# Does adoption always follow innovation?

Oliwia Kurtyka, Rania Mabrouk

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Oliwia Kurtyka, Rania Mabrouk. Does adoption always follow innovation?. Resource and Energy Economics, 2025, 83, pp.101514. 10.1016/j.reseneeco.2025.101514. hal-05244378

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# Does adoption always follow innovation?

Oliwia Kurtyka ID *, Rania Mabrouk

Univ. Grenoble Alpes, CNRS, INRAE, Grenoble INP, GAEL, 38000, Grenoble, France

## ARTICLE INFO

JEL classification:

Code
D43
H23
L13
Q42
Q58

Keywords:

Environmental innovation
Abatement technology
Clean technology
End-of-pipe equipment
Vertical chain
Regulation
Bargaining

## ABSTRACT

The extent to which innovation is good news for environment depends not only on the research and development incentives but also on adoption stimulus. We analyze firm's choice of abatement technology in vertical chains. A downstream polluting monopoly can sign a contract with an upstream supplier of mature end-of-pipe equipment or develop an in-house clean technology. We show that contracting plays a crucial role in the efficiency of environmental regulation in spurring adoption. We find that polluter's innovation may be undertaken only to increase bargaining power and a share of industry profits he manages to capture. Consequently, polluter's and regulator's interests are not always aligned.

The role of regulator as a technology forcing authority is partially confirmed in regions of under-investment. However, the regulator may not be able to trigger innovation and/or adoption if clean technology increases marginal costs too much. On the other hand, regulator may become laxer and oppose innovation in case of over-investment. All these results rely upon the creation of total profits from the integrated vertical structure and the partitioning rule.

## 1. Introduction

In response to increasingly urgent economic and ecological crises, governments are promoting environmental innovations as shown by the European Commission's "Europe 2020" report which followed the report of Lisbon (2000). Environmental innovations are typically divided in two distinct types: end-of-pipe solutions and clean technologies. The former occur at the end of production process to mitigate environmental impacts of economic activities without changing the production process itself. In contrast, clean innovations, which are generally argued as being preferable in the long run (Frondel et al., 2007; Porter and van der Linde, 1995; Yarime, 2008), minimize pollution at source by using cleaner inputs and production methods. However, they often require intensive changes to productive systems and a significant commitment in terms of financial and human resources.

Empirical studies show that factors such as environmental regulations, size of firms (measured by the revenue), and energy prices are more likely to lead to the adoption of end-of-the-pipe solutions (Frondel et al., 2007; Hammar and Löfgren, 2010). On the other hand, market-driven forces — such as cost savings, learning-by-doing and knowledge (measured by expenditures on green R&D) or environmental management tools tend to increase the probability of investment in clean technologies (Frondel et al., 2007; Hammar and Löfgren, 2010).

The belief in innovations as an ultimate solution however, should not be taken for granted. It relies on the assumption of its consequent adoption. Despite empirical evidence on induced innovation,<fnref n="1" /> the question of its adoption stays open. Firms'

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: oliwia.kurtyka@grenoble-inp.fr (O. Kurtyka), Rania.Kamoun@gmail.com (R. Mabrouk).</footnote>

<footnote n="1">¹ See the excellent surveys of Jaffe et al. (2003), Requate (2005).</footnote>
technological responses to regulation are still largely unexplained: some regulations lead to technology adoption, mainly end-of-pipe, and no innovation whereas some others result in innovation but no subsequent adoption. As mentioned by Calel (2020), in several environmental programs, emission reductions have been mainly achieved through adoption of pre-existing techniques and equipment with no innovation activity happening in parallel (the examples for emission trading schemes are: Acid Rain program, phaseout for leaded petroleum). Calel (2020) illustrates alternative pattern under EU Emissions Trading System (EU ETS) where firms have not adopted new technologies, however a significative low-carbon R&D spending and patenting were evidenced. Such behavior may be triggered by expectations of stricter future regulation, far beyond the levels that could be met with existing mature technologies. Yet, the possibility to achieve current, modest emission reduction targets at reasonable cost with current technologies may reduce the incentives to deploy new innovations.

Our paper addresses the question of technology choice through the lens of strategic use of environmental innovation. The purpose of this paper is to contribute to environmental literature by examining the innovation and technology adoption decisions in vertical chains. We provide a theoretical framework capable of predicting different innovation and adoption patterns that can emerge. Innovation is defined as creation of new opportunities for pollution abatement (through development of previously nonexistent technology or process change) while adoption refers to the decision to effectively use a newly developed technology in the production activity. The disconnect between innovation and adoption can be explained by considering a setting where bargaining occurs in a vertical relationship, with environmental tax as the policy instrument. In this context, the downstream company engages in bargaining process with an upstream supplier, negotiating a two-part tariff and profit sharing.<fnref n="2" />

To strengthen its bargaining position, the downstream polluter can innovate on his own and use the potential profits from the new technology as a threat in the event of a negotiation breakdown. This in turn alters the profits the polluter can obtain from the relation with the supplier. This type of in-house innovation is supported by empirical research. Lanjouw and Mody (1996) estimate that worldwide 20% of patents for pollution control technologies are taken up by insiders. Jaffe and Palmer (1997), Brunnermeier and Cohen (2003) and others evidence outlays on pollution-control R&D made by polluting firms and environmental services sector.

Our main hypothesis is that polluting firm can develop R&D activities for clean technologies in order to increase its strategic advantage over an existing supplier of an end-of-pipe solution. Delgado et al. (2020) argue that business to business (B2B) setting tend to trigger more innovation in chains that business to consumers (B2C) ones. In our setting, the supplier of the end-of-pipe solution has a mature technology and he does not invest in further research. We show that as environmental taxation increases, the adoption may not necessarily follow.

Our contribution to the literature on strategic use of innovation is twofold. First, we explain that the adoption of innovation arises from competition between different types of technologies. On one hand, the clean technology developed by the downstream firm is more effective in abating pollution, but it is more expensive. On the other hand, the end-of-pipe technology sold by an upstream firm is cheaper but offers less pollution abatement. These cost differences are further amplified by the downstream firm's improved bargaining position due to innovation. Second, we study how environmental policy should be adjusted when innovation is used strategically within vertical supply chains.

Our analysis brings to light several important insights. It is well known that when firms expect regulators to ratchet up the standards ex post innovation, policy maker encounters the problem of underinvestment. In our setting, because the R&D effort of polluting firm does not affect the regulator's proposed solution, the strategic reasons discussed above are absent. Nonetheless, both underinvestment and overinvestment still occur, driven by the misalignment of interests between the regulator and the innovating firm, which stems from the bargaining process and profit-sharing dynamics. While the regulator is indifferent to how industry profits are split, this division of profits is crucial for the firms involved in deciding on transactions.

