consumption taxes in addition to a pollution tax and overshoots first best levels. Given production levels, the instruments do not affect the regulator’s budget.


Taxation Feed-in tariffs Externalities Renewables Entry Pollution 

JEL Classification

D21 D61 H23 

1 Introduction

In order to curb global warming, countries all over the world have pledged to fundamentally overhaul their energy systems. A major part of this overhaul is a switch from the use of carbon intensive technologies to renewables for generating electricity.1 The switch does not only involve the construction of large scale production facilities such as offshore wind farms, it also involves investments in R&D for developing more efficient technologies, in expanding the electricity transmission systems to connect these renewables to the grid, and setting up facilities that store electricity due to intermittency. A substantial part of the required capital costs associated with the switch is therefore of a once-and-for-all nature.

To bring about and finance the switch, most countries do not use heavy handed command-and-control systems but instead opt for a more market based approach. In the hope that free markets can bring about the transformation most efficiently, they leave actual production and technology decisions up to private enterprises and consumers, but use tools such as taxes and subsidies to steer markets in the right direction. More specifically, most countries put their faith in a combination of (direct or indirect) polluter taxes and subsidies in the form of feed-in subsidies for renewables.2 \(^,\) 3 The popularity of this tool set raises the question to what extent they are indeed able to lead to an efficient production structure.

An efficient production structure has to deal with two problems. It must, first, solve the CO2 externality of conventional electricity production and, second, provide the right amount of entry in renewables. In addition to these problems, most governments also have to deal with budgetary problems and for this reason many have resorted to a further tool, a consumption tax on electricity consumption, to finance their intervention schemes.4

An intuitive rationale for this tool set is as follows: Use a polluter tax to solve the externality problem, use a feed-in subsidy to solve the entry problem, and, finally, use a consumption tax to balance budgets. In line with the classical Tinbergen rule of “one instrument per policy objective”, the suggestion is that these three instruments are able to solve the two allocative problems and the budgetary problem of the government.

In this paper, we caution that, even though the above reasoning sounds intuitive, it is misleading. We instead argue that, because the switch to renewables is mainly a fixed cost problem, the set of instruments is much less effective.

We derive our results in a market setup with dirty incumbents and costly entry by clean production technologies.5 We emphasize that these entry costs involve more than only the construction of facilities. In this setup, the entrant’s incentives to bear the cost of entry are suboptimally low, because it disregards the contribution to social welfare that is appropriated by the consumer surplus. Consequently, our market setup represents a minimalist setup for modeling the problem discussed in the policy debate: the externality problem of the dirty incumbents and too little incentives for clean producers to enter.

For this market setup, we first of all show that feed-in subsidies and consumption taxes are ineffective instruments for inducing the first best. More precisely, we show that a social planner is just as well off between using only a tax on polluters or only using a combination of feed-in subsidy and consumer taxation. Put differently, if the social planner can attain the efficient outcome with the three instruments, she can also reach it with only a tax on polluters (or alternatively, only with a combination of feed-in subsidies and consumer taxation). Hence, complementing a tax on polluters by a feed-in subsidy, a consumption tax, or a combination of the two is redundant.6 The reason for this failure is a market interaction of the instruments, which prevents their use as independent policy instruments. As a consequence, the more robust Tinbergen logic is that the three “candidates” should not be seen as targets.

We further show that, for intermediate entry costs, no combination of the three instruments exist that induces efficient production, efficient entry and budget balance. This establishes the imperfectness of the set of instruments for addressing the three policy goals. In fact, this set of instruments is unable to deal even with the first two policy objectives, i.e., pollution control and entry promotion.

Since these policy instruments are in general unable to achieve the first best, we further study the second best. Intuitively, it trades off reductions in the incumbent’s dirty production against inducing entry. In order to induce entry, the second best distorts upwards the production of the potential entrant to enable it to recover its entry costs. Interestingly, the second best overcorrects the polluter’s output by inducing a production level below the efficient one. A social planner can achieve this second best with a tax on dirty production and a feed-in that subsidizes entry. Hence, only with regard to the second best, the feed-in subsidy becomes an effective, albeit suboptimal instrument. In addition to these two instruments, the consumption tax is however still redundant in that it does not enable the social planner to attain a higher welfare than using only the polluter tax and the feed-in subsidy. Since the second best allocation uniquely determines the budget, the consumption tax is also ineffective in balancing the budget of the overall set of instruments.

In conclusion, our results cast doubt on the policy debate such as COM (2008, p. 3), which states “Well-adapted feed-in tariff regimes are generally the most efficient and effective support schemes for promoting renewable electricity”.7 Since recent directives such as COM (2013, p. 9) and COM (2014) suggest to switch from feed-in tariffs to feed-in premiums and tenders, also the newer directives favor feed-in subsidies and changed their opinion only on the exact implementation of such subsidies.

The rest of the paper is organized as follows. In the next section we discuss the relevant literature and its relation to our results. In Sect. 3 we introduce our formal framework and derive the two market failures: too much pollution and too little entry. In Sect. 4 we introduce the regulatory instruments and study their ability to induce the first best, characterize second best outcomes, and discuss the general effectiveness of the policy instruments. In Sect. 5 we conclude the paper with a discussion of potential extensions.