Overinvestment arises when the polluting firm has interest in innovating, but the regulator prefers the end-of-pipe technology. When the polluter innovates in order to increase his bargaining power, the regulator perceives it only as the transfer of benefits between upstream firm and downstream firm. Such a transfer is costly from the society point of view. In such cases of overinvestment, the regulator must be laxer in order to prevent unnecessary innovation. Indeed, clean technology becomes attractive when taxation is sufficiently high, which may lead the polluting company to innovate for wrong reasons. Although total industry profits may be lower than if no innovation occurred, the polluter's share of the profits increases when he innovates, motivating him to take suboptimal decisions from the welfare perspective. To counteract polluter's wasteful R&D expenses, the regulator must reduce taxes and render the clean technology less appealing.

The regulator's role as a technology-forcing authority is partially confirmed in regions of underinvestment. For relatively low levels of taxation, there is room for more stringent regulation that forces the polluter to innovate and adopt new technologies. Paradoxically, the regulator may oppose the research if it cannot lead to the welfare enhancing adoption. For high levels of taxation, the new technology will not be adopted. Hence in order to deter the wasteful innovation and spending, the regulator may have to lower taxes and accept the use of end-of-pipe solutions. It is important to note that all these results rely upon the creation of total profits from the integrated vertical structure.

The paper is organized as follows: Section 2 reviews existing literature, Section 3 sets up the model. Section 4 detail the production and bargaining stage respectively. Sections 5 and 6 addresses R&D incentives, while Sections 7 and 8 examine the regulator's response. Finally, Section 9 discusses financial aspects of such investments. At the end, conclusion provides a summary of results. All calculations are provided in the mathematical appendix. Since closed-form solutions for tax thresholds between different regions are too complex to derive, we use numerical simulations to illustrate key concepts.

<footnote n="2">² This is a standard assumption in bargaining models, see Muthoo (1999). One could consider only a fixed fee for the license, as it boils down to the same solution.</footnote>
## 2. Literature review

Early approaches to environmental innovation typically assumed that a polluter was also the innovator, and that a technological discovery would result either in a downward shift in the marginal abatement curve (Milliman and Prince, 1989; Montero, 2002a,b) or in a reduction of the rate of emissions per output, simultaneously increasing the marginal cost of production (Requate, 1998). The initial hypothesis of polluter-innovator was later replaced by models incorporating vertical market structures. Parry (1998) models the R&D sector as a competitive, free entry sector where the innovator obtain a patent and sells the discovery to polluting firms. Requate (2003) models the R&D sector as a monopolistic one, with a certain probability of discovery, while polluting firms exhibit heterogeneous abatement costs which are reduced to varying different degrees by innovation. Greaker and Rosendahl (2008) introduce imperfect upstream competition, where companies determine how much R&D to undertake. The competition between in-house technology and an outsourced one from independent supplier has been explored in Nimubona and Sinclair-Desgagné (2011). They show that the performance of eco-industry depends on the substitutability or complementarity of abatement technologies. However, the question of innovation in technologies is not explicitly modeled. Heyes and Kapur (2011) focus on the competition between vertical innovators, allowing both sectors to independently develop abatement technologies.

In our model, the negotiation between the two vertically related firms relies on the adoption of Nash bargaining solution through a two part tariff contract where the insider can improve his outside option through innovation. Yan et al. (2018) identifies that revenue share, fixed fee, investment levels, quantity discounts are typical contractual parameters for the two firms to decide on their relation. This particular point links us to the literature dealing with the extraction of a larger slice of a pie (i.e. bilateral joint profits). Different strategies to increase bargaining power in supply chains are common in several industries: creating buying alliances, vertical mergers, store brands, open access initiatives, spot market manipulations, and cooperatives (Carstensen, 2017). In food retailing sector, labels (Inderst and Mazzarotto, 2006) and supplier differentiation (Chambolle and Villas-Boas, 2015) are widely used for the same purposes. Some of these strategies result in welfare decreasing outcomes, allowing firms with bargaining power to get a larger slice of a smaller pie (Chambolle and Villas-Boas, 2015; Draganska et al., 2010). Bacchiega et al. (2013) show that downstream monopolists may enter into a costly contractual relationship with a low-quality supplier with the sole intention of improving its bargaining position relative to a high-quality supplier, without ever selling the good produced by that firm. Moreover, customer firms with strong bargaining power significantly influence supplier firms' financial policies, capital structure (Fabbri and Klapper, 2016), accounting policies (Hui et al., 2012), and innovation (Krolikowski and Yuan, 2017). However, the cited papers mostly concentrate on product competition, whereas our framework is about the (environmental) technology provision.

Innovation can be strategically employed by firms, and several studies explore innovation decisions in relation to competitors. Most of these studies focus on horizontal R&D, where firms conducting research compete in the same product market. In this horizontal R&D context, a firm's cost-reducing investment results from two effects: a cost minimizing effect and a strategic effect (Montero, 2002b). The strategic effect enables the innovator to steal market share from its rivals without affecting their cost structures. Raising rivals' costs are also a common explanation for innovation (Salop and Scheffman, 1983). Although vertical R&D has received less attention, Banerjee and Lin (2003) show that downstream firms have greater incentives to innovate when a price adjustment by the input supplier increases production costs for all rival firms. Additionally, Biglaiser and Horowitz (1994) find that the presence of standards may discourage innovation, as firms may prefer to adopt someone else's technology rather than innovate on their own.

Innovation in supply chain networks, particularly environmental innovation, has been the focus of recent empirical and management literature. Relying on external innovations may weaken the companies as it limits their own ability to explore new ideas (Kim et al., 2016). However, Pihlajamaa et al. (2017), Marchi and V (2012) argue that external innovation can substitute for internal R&D, provided that supplier management practices are well developed within chains. The spread of environmental innovation efforts within supply chains can originate from the bottom (Schiller, 2018; Dai et al., 2021; Isaksson et al., 2016) or from the top of the chain (Dong et al., 2023; Costantini et al., 2017). Collaboration between suppliers and clients offer multiple benefits: shorter time to market, improved product quality, reduced development costs, access to technologies, ideas about products, etc (Johnsen, 2009). Furthermore, the relationship between upstream firms' innovation and their carbon impact on clients has been established (Hege et al., 2023; Costantini et al., 2017). Yan et al. (2018) study how buying companies set contractual terms to incentivize suppliers to accept the contract in a joint new product development context. Environmental regulatory pressures faced by customer firm have been shown to increase green patent applications by suppliers (Lin et al., 2024), particularly when suppliers are financially strong, receive limited R&D government subsidies, or enjoy high ESG ratings. Additionally, Nanda and Dalla Fontana (2022) examine patent citations, revealing that fundamental science patents often emerge from collaborations between innovators and venture capitalists. Finally, Hege et al. (2023) show that process innovations created by suppliers do not bring about any significant emission reductions downstream, unlike product innovations. The impact depend on technology adopted, type of pollutant and the length of relation between companies (Hege et al., 2023; Costantini et al., 2017; Isaksson et al., 2016). Schiller (2018) show that the spread of environmental policies within supply chains is stronger when customers hold greater bargaining power.

Sinclair-Desgagné (2008) were the first to consider environmental regulation in vertical chains. They show that combining an emission tax to a subsidy to polluters cannot achieve the first-best outcome, while the opposite holds if the subsidy is granted instead to eco-industry. David and Sinclair-Desgagné (2010) point out that, when abatement is provided by an oligopolistic eco-industry with free-entry, the optimal emission tax may exceed, fall short or match the Pigouvian rate, depending on its effect on total abatement supply relative to entry in the eco-industry. However, innovation is absent in their framework. Biglaiser and Horowitz (1994) find that technology adoption standards are part of the optimal regulation, but stricter adoption standards reduce incentives
for research. Greaker and Rosendahl (2008) focus on the impact of policy on upstream firms, showing that regulator may strategically influence their behavior, thereby lowering abatement costs. Our model fills in the existing gap by considering a framework with competing abatement technologies, where innovation is driven by value partitioning motivations.

While numerous studies have explored the impact of environmental regulations on innovation, few papers have addressed the issue of investment in differentiated technologies and the choices surrounding their adoption. The importance of the abatement technology choice and its impact on profits has been studied in Meunier and Nicolaï (2012), who show that, the impact of environmental regulation on firms' profits can be either positive or negative, depending on the type of technology used. Similarly, Christin et al. (2013) analyze the effect of a cap-and-trade system on industry profits under imperfect competition and highlight that the abatement technology type is fundamental to answer this question. They show that industries utilizing process-integrated technologies are more affected than those relying on end-of-pipe technologies. The sources of different technologies however, are not the interest of these papers.

Several papers study strategic innovations in order to influence regulatory policy (see: Puller (2006), Requate (2005)). This strand of literature relates to the timing of a game and commitment issue. Requate (2003) shows, that when the regulator commits to regulation *ex ante* innovation, the optimal policy response to address the overpricing problem by an R&D firm is to adopt taxes rather than permits. Moreover, the most effective approach for regulators is to design a menu of policy instruments that are conditional on innovation. The earlier the regulator intervenes, the greater the welfare benefits, given some flexibility over instrument setting.

When regulation is established *ex post* innovation, two countervailing incentives drive firms' innovation decisions. First, when regulator cannot commit to a policy, firms have lower incentives to innovate, as they anticipate the regulator to ratchet up the policy once the innovation developed, effectively expropriating the gains from innovation (Puller, 2006). This discourages innovation. On the other hand, firms may also choose to increase their R&D efforts to strategically influence the policy and raise rivals' costs, thereby penalizing competitors (Puller, 2006).

In presence of rent seeking behavior, an unbiased regulator may not be desirable. Heyes and Kapur (2011) show that social planner should delegate regulation to an impartial authority to mitigate regulatory capture and the resulting underinvestment. Wang and Lin (2022) demonstrate that the impact of regulation on firms is moderated by their bargaining power, defined as the ratio of a firm's employees to the total number of employees in the province. Firms with greater relative power in terms of employment, ownership, and financial position can leverage political connections to influence local governments and secure more favorable tax reductions (Wang et al., 2003).

### 3. The model

A firm with a monopoly power faces a linear demand function $Q = A - p$ where $p$ is the price on the final market and $A > 0$. Production costs are linear and equal to $cq$, $c > 0$. While producing, the firm generates pollution $e$ as a by product of its business activity. A pollutant $e$ is proportional to output $q$ and given by $e = \theta q$. For simplicity, we assume that $\theta = 1$.

An environmental tax $t$ is imposed by a regulator on the polluting monopoly in order to motivate him to undertake costly abatement. The polluting company may either continue polluting and pay the tax on total emissions or to use a technology to abate some emissions. In case the decision to abate is taken, the polluter must decide on the type of technology he will use. The abatement technology stems from two different sources: internal research done by the polluter that modifies his production process (and therefore his production costs) or external licensing of an end-of-pipe equipment from an upstream supplier. Note that the alternative pattern of technology provision does not change qualitatively the results. Contracting with the external upstream technology provider happens through bargaining process over a two part tariff where two parties maximize their common profits and decide on sharing. The partition of profits depends on outside opportunities of both players and their respective bargaining powers.

In our model, three elements impact the polluter's decision to innovate internally. First, due to innovation, production costs change, i.e. they become $(c + \lambda)q$. If costs decrease ($\lambda < 0$), this motivates the polluter, other things equal, to do research as products become cheaper to produce. Examples of such innovations can be found in a paper and pulp industry (bleaching technology — see Bergquist and Söderholm (2015)). The same applies to solar electricity production. In case of the increase of production cost ($\lambda > 0$), this hampers the downstream firm's innovation incentives. This clearly applies to organic products where production becomes more expensive. In metal parts cleaning, operating costs for aqueous cleaning systems are higher compared to solvent cleaning systems due to higher energy demand for an additional drying step in aqueous cleaning. Higher operating costs can also come from the cost of chemical additives, wastewater treatment, and downtime (Slunge et al., 2022).

Second, we assume that the internal technology, which is a process-integrated one, results in an emission reduction that depends on abatement efficiency parameter $\beta$ and production level, i.e. $e^{clean} = (1 - \beta)q$ while the external end-of-pipe technology has a marginal efficiency of emission reduction of 1, i.e. $e^{eop} = q - a$ and imposes an additional cost of adoption $\gamma a^2/2$. In other words, the abatement technology efficiencies are different for the downstream's and the upstream's technology.

Third, the polluter is also motivated by the possibility to obtain a larger share of a pie in bargaining due to a higher outside option created by the new investment (see also Heyes and Kapur (2011)). However, the increase in bargaining position of the polluter is done at a cost of technology development $r$. The downstream firm must incur this cost whether he strikes a deal with the upstream firm or not.

To sum up, in case of end-of-pipe technology adoption, total costs borne by the polluter are of four different types: production costs $cq$ that remain unchanged with respect to no technology case, a two-part tariff license fee, $(va - f)$, whose value changes with the bargaining position, the adoption costs $\gamma a^2/2$ for the technology and the tax he owes to the regulator $t(q - a)$ where $a$ represents
the level of abatement. The clean technology generates three types of two costs: initial and additional production cost ($c + \lambda q$), tax due $t(1 - \beta)q$ and the fixed R&D cost $r$. As production costs differ depending on the technology choice, this also modifies the output level and consequently the surplus of consumers. The consequences of industrial choices thus differ from the welfare point of view.

As mentioned before, in our paper the regulation is of an innovation-incentivizing type. The timing of the game is as follows:

Stage (1) (Regulation) The regulator sets a pollution tax $t$ for each unit of pollutant emitted $e$.