2 Related Literature

Although both policy makers and practitioners are aware that large fixed and lumpy entry costs are to be incurred if renewables are to curb global warming, public economics has not focused much on the lumpy character of these investments. Instead, public economics has mostly analyzed entry under the assumption that it is a continuous and smooth process. Studies like Carlton and Loury (1980, 1986) and Spulber (1985), for instance, focus on the problem of optimal entry under negative production externalities, but specifically assume that entry is smooth and thus the implementation of a proper marginal instrument leads to the efficient outcome.8 \(^{,} \) 9 More recently, Bläsi and Requate (2010) and Currier (2015) consider fixed capital costs for clean entrants, but these studies also assume that entry is a smooth non-lumpy process.

Moreover, most existing studies focusing on feed-in subsidies abstract from fixed entry costs altogether (e.g., Schneider and Goulder 1997; Fischer and Newell 2008; Johnstone et al. 2010; Acemoglu et al. 2012, 2016; Reichenbach and Requate 2012; Lehmann 2013; Eichner and Runkel 2014; Ambec and Crampes 2015; Eichner and Pethig 2015). These papers focus, instead, on the marginal effects on investment incentives and analyze how feed-ins mitigate externalities and improve welfare through different channels such as the presence of learning by doing, spill-over effects in R&D, capital mobility and future uncertainty regarding prices or the supply from renewables due to intermittency.10 \(^{,}\) 11 Although we view these additional externalities as important, we point out that they capture a different problem than entry.

Our paper is further related to the vast literature in public economics on the effectiveness of different Pigou-tax bases when dealing with both single and multiple market failures. In the context of environmental externalities, Palmer and Walls (1997), Schöb (1997), Walls and Palmer (2001), and Fullerton and Wolverton (2000, 2005) point out that instead of taxing the polluter, a social planner may equivalently tax other participants. Fullerton and Wolverton (2005) combine this with revenue considerations of the government. This result is much in-line with our result that in order to implement the first best, the regulator only needs to tax the polluter or, equivalently, use a combination of consumer taxation and feed-in subsidies.

In line with the classic Tinbergen rule, dealing with multiple market failures usually requires a mix of different policy instruments. In the context of environmental externalities, Fischer and Newell (2008), Goulder and Parry (2008), and Garcia et al. (2012) for instance argue that multiple instruments are needed to address all the relevant dimensions. This stands in contrast to our insight that, when the first best is feasible in the presence of two imperfections, a single emission tax suffices to correct both market imperfections at the same time. Since this result no longer holds in the second best, our results are more in line with the literature on the second best use of multiple policy instruments such as Bennear and Stavins (2007).

There is also a growing literature on the dynamic implications that may arise from the introduction of these policies (e.g., Grafton et al. 2012; Hintermann and Lange 2013). Such dynamic considerations are however orthogonal to the issues we address and we therefore abstract from such concerns. However, as already argued by Petrakis et al. (1997), entry in a dynamic environment effectively implies that the firm and the social planner compare the discounted profits to the entry costs. Hence, if the social planner and the entrant have a common discount factor, then adding dynamics to our framework would not lead to any additional effects. If, in contrast, the social planner has a smaller discount factor than the firm, then the entrant’s entry choice is further distorted downwards, which, in our framework, effectively means that the entry problem is intensified.

On a more abstract level, our study is related to Makowski and Ostroy (1995), who emphasize the role of appropriation in achieving efficiency.12 From their perspective, entry is inefficient in our framework, since the entrant cannot appropriate the full social surplus of its entry. We show that taxes and feed-in subsidies are in general unable to ensure that the entrant can appropriate the overall social surplus of entry. They are therefore inefficient instruments.

3 Setup and Market Failures

We consider an industry that produces a homogeneous good x. The representative consumer has a quasi-linear utility and obtains utility \(\Psi (x)\) from consuming a quantity x, where \(\Psi (x)\) is increasing and concave, and \(\Psi (0)=0\). The industry consists of a dirty sector, which produces with an increasing and convex cost function \(C_{d}(x_{d})\) and imposes a negative externality \(E(x_{d})\), which is increasing and convex, and exhibits \(E(0)=0\). Entry by a clean producer requires a setup cost \(F\ge 0\) after which the entrant produces with an increasing and convex cost function \(C_{c}(x_{c})\) with \(C_{c}(0)=0\).13 We adopt the Inada conditions, \(\Psi ^{\prime }(0)=C_{d}^{\prime }(\infty )=C_{c}^{\prime }(\infty )=\infty \), \(\Psi ^{\prime }(\infty )=C_{d}^{\prime }(0)=C_{c}^{\prime }(0)=E^{\prime }(0)=0\). Focusing on the effectiveness of the policy instruments, we abstract from competitive issues and model consumers and producers as price takers.14

3.1 First Best Efficiency

First best production levels maximize aggregate surplus and therefore solve
$$\begin{aligned} \max _{x_{d},x_{c}}W(x_{d},x_{c})-F\cdot \mathbf {1}_{x_{c}>0} \end{aligned}$$
where \(W(x_{d},x_{c}) \equiv \Psi (x_{d}+x_{c})-C_{d}(x_{d})-C_{c} (x_{c})-E(x_{d})\) expresses welfare gross of entry costs and \(\mathbf {1} _{x_{c}>0}\) is an indicator function, denoting whether entry occurs and, hence, costs F are paid.
First best levels satisfy the usual optimality conditions that marginal utility equals marginal social costs. With entry this means that first best levels \((x_{d}^{*},x_{c}^{*})\) satisfy
$$\begin{aligned} \Psi ^{\prime }(x_{d}^{*}+x_{c}^{*})=C_{d}^{\prime }(x_{d} ^{*})+E^{\prime }(x_{d}^{*}) \text{ and } \Psi ^{\prime }(x_{d}^{*}+x_{c}^{*})=C_{c}^{\prime }(x_{c}^{*}). \end{aligned}$$
If, in contrast, the clean producer does not enter, first best level \((\hat{x}_{d}^{*},\hat{x}_{c}^{*})\) satisfy
$$\begin{aligned} \Psi ^{\prime }(\hat{x}_{d}^{*})=C_{d}^{\prime }(\hat{x}_{d}^{*})+E^{\prime }(\hat{x}_{d}^{*}) \text{ and } \hat{x}_{c}^{*}=0. \end{aligned}$$
Contrasting the cost of entry to the two associated welfare levels, we obtain the result:

Proposition 1

Let \(F^{*} \equiv W(x_{d}^{*},x_{c}^{*})-W(\hat{x}_{d} ^{*},0)\). For \(F\le F^{*}\), entry is socially desirable and first best levels are \((x_{d}^{*},x_{c}^{*})\). For \(F > F^{*}\), entry is not desirable and first best levels are \((\hat{x}_{d}^{*},0)\). Moreover, \(x_{d}^{*}<\hat{x}_{d} ^{*}<x_{d}^{*}+x_{c}^{*}=x^{*}\).

In line with standard intuition, entry is only socially efficient if the cost of entry is small enough. \(F^{*}\) represents the exact threshold level below which this is the case. Moreover, the efficient level of the dirty sector is smaller with entry than without entry, whereas the overall efficient level of production is larger with entry.

3.2 Two Market Failures

Let p represent the market price for good x. Consumers maximize their utility \(\Phi (x) =\Psi (x)-p x\), resulting in a demand function D(p) that satisfies the first order condition \(p=\Psi ^{\prime }(D(p))\). Given entry, the clean entrant maximizes \(\Pi _{c}(x_{c})=p x_{c}-C_{c}(x_{c})\), resulting in the supply function \(S_{c}(p)\), which satisfies the first order condition \(p=C_{c}^{\prime }(S_{c}(p))\). The dirty sector maximizes \(\Pi _{d}(x_{d})=p x_{d}-C_{d}(x_{d})\), yielding the supply function \(S_{d}(p)\), which satisfies the first order condition \(p=C_{d}^{\prime }(S_{d}(p))\).15

Given that entry occurs, the market equilibrium price \(p^{m}\) satisfies \(D(p^{m})=S_{d}(p^{m})+S_{c}(p^{m})\). The equilibrium outcome satisfies \(x^{m}=D(p^{m})\), \(x_{d}^{m}=S_{d}(p^{m})\), \(x_{c}^{m}=S_{c}(p^{m})\) with
$$\begin{aligned} p^{m}=\Psi ^{\prime }(x^{m})=C_{d}^{\prime }(x_{d}^{m})=C_{c}^{\prime }(x_{c} ^{m}). \end{aligned}$$
The following proposition addresses the question whether the entrant can recoup its fixed cost of entry so that it finds it actually profitable to enter.

Proposition 2

Let \(F^{m}\equiv p^{m} x_{c}^{m}-C_{c}(x_{c}^{m}).\) It holds \(F^{m}<F^{*}\). Moreover, the market output of dirty production exceeds first best levels (\(x_{d}^{m}>x^{*}_{d} \)) and entry is profitable only if \(F\le F^{m}\).

Hence, for intermediate entry costs, \(F \in (F^{m},F^{*})\), the market exhibits two market failures: (1) too much dirty production, because the sector does not internalize the externality; (2) too little entry, because the potential entrant can appropriate the additional surplus generated by its entry only partially. In the remainder we focus on such intermediate entry costs.