Stage (2) (R&D stage) The polluting firm decides whether or not to invest in R&D to develop a clean technology at a cost $r$. Once developed, the value of gains from the technology become common knowledge.

Stage (3) (Bargaining) The polluter decides which option to choose: paying the tax without any abatement, using a process-integrated technology if such technology has been invented in stage 2, or bargaining with external upstream supplier to use the end-of-pipe technology.

Stage (4) (Production) The polluting monopoly decides on the price on the final market and the abatement level if any.

As usual, we solve the model backwards.

Let $p_{\theta}^*, p_c^*, p_{eop}^*$ denote the equilibrium prices absent abatement technology, with clean technology and with end-of-pipe equipment respectively. $a_{eop}^*$ on the other hand, represents the abatement from the end-of-pipe technology. These strategic variables result from the following maximization programmes:

$$p_{\theta}^* = \arg\max_{p} \pi_{\theta}(p) = pq(p) - cq(p) - tq(p), \quad (1)$$

$$p_c^* = \arg\max_{p} \pi_c(p) = pq(p) - (c + \lambda)q(p) - t(1 - \beta)q(p) - r, \quad (2)$$

$$p_{eop}^*, a_{eop}^* = \arg\max_{p,a} \pi_{eop}^{down}(p, a) = pq(p) - cq(p) - va - f - \gamma a^2/2 - t(q(p) - a), \quad (3)$$

where $r$ is a fixed R&D cost of clean technology, $\gamma a^2/2$ adoption costs of end-of-pipe technology, $(v, f)$ represent the two-part tariff for end-of-pipe equipment and $\lambda$ represent variable production costs. As mentioned above the value of $\lambda$ is industry specific.

As expected, in the benchmark case with no abatement technology environmental tax increases the price of the monopoly $p_{\theta}^*$, decreasing the total demand $q(p_{\theta}^*)$ and the polluter's profit $\pi_{\theta}(p_{\theta}^*)$. Taxation influences the abatement decisions under the end-of-pipe technology. Note that production decisions are unaltered by the use of the end-of-pipe technology and are equal to the case where abatement technology is absent.

Monopoly decisions about the development of clean technology is driven by the taxation. Indeed, when the clean technology increases variable cost of production ($\lambda > 0$), the polluter never adopts this technology without environmental regulation. The more efficient the technology in terms of emission ($\beta$), the lower the impact of taxation on production. In addition, the higher R&D cost gets, the less incentivizing the technology development is.

All calculations below are based on the following assumptions:

**Assumption 1.** $c + \lambda > 0$: production costs are positive

**Assumption 2.** $\text{Min}[(A - c - \lambda)/(1 - \beta), A - c, (A - c)\gamma/(2 + \gamma)] \ge t \ge (-\lambda - c - A)/(1 - \beta)$: for quantities, prices and emissions to be positive

**Assumption 3.** $(-A + c + (1 - \beta)t + \lambda)^2 \ge 4r$ and $1/4\lambda(\lambda - 2A - 2c) < r$: monopoly's profit is positive when using clean technology, but the use of this technology is never profitable before introduction of a tax, i.e. profit with no technology is higher than with clean technology.

## 4. Bargaining

To acquire the end-of-pipe technology, the polluting monopoly bargains with an external upstream company over a two-part tariff contract $(v, f)$, where $v$ is a per-unit charge and $f$ is a lump-sum fee.<fnref n="3" />

We assume that the monopolist's bargaining power in negotiations is $\alpha \in [0, 1]$ and $(1 - \alpha)$ is the bargaining power of the external supplier (all exogenously given). The Nash product of bargaining is given by:

$$B(v, f) = (\pi_{eop}^{down} - \pi^{down*})^{\alpha}(\pi_{eop}^{up} - \pi^{up*})^{(1-\alpha)} \quad (4)$$

where $\pi_{eop}^{down}$ as defined in (3) and $\pi_{eop}^{up} = v * \omega + f$ are the profits of the downstream polluter and upstream supplier respectively. We use the superscripts for the company (down for downstream, up for upstream and Ind for industry) and subscripts for the technology used (eop for end of pipe, c for clean), star stands for equilibrium values. The outside options for these companies, i.e. the alternative source of profits if negotiations fail, are given by $\pi_{eop}^{down*}$ and $\pi_{eop}^{up*}$. For simplicity, we assume that the outside option of the supplier

<footnote n="3">³ This is a standard assumption in bargaining models, see Muthoo (1999). One could consider bargaining over a fixed fee for the license, however it would not change the solution. It is well known that the optimal level of variable fee in vertical relation is equal to marginal cost of the technology (in our case equal to 0) in order to maximize the industry profits. The bargaining consists then on sharing the gains through the fixed fee.</footnote>
is zero.<fnref n="4" /> However, $\pi^{down*}$, the outside option of the polluting monopoly is positive. It is the profit from the clean technology if he invests or the profit without any technology if he chooses not to invest in R&D. The results of the bargaining stage depend on which outside option prevails. Below, we solve the negotiation stage for the two cases.

## 4.1. No technology as the monopoly's outside option

When the polluter decides to not develop the clean technology, the Nash product of bargaining is given by

$$B_{\emptyset}(v, f) = (\pi_{eop}^{down} - \pi_{\emptyset}^{*})^{\alpha}(\pi_{eop}^{up})^{(1-\alpha)} \quad (5)$$

where $\pi_{\emptyset}^{*}$ is the equilibrium profit determined in (1). Maximizing $B_{\emptyset}(v, f)$ with respect to $v$ and $f$ gives $v^{*} = 0$<fnref n="5" /> and $f^{*} = (1 - \alpha)(\Pi_{eop}^{Ind*} - \pi_{\emptyset}^{*})$ where $\Pi_{eop}^{Ind*}$ is the equilibrium profit generated by the industry using the end-of-pipe technology. The industry profit is defined as follows:

$$\Pi_{eop}^{Ind} = \max_{p,a} pq(p) - cq - \gamma a^2/2 - t(q(p) - a). \quad (6)$$

The total size of the cake, $\Pi_{eop}^{Ind}$, increases as the end-of-pipe technology is introduced. The polluting company no longer pays the environmental tax as a part of its emissions are abated. The cost of adoption being lower than tax savings, this profits the industry. Remark that the double marginalization problem is absent in our framework. The upstream company is licensing the technology at a zero marginal cost and extracting a part of the total gains in the form of a lump sum payment. The polluter's profit in this case is

$$\pi_{eop/\emptyset}^{down*} = \pi_{\emptyset}^{*} + \alpha(\Pi_{eop}^{Ind*} - \pi_{\emptyset}^{*}) \quad (7)$$

and reflects the well known result of the bargaining game: the need to compensate the parties for their outside options and the sharing rule for the remaining surplus (see: Muthoo (1999)). Again the subscripts reflect the technology pattern ($eop/\emptyset$ stands for end of pipe with no technology as outside option, $eop/c$ for end of pipe with clean technology as outside option). As the polluting monopoly has a positive outside option, this is the minimum amount it must receive from negotiations, the rest of the cake being shared with the upstream firm according to bargaining powers.