4 Regulation

Following the motivation in the introduction, we consider a combination of three regulatory instruments: (1) a (specific) tax \(t_{d}\) on the dirty production; (2) a feed-in subsidy \(t_{c}\) to subsidize the entrant’s clean production; 3. a (specific) tax, \(t_{\psi }\), on the consumption. As is standard, the instruments affect market outcomes, because they change the effective prices of the market participants and, thereby, the supply and demand functions. Given \((t_{d},t_{c},t_{\psi })\) and a price p, the dirty producers supply \(S_{d}(p-t_{d})\), the clean producers supply \(S_{c}(p+t_{c} )\), while consumers demand \(D(p+t_{\psi })\). Consequently, the regulated equilibrium price with entry, \(p^{r}\), satisfies
$$\begin{aligned} D(p^{r}+t_{\psi })=S_{d}(p^{r}-t_{d})+S_{c}(p^{r}+t_{c}). \end{aligned}$$
We say that the instruments \((t_{d},t_{c},t_{\psi })\) implement an allocation \((x_{d},x_{c})\) with \(x_{c}>0\) if and only if there exist some price \(p^{r}\) such that
$$\begin{aligned} x_{d}+x_{c}= & {} D(p^{r}+t_{\psi }); x_{d}=S_{d}(p^{r}-t_{d}); x_{c}=S_{c}(p^{r}+t_{c}); \Pi _{c}^{r}(x_{c}) \nonumber \\= & {} (p^{r}+t_{c})x_{c}-C_{c} (x_{c})\geqslant F. \end{aligned}$$
A regulator may also have budgetary concerns. Given an equilibrium price \(p^{r}\), the budget of the policy mix \((t_{d},t_{c},t_{\psi })\) is
$$\begin{aligned} B\equiv t_{d} S_{d}(p^{r}-t_{d})-t_{c} S_{c}(p^{r}+t_{c})+t_{\psi } D(p^{r}+t_{\psi }). \end{aligned}$$
Condition (4) restricts the policy outcomes \((x_{d},x_{c})\) that are implementable. The following lemma makes precise how this limits the effectiveness of the instruments:

Lemma 1

Instruments \((t_{d},t_{c},t_{\psi })\) implement allocation \((x_{d},x_{c})\) with \(x_{c}>0\) if and only if
  1. (i)

    \(t_{\psi }=\Psi ^{\prime }(x_{d}+x_{c})-C_{d}^{\prime }(x_{d})-t_{d} =\Psi ^{\prime }(x_{d}+x_{c})-C_{c}^{\prime }(x_{c})+t_{c}\);

  2. (ii)

    Entrant’s profits are \(\Pi _{c}^{r}=C_{c}^{\prime }(x_{c})x_{c}-C_{c} (x_{c})-F\ge 0\);

  3. (iii)

    Consumers’ net surplus is \(\Phi ^{r} =\Psi (x_{d}+x_{c})-\Psi ^{\prime }(x_{d}+x_{c})(x_{d}+x_{c})\);

  4. (iv)

    Incumbent’s profits are \(\Pi _{d}^{r}=C_{d}^{\prime }(x_{d})x_{d} -C_{d}(x_{d})\);

  5. (v)

    The budget equals \(B=[\Psi ^{\prime }(x_{d}+x_{c})-C_{d}^{\prime } (x_{d})]x_{d}+[\Psi ^{\prime }(x_{d}+x_{c})-C_{c}^{\prime }(x_{c})]x_{c}\).


The lemma is a direct implication of Condition (4) and expresses the restriction on an effective use of the instruments. The crucial observation is that conditions (ii)–(v) only depend on the allocation \((x_{d},x_{c})\). This means that any set of instruments that implements an allocation \((x_{d},x_{c})\) yields the same profits, consumer surplus, and budget. Hence, even if the regulator is able to attain a certain allocation \((x_{d},x_{c})\) with different combinations of instruments, she cannot use them for fine-tuning entry and budget problems.

4.1 First Best Regulation

We obtain the following result by considering the lemma’s implication with respect to the first best allocation \((x^{*}_{d},x^{*}_{c})\):

Proposition 3

Let \(F^{r}\equiv C_{c}^{\prime }(x_{c}^{*})x_{c} ^{*}-C_{c}(x_{c}^{*}).\) It holds \(F^{m}<F^{r}<F^{*}\). Moreover,
  1. (i)

    For \(F \in (F^{r},F^{*})\) a set of instruments implementing the efficient outcome fails to exist.

  2. (ii)

    For \(F\in (F^{m},F^{r})\) a set of instruments which implements the efficient outcome exists. For any such set of instruments, it holds \(t_{\psi }^{*}=t_{c}^{*}=E^{\prime }(x_{d}^{*})-t_{d}^{*}\). One particular set of instruments is \(t_{d}=E^{\prime }(x_{d}^{*})\) and \(t_{c}=t_{\psi }=0\).

Figure 1 illustrates the intuition behind the results of the proposition. The figure depicts the social costs of the dirty sector, \(S_d+E'\), the combined social costs of the dirty and clean sector, \(S_d+S_c+E'\), and the (inverse) aggregate supply function of the clean and dirty sector, \(S_d+S_c\). The intersection of the latter curve with the consumer’s aggregate demand function describes the unregulated market outcome, \((p^m,x^m)\), and comparing it to the socially efficient outcome \((p^*,x^*)\) shows the economic inefficiency: \(x^m>x^*\).
Fig. 1

Efficient and market outcomes

The triangle \(F^m\) depicts the profits of the clean sector gross of entry costs in the unregulated market. This is so, because the difference between the two curves \(S_d+E'\) and \(S_d+S_c+E'\) is simply \(S_c\), which corresponds to the marginal costs of the clean sector. Likewise, the larger triangle \(F^r\) represents the gross profit of the clean sector under the efficient outcome \((p^*,x^*)\). Finally, the triangle \(F^*\) illustrates the overall social gain from the clean sector’s entry, because without the entry the efficient output is \(\hat{x}^*\), whereas it is \(x^*\) with entry. Because a part of this social gain is captured by consumers in the form of consumer surplus, it logically follows that the differences in gross profits are smaller than the differences in aggregate surplus: \(F^r<F^*\).