The situation is slightly more complicated when the clean technology becomes an outside option.

## 4.2. Clean technology as the monopoly's outside option

In this subsection we consider that the polluting monopoly uses the equilibrium profit with clean technology $\pi_{c}^{*}$ defined in (2) as an outside option. When the polluter decides to develop the clean technology, the Nash product of bargaining is given by:

$$B_c(v, f) = (\pi_{eop}^{down} - \pi_c^*)^\alpha (\pi_{eop}^{up})^{(1-\alpha)}. \quad (8)$$

Solving the maximization stage of $B_c(v, f)$ with respect to $v$ and $f$ yields $v^{*} = 0$ and

$$\pi_{eop/c}^{up*} = f^* = (1 - \alpha)[(\Pi_{eop}^{Ind*} - r) - \pi_c^*] \quad (9)$$

for the upstream firm and

$$\pi_{eop/c}^{down*} = \pi_c^* + \alpha[(\Pi_{eop}^{Ind*} - r) - \pi_c^*] \quad (10)$$

for the downstream firm. Whenever $(\Pi_{eop}^{Ind} - r)$ is higher (lower) than the outside option $\pi_{c}^{*}$ of the polluter, the polluting firm adopts the end-of-pipe (clean) technology.

One point deserves more attention. The results of bargaining as shown above say that because the innovation is done whether the technology will be used or not, a part of the integrated industry profit, that represents a cake to share, is lost due to unnecessary innovation, $(\Pi_{eop}^{Ind} - r)$. The outside option of the downstream company also incorporates the innovation costs, i.e. it consists of the profit from clean technology net the investment costs. We can re-express the downstream's and upstream firm's payoff in the following way: $\pi_{eop/c}^{down*} = \pi_c^* + \alpha(\Pi_{eop}^{Ind*} - \pi_c^*) - \alpha r$ and $\pi_{eop/c}^{up*} = (1 - \alpha)(\Pi_{eop}^{Ind*} - \pi_c^*) - (1 - \alpha)r$. It suggests that the innovator does not cover all its investment costs. A part of these costs are passed on the external technology provider. In other words, the investment in new technology represents a loss for the integrated industry and therefore decreases the total size of industry profits available to both firms in bargaining process. However, the loss is shared by both downstream and upstream firm according to their bargaining powers as shown by the third element of the profit $\pi_{eop/c}^{down*}$. Interestingly, the result is also equivalent to a bargaining situation based on operating short-term profits (marked by ST superscript), i.e.

$$\pi_{eop/c}^{down*} = \pi_c^{ST} + \alpha(\Pi_{eop}^{Ind*} - \pi_c^{ST}) - r \quad (11)$$

$$\pi_{eop/c}^{up*} = (1 - \alpha)(\Pi_{eop}^{Ind*} - \pi_c^{ST}),$$

<footnote n="4">⁴ An alternative assumption is discussed in the discussion about private incentives for investment and its adoption part of the paper.</footnote>

<footnote n="5">⁵ The variable part of the tariff $v^*$ is set so as to maximize the joint profits of the supply chain.</footnote>
where $\pi_c^{ST} = p_c^* q_c^*(p_c^*) - (c + \lambda)q_c^*(p_c^*) - t(1 - \beta)q_c^*(p_c^*) = \pi_c^* + r$. Here when considering only operational costs, one can see that the total innovation costs are borne by the downstream firm. Those two expressions will be useful further on when discussing the R&D stage.

Secondly, notice that environmental taxation influences both the integrated industry profits and outside option. Consequently, the polluter's and upstream firm's payoffs depend on taxation through its impact on integrated industry profit. To sum up, the integrated industry profit, downstream and upstream firms' payoffs, and hence the incentives for bargain, change with taxation.

**Proposition 1.** When the downstream firm uses no technology as an outside option, the profits of downstream firm, the upstream technology provider are given by:

$$ \pi_{eop/\theta}^{\text{down*}} = \pi_{\theta}^{*} + \alpha(\Pi_{eop}^{\text{ind*}} - \pi_{\theta}^{*}); \pi_{eop/\theta}^{\text{up*}} = (1 - \alpha)(\Pi_{eop}^{\text{ind*}} - \pi_{\theta}^{*}) \quad (12) $$

When the downstream firm uses clean technology as an outside option, the profits of downstream firm, the upstream technology provider are given by:

$$ \pi_{eop/c}^{\text{down*}} = \pi_c^* + \alpha(\Pi_{eop}^{\text{ind*}} - \pi_c^*); \pi_{eop/c}^{\text{up*}} = (1 - \alpha)(\Pi_{eop}^{\text{ind*}} - \pi_c^*) \quad (13) $$

where the industry total profits are equal to:

$$ \Pi_{eop}^{\text{ind*}} = p_{eop}^{*}q(p_{eop}^{*}) - c q_{eop}^{*}(p_{eop}^{*}) - \gamma a_{eop}^{*2}/2 - t(q_{eop}^{*}(p_{eop}^{*}) - a_{eop}^{*}) \quad (14) $$

with $p_{eop}^*$ and $a_{eop}^*$ given by Eqs. (3) and outside option by Eqs. (3) and (1).

## 5. R&D stage

We turn now to R&D choices of the polluter. As long as the industry profit generated through bargaining, $\Pi_{eop}^{\text{Ind*}}$ is above the profit with no abatement technology, $\pi_{\theta}(p_{\theta}^*)$, the cooperation with technology supplier will take place. In other words, the industry profit must at least generate the outside option of the downstream. This is always the case when the environmental taxation is imposed.

When later engaged in the bargaining process, the polluting company's motivation to undertake research arises for two reasons.

First, the clean technology may be interesting in itself and the firm decides to innovate and to adopt it. This happens when $\pi_c^* > \max\{(\pi_c^{ST} - (1 - \alpha)(\Pi_{eop}^{\text{Ind*}} - \pi_c^{ST}) - r); (\pi_{\theta}^* - (1 - \alpha)(\Pi_{eop}^{\text{Ind*}} - \pi_{\theta}^*))\}$. It means that the profit with integrated technology is higher than the profit with end-of-pipe technology whatever the outside option.