The ordering \(F^r<F^*\) implies that in a market with efficient production levels, the clean sector’s incentives to enter are inefficiently low. Indeed for entry costs \(F \in (F^r,F^*)\), entry is socially efficient (since \(F<F^*\)), but the clean sector will not do so since the profits from entry \(F^r\) are lower than its costs F. This observation implies the statement (i) of the proposition, which is effectively driven by Lemma 1(i). Although there are more instruments than policy goals, they are, in general, unable to achieve the joint policy goals of efficient production levels and efficient entry. Hence, the regulatory instruments are imperfect. The first best outcome can only be achieved if the entry problem is “small”, \(F\le F^{r}\).

Statement (ii) of the proposition makes precise the sense in which the feed-in subsidy and the consumption tax are redundant for implementing efficient outcomes. It follows immediately after combining Lemma 1(i) and (ii) with the conditions for efficiency described in (1). It implies that if the efficient outcome is implementable, then the regulator is able to do so with only a polluter tax. The feed-in subsidy and the consumer tax are therefore completely redundant for implementing the first best, because the result logically implies that if the regulator is unable to attain the first best with only a polluter tax, then she is also not able to reach first best by using the feed-in subsidy and the consumption tax as additional instruments.

The proposition however also notes a multiplicity. For \(F\le F^{r}\), the regulator can achieve the first best with multiple combinations.16 In economic terms, these different combinations lead, however, to identical outcomes. The multiplicity result can therefore only be helpful if the regulator is somehow restricted in their use. For example, if the polluter tax is not under the full control of the regulator and does not match the marginal externality, then she may use an appropriate combination of feed-in subsidy and consumption tax to correct this.17

4.2 Second Best Regulation

For intermediate entry costs, \(F \in (F^{r},F^{*})\), the instruments are unable to implement the efficient outcome. In this case, we must lower our goals and give up our focus on first best efficiency. Instead we are led to consider the constrained optimal use of the instruments and to ask the question, which set of instruments maximizes social welfare over those outcomes that are implementable. The question leads us to second best considerations, which trades off inducing entry against regulating the externality. Intuitively, the second best either focuses on the externality problem of the dirty sector and forgoes on entry, or it focuses on entry and compromises on the externality problem.

If the second best foregoes on entry, it is straightforward to see that the second best coincides with the efficient outcome without entry as defined in (2): \((\hat{x}_{d}^{sb},\hat{x}_{c}^{sb})=(\hat{x}_{d} ^{*},0)\). Indeed, this outcome maximizes social welfare among all outcomes without entry. It is attainable, because the regulator can always prevent entry by a negative feed-in subsidy (i.e., tax).

We next address the welfare maximizing implementable outcome with entry, \((x_{d}^{sb},x_{c}^{sb})\). This outcome is a solution to the constrained maximization problem
$$\begin{aligned} \max _{x_{d},x_{c}} \ W(x_{d},x_{c}) \quad \text{ s.t. } C_{c}^{\prime } (x_{c})x_{c}-C_{c}(x_{c})\ge F. \end{aligned}$$
Disregarding the constraint yields the outcome \(x_{d}=x_{d}^{*}\) and \(x_{c}=x_{c}^{*}\) as defined in (1). It violates the constraint if \(F>F^{r}\). Since the problem is concave, the constraint then binds at the optimum. From this observation we obtain the following insight:

Proposition 4

For \(F\in (F^{r},F^{*})\), the second best allocation \((x_{d}^{sb},x_{c}^{sb})\) with entry is implicitly defined by \(C_{c}^{\prime }(x_{c}^{sb})x_{c}^{sb}-C_{c}(x_{c}^{sb})=F\) and \(\Psi ^{\prime }(x_{d} ^{sb}+x_{c}^{sb})=C_{d}^{\prime }(x_{d}^{sb})+E^{\prime }(x_{d}^{sb})\). The second best exhibits \(x_{c}^{sb}>x_{c}^{*}\), \(x_{d}^{sb}<x_{d}^{*}\) and \(x^{sb}=x_{d}^{sb}+x_{c}^{sb}>x_{d}^{*}+x_{c}^{*}=x^{*}\). It is implementable with any set of instruments \((t_{d}^{sb},t_{c}^{sb},t_{\psi }^{sb})\), where \(t_{c}^{sb}=C_{c}^{\prime }(x_{c}^{sb})-\Psi ^{\prime }(x_{d}^{sb}+x_{c} ^{sb})+t_{\psi }^{sb} \ge t_{\psi }^{sb}=E^{\prime }(x_{d}^{sb})-t_{d}^{sb}\).

For \(F>F^{r}\), the output \(x_{c}^{*}\) is too small to yield enough profits to compensate for the entry costs. The second best with entry, therefore, exhibits an output of the clean entrant that is distorted upwards, \(x_{c} ^{sb}>x_{c}^{*}\), so that enough revenues are generated to cover the fixed costs. Given that the entrant’s output is larger than in the first best, marginal benefits from consumption decrease. As a result, output of the dirty sector is lower than in the first best, \(x_{d}^{sb}<x_{d}^{*}\), because at the efficient production level, marginal benefits from consumption equal social marginal costs.

The proposition further characterizes the set of policy instruments that implements the second best allocation combining the optimality condition for dirty production described in (1) with Lemma 1(i). In particular, it shows that a polluter tax \(t_{d}\) alone is unable to attain the second best. In the second best a positive feed-in subsidy is needed. A specific set of instruments which achieves the second best, is the usual externality tax that equals the marginal externality, \(t_{d}^{sb}=E^{\prime }(x_{d}^{sb})\), together with a positive feed-in subsidy, \(t_{c}^{sb}=C_{c}^{\prime }(x_{c}^{sb})-\Psi ^{\prime }(x_{d}^{sb}+x_{c}^{sb})>0\). A further consumption tax is not needed, \(t_{\psi }^{sb}=0,\) so that the second best is attainable with only two of the three instruments.18

We can compare the welfare levels associated with \((\hat{x}^{*}_{d},0)\) and derive the optimal regulation \((x_{d}^{sb},x_{c}^{sb})\) in the second best.

Proposition 5

Let \(F^{sb}\equiv W(x_{d}^{sb}+x_{c}^{sb},x_{d}^{sb},x_{c}^{sb})-W(\hat{x}_{d}^{*},\hat{x}_{d}^{*},0)\). It holds \(F^{sb} \in (F^{r},F^{*})\). For \(F\in (F^{r},F^{sb}]\) the second best induces entry and outcome \((x_{d}^{sb},x_{c}^{sb})\). For \(F\in (F^{sb},F^{*})\) the second best induces outcome \((\hat{x}_{d}^{*},0)\) and no entry.

Figure 2 collects our results. Comparing the first and second row reveals how the market distorts entry downwards. The reason for this downward distortion is that, in a market, the entrant can extract only a part of the efficiency gains from entry while incurring its full cost. The third line shows that the three instruments are unable to achieve the first best for intermediate entry costs, while the fourth line demonstrates for these intermediate costs, whether under an optimal use of the instruments entry occurs.
Fig. 2

Summary of results

4.3 General Effectiveness of the Policy Mix

Until now we considered the effectiveness of the instrument mix to implement either first or second best allocations. In this section, we study the general effectiveness of the instruments to induce some market outcome with entry. This allows us to make more precise our statement that the at first sight intuitive argument presented in the introduction—the tax on dirty production is to address the externality problem, the feed-in subsidy is to alleviate the entry problem, and the consumption tax is to balance the budget—is misleading, because the three instruments exhibit an inherent dependency.

To show this, the next proposition states to what extent the restrictions of Lemma 1 limit the effectiveness of the policy instruments with entry in general.

Proposition 6

Suppose instruments \((t_{d},t_{c},t_{\psi })\) implement an outcome \((x_{d},x_{c})\) with \(x_{c}>0\) that yields net consumer surplus \(\Phi \), profit levels \(\Pi _{c}\), \(\Pi _{d}\), and a budget B. Then,
  1. (i)

    \((x_{d},x_{c})\) is also implementable by only a tax \(t_{d}^{\prime }\) and a feed-in subsidy \(t_{c}^{\prime }\) and yields the same net consumer surplus \(\Phi \), profit levels \(\Pi _{c}\), \(\Pi _{d}\), and budget B.

  2. (ii)

    \((x_{d},x_{c})\) is also implementable by only a tax \(t_{d}^{\prime }\) and a consumption tax \(t_{\psi }^{\prime }\) and yields the same net consumer surplus \(\Phi \), profit levels \(\Pi _{c}\), \(\Pi _{d}\), and budget B.


The proposition shows a general redundancy in the policy instruments. With respect to the market outcome, net consumer surplus, individual profits, and the overall budget, it suffices to use only two of the three instruments. Given that the regulator uses a tax \(t_{d}\) either the feed-in subsidy \(t_{c}\) or the consumer tax \(t_{\psi }\) is superfluous. Hence, the regulator can do just as well by using only two instruments instead of three.

The proposition, moreover, implies that we cannot use the three policy instruments independently for regulating the externality, ensuring entry, and budget concerns. The proposition therefore explains in what sense the Tinbergen logic of the introduction fails and that the intuitive argument presented in the introduction—the tax on dirty production is to address the externality problem, the feed-in subsidy is to alleviate the entry problem, and the consumption tax is to balance the budget—is incorrect.

Finally, we want to note that the budget irrelevance of the instruments as identified in Proposition 6 depends on the exact concept of the budget. In some countries that implement the polluter tax through a permit system, politicians seem more concerned with financing only the feed-in policy through the consumption tax.19 To address this concern we define instruments \((t_{d},t_{c},t_{\psi })\) as feed-in budget balanced if they implement an allocation \((x_{d},x_{c})\) so that
$$\begin{aligned} t_{c} x_{c}=t_{\psi } (x_{d}+x_{c}). \end{aligned}$$
For a policy mix that is feed-in budget balanced, the total expenditures associated with the feed-in subsidy match the overall revenues from the consumption tax.

For policy instruments that are feed-in budget balanced, we obtain the following characterization.