Second, he may innovate purely for bargaining considerations: this increases his negotiating position and hence the clean technology is not adopted once negotiations are concluded. It happens when two conditions are verified: the end-of-pipe technology is preferred to the clean one, $\pi_c^{\text{down*}} > \pi_c^*$ and the clean technology is preferred as the outside option when bargaining, $\pi_{eop/c}^{\text{down*}} > \pi_{eop/\theta}^{\text{down*}}$. They are equivalent to $0 < \alpha(\Pi_{eop}^{\text{Ind*}} - r - \pi_c^*)$ and $r < (1 - \alpha)(\pi_c^{ST} - \pi_{\theta})$. Recall from (10) that the former simply says that size of industry profit net investment costs must be higher than the outside option to generate additional gains from bargaining as opposed to adopting the clean technology. After compensating for outside option, there must be some gains left for sharing in vertical relation- a part $\alpha$ can be captured by the polluter.

The latter condition indicates the trade-off the innovator faces; by innovating he will increase the profit that he will be able to secure, i.e. move from $\pi_{\theta}$ to $\pi_c^{ST}$. By shifting to a higher outside option, he benefits only form a part of this increase, i.e. he can save on the share that would otherwise be paid to the supplier, $(1 - \alpha)(\pi_c^{ST} - \pi_{\theta})$. The other part would be received by the polluter anyway through cake partitioning. However, he needs to pay himself the innovation cost as can be seen in expressions (11) and (10). Whenever the innovation is cheaper than the profits he can capture, innovation takes place.

To sum up, the above conditions are equivalent to saying that as long as the clean profit $\pi_c^*$ lies within the $[\pi_{\theta}^* + \alpha/(1 - \alpha)r, \Pi_{eop}^{\text{Ind*}} - r]$ range, the company undertakes research in order to boost its bargaining position only. Once the profit obtained through the clean technology increases further, the polluting firm uses this technology and hence eliminates the upstream firm from the market.

**Proposition 2.** The downstream firm innovates only to increase its bargaining position when:

$$ \pi_c^* \in [\pi_{\theta}^* + \alpha/(1 - \alpha)r, \Pi_{eop}^{\text{Ind*}} - r] \quad (15) $$

and adopts the new technology when:

$$ \pi_c^* > \Pi_{eop}^{\text{Ind*}} - r. \quad (16) $$

## 6. Discussion about private incentives for investment and its adoption

Private investors' decisions discussed above depend heavily on the tax level chosen by the government. Despite the validity of Pigouvian tradition, the policy makers have not implemented an optimal tax proposal; even the economists themselves do not recommend a single policy. Indeed, Pindyck (2019) showed that among economist, the social costs estimations spread from 0 to 500 $. Environmental damages and social costs are difficult to calculate, and data needed to implement the optimal tax approach is often unavailable (Baumol, 1972). Moreover, dispersed information and uncertainties make it extremely difficult to centralize
information and correctly recommend the policy. Consequently, private objectives for innovation and adoption should be compared for a large range of values of tax available—the strategy we will follow below.

Let us recall the situation. The size of the cake that will be available for partitioning in vertical relationship represents the industry profit, $\Pi_{eop}^{Ind}(p, q, a; c, t, \gamma, A)$ defined in (6). In negotiations, the downstream polluter secures at least his outside option. The rest is shared in relation $\alpha : (1 - \alpha)$. Industry profit decreases with stronger taxation and therefore, everything else equal, may decrease the incentive to bargain with upstream technology producer. However, taxation influences as well the size of the outside option (in our case the clean technology). Whether the decrease of industry profit is stronger that decrease in clean profit is not obvious and the prevailing solution depends on some parameters.

Let us see in detail how environmental regulation changes the conditions for the case where the technology is developed to boost the bargaining power only, i.e. when innovation is used for negotiations $\pi_{eop/c}^{downs*} - \pi_{eop/\emptyset}^{downs*} = (1 - \alpha)(\pi_c^* - \pi_\emptyset^*) - \alpha r > 0$ and when innovation is not adopted $\pi_{eop/c}^{downs*} - \pi_c^* > 0$.

First of all, the regulation changes the willingness to adopt the clean technology as an outside option assuming that the vertical relation prevails, $\frac{\partial(\pi_{eop/c}^{downs*} - \pi_{eop/\emptyset}^{downs*})}{\partial t}$. Environmental tax influences this decision only through its impact on the outside option. Note that in this case, whatever the outside option chosen, the contract is signed with upstream supplier. The size of the cake will be changed with taxation in exactly the same amount whatever the outside option, so this impact cancels out. A quick look at the derivative of the above condition with respect to environmental tax yields $(1 - \alpha)(q^* - (1 - \beta)q_c^*) = (1 - \alpha)(e_\emptyset^* - e_c^*)$. Lower emissions from innovation with respect to emissions without it, $(e_c^* - e_\emptyset^*)$ makes the above derivative positive. It means that stronger taxation makes clean option more and more interesting for the firm point of view. By switching to clean outside option rather than making no investments, the polluter may capture $(1 - \alpha)$ of tax savings that otherwise (i.e. with zero outside option) would be a part of general pie and would be shared with the supplier through cake partition. Emission reduction intensity parameter, $\beta$, plays an important part in the innovation-forcing role of regulation. Higher emission reductions due to innovation result in higher cost savings when regulation becomes stricter, pushing for innovation. On the contrary, when emissions under clean technology are higher, stronger taxation will discourage company from undertaking the innovation activity.

The second condition $(\pi_{eop/c}^{downs*} - \pi_c^* > 0)$ states that regulation impacts additional gains of downstream firms obtained through the negotiations. Mathematical manipulation shows that the last equation is equivalent to $\alpha((1 - \beta)q_c^* - (q^* - a^*)) = \alpha(e_c^* - e_\emptyset^* + a^*)$, a relative efficiency of both abatement technologies in terms of emissions. The size of the cake left for sharing is composed of industry profit minus the clean profit (net innovation cost). Stronger environmental taxation reduces the industry profit by $(e_\emptyset^* - a^*)$ while decreasing the clean profit by $e_c^*$ at the same time. Therefore, if the clean technology results in higher emissions than end-of-pipe, then the size of the cake to split increases as well. Since the polluter captures an $\alpha$ part of cake, he will stick to upstream supplier. If, however, the emissions under clean technology are lower than end-of-pipe, the taxation will push the company to adopt the innovation.

The figure below shows different regions of innovation as a function of parameters $\lambda$ and $\beta$ on one hand and as a function of parameters $\lambda$ and $t$ on the other hand:

For a given emission efficiency parameter $\beta$, the higher production cost under clean technology everything else equal, the lower the output level and lower profits from clean technology. Consequently, the firm moves from adoption of clean innovation, through innovation for bargaining reasons to no innovation solution. The shift between states is driven here by market conditions and cost considerations. In the same way, as we fix $\lambda$ and increase the emission efficiency parameter $\beta$, the firm moves from vertical relation with no innovation towards innovation and adoption. Here the shift is driven by environmental considerations. With better technology, the firm gains on the tax that is due to the regulator, and therefore his outside option and profits from clean technology increase.