Proposition 7

Suppose instruments \((t_{d},t_{c},t_{\psi })\) implement an allocation \((x_{d},x_{c})\) with \(x_{d}>0\). Then there exist feed-in budget balanced instruments \((t_{d}^{\prime },t_{c}^{\prime },t_{\psi }^{\prime })\) that also implement \((x_{d},x_{c})\). In particular, a consumption tax \(t_{\psi }^{\prime }=(t_{c}-t_{\psi })x_{c}/x_{d}\), a polluter tax \(t_{d}^{\prime }=t_{d}+t_{\psi }-t_{\psi }^{\prime }\) and a feed-in subsidy \(t_{c}^{\prime }=t_{c}-t_{\psi }+t_{\psi }^{\prime } \) implement \((x_{d},x_{c})\) and are feed-in budget balanced.

Although the proposition holds for any allocation \((x_{d},x_{c})\) with \(x_{d}>0\), its interpretation is markedly different depending on whether or not it is applied to the first best allocation \((x_{d}^{*},x_{c}^{*})\). With respect to the first best allocation, the proposition effectively implies that feed-in budget balanced policy instruments cannot use feed-in subsidies or consumer taxation. To see this, recall from Proposition 3(ii) that any set of instruments which implements the first best requires \(t_{\psi }=t_{c}\). Given \(x_{d}^{*}>0\), such policy instruments only satisfy the feed-in budget balanced condition (6) if \(t_{\psi }=t_{c}=0\). Hence, any feed-in budget balanced set of policy instruments that implements the first best must use only a tax \(t_{d}\) (which then equals the marginal externality) and does not use a feed-in subsidy or consumer tax.

In contrast, the proposition identifies a specific role for consumer taxation when implementing an allocation \((x_{d},x_{c})\) for which \(\Psi ^{\prime } (x_{d}+x_{c})\not =C_{c}^{\prime }(x_{c})\). Such allocations are necessarily inefficient, but restricting to feed-in budget balanced instruments, they do require a specific non-zero consumer tax. This consumer tax is at most as large as the feed-in subsidy.

5 Concluding Remarks

The currently popular combination of regulatory instruments—taxation on polluters, feed-in subsidies for renewables, and taxation of consumption—is, in general, unable to solve both externality and entry problems. Intuitively, subsidies and taxes are the wrong instruments for addressing entry problems, because entry is a lumpy fixed cost problem, whereas these instruments affect only marginal incentives. Contradicting popular belief as, for instance, expressed in COM (2008, 2013, 2014), we, therefore, obtain the result that feed-in subsidies are not the right instrument for promoting renewable electricity.

In contrast, a tax on polluters that equals the marginal externality together with a lump-sum subsidy conditional on entry which covers the entrant’s entry costs in excess of its expected profits in the market, is an example of a set of instruments that induces the first best.20 From a policy viewpoint such fixed, quantity independent transfers may seem suspicious and difficult to implement. Feed-in subsidies are, however, not an adequate alternative for such lump sum transfers, because they affect marginal considerations and are therefore distortive.

We stress that we obtain our inefficiency results already in a surprisingly parsimonious setup that captures the essence of the externality and entry problem in a most elementary way. The plainness of the setup allows us to identify clearly that the market interaction of the policy instruments severely restricts their effectiveness. We are however confident that our results hold in more elaborate environments, because the source of the inefficient entry is the entrant’s inability to appropriate the entire surplus of its entry. As argued by Makowski and Ostroy (1995), full appropriation is however a necessary condition for guaranteeing efficient entry. From this perspective, our contribution is therefore to point out that taxes and feed-in subsidies are unable to induce a full appropriation by the entrant. Our results also obtain in a more fully fledged general equilibrium analysis, since the lumpy investment creates a non-convexity in production and a Pareto-efficient market outcome simply does not exist.

Hence, if the entry problem is significant but regulation is restricted to the exclusive use of the three aforementioned instruments, then it can lead at most to a second best. This second best policy is suboptimal in that it either distorts entry downwards or overshoots in reducing dirty production together with overproduction in the clean technology.

In our context of renewables, we find a modeling of entry as a lumpy fixed cost problem as highly compelling, because the entry of renewables not only involves the construction of large scale production facilities, but also requires investments in expanding the electricity transmission systems to connect these renewables to the grid and investments in R&D for developing more efficient production technologies and investments in new technologies such energy storage capabilities to deal with problems of intermittency.

Yet, we also find the lumpy fixed costs perspective appropriate if one considers only the construction costs of production facilities, because current reduction targets in CO2 emissions are so ambitious that they can only be met by the entry of large scale projects such as solar plants, offshore wind parks, and large dam-systems for water power facilities. Gillis (2015) for instance reports that, in order for the US to attain these targets, 156,000 wind turbines are to be built off American coasts in the next 35 years. He then compares this number to the mere 3000 offshore turbines which European countries have build during the last 20 years. For offshore wind parks, the European Wind Energy Association (2009) computes that their fixed setup costs accounts for 75 % of overall costs. Hence, these projects are lumpy in nature and not arbitrarily divisible.

Indeed, entry would not be a problem if we model it as a completely smooth, continuous process. Such a modeling approach would however not reflect economic realities and would lead to the rather extreme conclusion that market entry cannot be a problem at all.21 Hence, if one views entry of renewables as insufficient when left to an unregulated market (a view to which practitioners and policy makers evidently prescribe), then one is compelled to give up the technical convenience of modeling entry as a continuous variable. Moreover, it does not matter for our arguments whether profits or costs are uncertain or dynamic. It is also immaterial whether the entry costs reflect the development cost of some new technology, operational costs which are invariable over time, or some other more mundane setup cost.

Introducing additional aspects, such as asymmetric information, spill-overs, or transboundary pollution, may lead to additional effects which, when strong enough, can affect our results. We consider any such extension worthwhile, but point out that our insight of the basic limitations of the instruments due to their market interaction is a robust feature. They represent economic realities that will also play a role in more complicated setups.


  1. 1.

    E.g. the Presidential Memorandum on December 5, 2013, White House (2013) states a target share schedule for renewables of 20 % as of 2020 up from 10 % for 2015 in the US. COM (2014) sets a similar target of 20 % in 2020 for the whole European Union. According to the same source this level is expected to rise up to 27 % by 2030. Wharton (2013) reports that the Japanese government has set renewable targets of between 25 and 35 % of total power generation by 2030.

  2. 2.

    We consider any type of subsidy that raises the production-price of clean energy as a feed-in subsidy and, hence, do not distinguish between feed-in tariffs, feed-in premiums or tenders.

  3. 3.

    According to the database of IEA (2014), more than 60 countries world wide use feed-ins subsidizing renewables, including the US, Canada, the European countries, Japan, and even China. Under indirect polluter taxes we also count emission trading mechanisms such as the EU ETS.

  4. 4.

    RES (2014) reports that these taxes are standard in Europe, including all major countries UK, Germany, France, Italy, and Spain.

  5. 5.

    Since we analyze a perfect competitive market, the ownership of these technologies is immaterial. They can be owned by the dirty incumbents or new firms.

  6. 6.

    We note that the extra instrument might however be useful when the regulator does not have full control over the tax on polluters, due to political economy constraints or international agreements.

  7. 7.

    See also IEA (2008), which expresses similar views.

  8. 8.

    Carlton and Loury (1980, 1986) point out that there is no Pigouvian tax rate such that the long run competitive equilibrium corresponds to the socially efficient allocation. The rationale suggested (see Carlton and Loury 1980, p. 563) is that there are two targets to fulfill, i.e., production and number of firms, with solely one instrument. Our findings suggest that this is imprecise as we illustrate that despite the introduction of a larger set of policy instruments with respect to the targets we still obtain inefficient outcomes.

  9. 9.

    Katsoulacos and Xepapadeas (1995) study entry when the market structure is imperfectly competitive.

  10. 10.

    Although not mentioned explicitly studies by Jaffe et al. (2005), Helm and Schöttner (2008) and Ambec and Crampes (2012) also support promoting policies for similar reasons.

  11. 11.

    Using data from OECD countries, Nesta et al. (2014) find empirical support for the hypothesis that current renewable energy policies foster green innovation. In a Nordic case study based on wind power, Boomsma et al. (2012) verify that a feed-in subsidy encourages earlier investment.

  12. 12.

    See also Burrows (1979) and Collinge and Oates (1982) who argue that taxation of large scale firms may discourage entry as the tax bills paid by the individual firm exceed the damages caused by that firm’s entry. This problem can be solved by the implementation of command and control or non-linear taxation, while it appears not to be a problem in a general equilibrium framework (see Kohn 1994). Our problem is of a different nature attributed to the fact that clean entrants cannot fully appropriate the benefits from entry.

  13. 13.

    Note that production technologies with constant marginal cost up to some fixed capacity are convex.

  14. 14.

    Perfect competition is not essential for our arguments. It however presents the natural framework to study the effectiveness of the instruments, since they are not intended for competition policy. In line with Makowski and Ostroy (1995) of an “occupational-choice equilibrium”, we assume that the firm takes into account changes in the equilibrium price. Contrary to a pure Walrasian analysis of our setup, this approach ensures existence of equilibrium (for more details, see footnote 7 in Makowski and Ostroy 1995).

  15. 15.

    Our Inada conditions together with our convexity assumptions imply that the first order conditions are sufficient and lead to well-defined and positive demand and supply for any \(p>0\).

  16. 16.

    In a different setup, this degree of freedom is also noted in Palmer and Walls (1997), Schöb (1997), Walls and Palmer (2001), and Fullerton and Wolverton (2000, 2005).

  17. 17.

    E.g., the result rationalizes COM (2013, §108): “the EU ETS and national CO2 taxes internalise [...] may not (yet) ensure the achievement of the related, but distinct EU objectives for renewable energy [...] the Commission therefore presumes that a residual market failure remains, which aid for renewable energy can address.”

  18. 18.

    Recall from Lemma 1 that there is also no role for the consumption tax to fine-tune the budget.

  19. 19.

    This view may change as countries start to auction off rather than give away these permits for free with “grandfathering” schemes.

  20. 20.

    Clearly, first best only obtains when the transfer is not financed by a distortionary consumption tax.

  21. 21.

    Our result that feed-in subsidy and consumer taxes are redundant would however still remain valid.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Institute for Economic Theory 1Humboldt-Universität zu BerlinBerlinGermany

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