What is interesting, is that even with strong taxation the government will never be able to create enough incitation for innovation to be adopted if the cost parameter $\lambda$ is of high value. Recall the clean technology decreases the marginal cost of production by $(t\beta - \lambda)$. In similar spirit, as $\beta$ gets higher, the region of “innovation and adoption” in Fig. 1(b) gets smaller and moves downwards. In other words, if emission efficiency of clean technology goes down, the vertical relation solution prevails. This happens because both emission efficiency and cost parameter impact marginal costs of polluter. Their impact is therefore similar. However, further simulations show that as bargaining force of the polluter $\alpha$ increases, the area of “end-of-pipe and no innovation” increases to the detriment of the end-of-pipe technology with innovation as outside option. This is intuitive given the discussion above: the higher $\alpha$, the lower the part of the cake that the polluter can get from improving his outside option. As the bargaining power goes up, the smaller a part of the industry profit the company can capture for himself after changing outside option.

**Proposition 3.** *When environmental tax deviates from Pigouvian tradition, stronger taxation need not lead to adoption of innovation. When the clean technology penalizes sufficiently the polluter in terms of marginal cost of production, even if it decreases substantially emissions, a stringent regulation may have no impact on innovation or, on the contrary, may motivate the polluter to innovate but only for bargaining reasons. New technology will never be adopted leading to a pure loss from the welfare point of view. The crucial elements for this result lie in relative emission efficiency of technologies.*

In our model, the upstream firm faces a disadvantage due to the lack of an outside option. If multiple downstream firms source their technology from this same supplier, the upstream firm gains some positive outside option. This positive option must be subtracted from industry's total profit at the onset of negotiations. In other words, for the bargaining to succeed, the size of the cake available for distribution must remain sufficiently high after deducting the supplier's outside option. This positive outside option for the supplier would potentially influence innovation decision of a polluting monopoly, assuming all other factors remain
<figure><img src="image_4.png" /><figcaption>Fig. 1. (a) and (b): Different regions of investment and adoption depending on parameters $\lambda, t$ and $\beta$, assuming the following values of other parameters: $\gamma = 1$, $\alpha = 0.3$, $\Lambda = 2$, $c = 0.8$, $r = 0.007$, $\beta = 0.8$ (for the graph b) on the right) and $t = 0.29$ (for the graph a) on the left). Region “eop and no innovation” means that the company is engaged in vertical relationship with the supplier and decides not to innovate, so that his outside option is just the profit with no technology. Region “innovation and no adoption” means that the company uses the end-of-pipe technology from the upstream supplier and innovates to increase his outside option. However, the innovation is not used. The last region “innovation adopted” indicates the parameters that lead to innovation that will be adopted at the end by the innovator, so no contractual relation takes place with upstream supplier.</figcaption></figure>

constant. Specifically, one prerequisite for innovation is that the profit remaining after accounting for outside options must be large enough to cover investment costs. Therefore, the supplier's outside option could significantly affect the likelihood of an innovation strategy emerging. If downstream firms operate in distinct industries, this supplier outside option would be the only modification to our results. Additionally, given that the upstream technology serves as an end-of-pipe solution, downstream profits should remain unaffected if innovation is not deployed, even if some downstream firms operate within the same industry.

However, if the innovation is implemented, it will alter the position of the polluting monopoly in its final market. The conditions influencing the innovator's decision to adopt the technology would change accordingly. If the clean technology increases production costs and reduces output, the company could lose market share and see profits diminish, making it less inclined to deploy the technology, all else being equal. Conversely, if the innovation reduces marginal costs, the company could strengthen its market position and be more likely to adopt the technology.

An interesting extension to consider is a scenario in which the innovator decides to license its innovation to other companies (in the industry or outside). This approach could introduce competition for the supplier, thereby reducing the supplier's outside option. This, however, lies beyond the scope of the present paper.

## 7. Regulation

Last question concerns the optimal welfare. As we have already mentioned in the introduction, the level of environmental damage depends on technology choice in equilibrium. Let $W_c(t)$, $W_{eop/t}(t)$ denote welfare functions under clean and end-of-pipe technology with $i = \{c, \emptyset\}$ as outside option respectively. These functions are given by the following equations:

$$W_c(t) = \int_{0}^{q_c} (A-s)ds - (c+\lambda)q_c(t) - r - D((1-\beta)q_c(t)), \quad (17)$$

$$W_{eop/c}(t) = \int_{0}^{q_{eop}} (A-s)ds - cq_{eop}(t) - \frac{\gamma a(t)^2}{2} - D(q_{eop}(t) - a(t)) - r, \quad (18)$$

$$W_{eop/\emptyset}(t) = \int_{0}^{q_{eop}} (A-s)ds - cq_{eop}(t) - \frac{\gamma a(t)^2}{2} - D(q_{eop}(t) - a(t)). \quad (19)$$

where $D(e) = e^2/2$ is the damage function. From the welfare point of view, using clean technology in the bargaining process serves only to redistribute the industry profit in favor of the polluter. Consequently, the welfare decreases by the amount of the level of
R&D expenses r. Maximization of the welfare function $W_{eop/i}(t)$ under different outside options implies the maximization of the same welfare function.

Since taxation induces innovation and at some point assures its adoption, one needs to verify the private and public incentives for innovation. We check if interests of polluting companies and regulator are aligned. A situation where polluter innovates and does not adopt is not desirable from the regulator point of view as it decreases the welfare by the cost of innovation without inducing a creation of additional gains. Consequently throughout the rest of analysis, for welfare comparisons we will consider only the welfare function $W_{eop/\theta}(t)$ where profit with no technology is used as an outside option in negotiations.

## 8. Alignment of private and social objectives

Consider again the two welfare functions $W_{eop/i}(t)$, $i = \{c, \emptyset\}$ and $W_c(t)$. To get a better understanding of different components that stimulate social welfare under each technology choice, let us start with consumers' surplus. The surplus is the same under no technology regime and under bargaining solution whatever the outside option used (optimal taxes are the same for both options, see mathematical appendix for formulas). This is due to the fact that end-of-pipe technology has no impact on production decisions. However, the clean technology modifies the production costs, and therefore the impact on consumers is ambiguous. It depends on the change in marginal costs driven by clean technology, i.e. the sign of $(\beta t - \lambda)$.

Note that environmental tax plays an important role in determining the preferences concerning technology choice from the consumers' point of view. Whenever the clean technology decreases production costs $\lambda$, no matter what is the level of the tax (as long as it stays positive), the clean technology is always be preferred. When production costs increase with clean technology ($\lambda > 0$), as long as the taxation stays at moderate levels ($< \lambda/\beta$), the resulting consumers' surplus shifts the preferences towards the end-of-pipe type of equipment. Only very strong taxation encourages the clean technology from the consumers' point of view.

The impact of technology choice on profits was studied in details in production and bargaining sections. One issue merits some attention. Taxation has an important impact on the total industry profits. The gains in industry profits under the end-of-pipe equipment stem from the savings companies make in taxes less adoption costs, $(ta^* - \gamma a^{*2}/2)$. The higher the tax, the higher potential gain for the whole industry with respect to no technology. Moreover, the clean outside option negatively influences the industry profits. It results in a pure loss r.

Note that for some levels of production costs $\lambda$, the end-of-pipe solution leads to higher pollution (see mathematical appendix for formulas). This is so due to several reasons. Firstly, when clean technology leads to higher variable cost of production, the end-of-pipe technology will most probably prevail. The probability of clean technology imposing itself decreases with marginal production cost $\lambda$ (see Fig. 1). Secondly, as cost of R&D gets higher, clean technology looses its advantage and it gets more difficult to make the firm choose this technology on its own. Since the emissions are proportional to output, higher pollution, and therefore damages, may be compatible with higher profits. Notice that closed form solutions for tax/production costs thresholds are too difficult to obtain so we mainly reason based on numerical simulations.

Indeed, welfare with end-of-pipe technology can be higher or lower than the welfare with clean technology as shown below.

In cases where regulator prefers the end-of-pipe solution (graph 2b on the right), three scenarios may happen: firm may obtain the highest profit from the socially preferred technology. The private and social objectives are perfectly aligned and no investment takes place. The region of no investment in R&D in the second stage, $\max\{\pi_c^*(t), \pi_{eop/c}^*(t)\} < \pi_{eop/\theta}^*(t)$, poses no problem to the regulator. The best response of the regulation to keep the tax $t$.

Define $t_{eop}^{opt}$, $t_c^{opt}$ as taxes that under no constraints maximize welfare functions given in (19) and (17) respectively, i.e.:

$$t_{eop}^{opt} = \arg \max_{t} W_{eop/\theta}(t) \qquad (20)$$

$$t_{clean}^{opt} = \arg \max_{t} W_{c}(t) \qquad (21)$$

**Proposition 4.** In a case where the end-of-pipe regime dominates the clean regime in terms of welfare, $W_c(t_c^{opt}) < W_{eop/\theta}(t_{eop}^{opt})$, and interests of a polluter and a regulator are aligned $(\pi_{eop/\theta}^*(t_{eop}^{opt}) > \max\{\pi_c^*(t_{eop}^{opt}), \pi_{eop/c}^*(t_{eop}^{opt})\})$, the regulator should choose the optimal unconstrained tax $t_{eop}^{opt}$.

It may happen however that the private objective is in conflict with the social one: the firm may decide to innovate nevertheless and overinvest. It may then adopt the technology (region of R&D adoption) or develop it for negotiations only (no adoption). Faced with such a dilemma, the regulator may opt to keep the tax it fixed and undergo a welfare loss, or to change the tax level to discourage the company from innovation.

To illustrate the case look back Fig. 2(b). In the region of R&D adoption where $\max\{\pi_{eop/\theta}^*(t); \pi_{eop/c}^*(t)\} < \pi_c^*(t)$, the monopoly profit is higher with clean technology than with end-of-pipe. Confronted with this situation, the regulator can keep the tax unchanged and undergo a net welfare loss resulting in welfare $W_c^*(t)$, or modify its policy and set a tax $\hat{t}$ such that:

$$\pi_c^*(\hat{t}) < \max\{\pi_{eop/\theta}^*(\hat{t}), \pi_{eop/c}^*(\hat{t})\}. \qquad (22)$$

Depending on some parameters value, the company may switch directly to no innovation or innovate for bargaining reasons first before resigning totally from innovation. The choice of the regulator in the latter case (to decrease tax even lower) will depend on the trade-off between lower tax and cost of innovation.
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** (a) and (b): Different regions of investment depending on parameters $\lambda$ and $\tau$ assuming the following values of parameters: $\gamma = 1$, $\alpha = 0.35$, $A = 2$, $c = 0.8$, $r = 0.007$, $\beta = 0.95$ (values in brackets for the graph on the right). Graph on the left shows region where clean welfare dominates the end-of-pipe welfare, whereas on the graph on the right the end-of-pipe welfare dominates the clean welfare. When clean welfare dominates (graph 2a on the left), the private incentives may not be aligned resulting in underinvestment with no innovation (area on the left) or no adoption (area on the right). On the other hand, when end-of-pipe welfare dominates (graph 2b on the right), private incentives may result in overinvestment with adoption (area in the middle) or no adoption (area on the right).</figcaption></figure>

**Proposition 5.** In a case of over-investment, where the end-of-pipe regime dominates the clean regime in terms of welfare at its optimum, $W_c(t_c^{opt}) < W_{eop/\theta}(t_{eop}^{opt})$, and a polluter wants to adopt innovation ($\pi_c^*(t_{eop}^{opt}) > \max\{\pi_{eop/\theta}^*(t_{eop}^{opt}), \pi_{eop/c}^*(t_{eop}^{opt})\}$), the regulator may oppose such an effort and set environmental policy so as to discourage the firm from innovating. This is the best strategy when the welfare under a new, lower tax $\hat{t}$, is higher than welfare at initial situation. Unfortunately, even by decreasing the tax, the regulator might not always prevent the polluting firm from useless innovation if $\pi_{eop/\theta}^*(\hat{t}) < \pi_{eop/c}^*(\hat{t})$.

As shown above, when the lower tax $\hat{t}$ makes the firm pass first through the stage of overinvestment and no adoption to no investment region, a lower tax does not totally eliminate the incentives for R&D. When the new tax $\hat{t}$ makes the polluting industry overinvest in R&D just to boost its bargaining power, this results in a decrease in total welfare. It forces the regulator to either support the consequences of the firm's choice, or to further change the level of taxation ($\hat{t}$) to eliminate all innovation efforts. The regulator may further decrease the tax by maximizing the welfare $\hat{t}$: $\arg\max_{\hat{t}} W_{eop/\theta}(\hat{t})$ s.t. $\pi_{eop/\theta}^*(\hat{t}) > \max\{\pi_c^*(\hat{t}), \pi_{eop/c}^*(\hat{t})\}$ or to support the welfare loss from R&D expenditure $\tau$, while keeping the tax at the level of $\hat{t}$. The logic the regulator follows is the same as in the proposition below.

In the third, region where investment is undertaken to *boost bargaining power*, i.e. where $\max\{\pi_{eop/\theta}^*(t); \pi_c^*(t)\} < \pi_{eop/c}^*(t)$, the society incurs the investment cost decreasing the welfare. Look back Fig. 2(b). Indeed, the polluting monopoly invests in R&D in order not to use the clean technology in the production process, but only to enhance its outside option when bargaining with the end-of-pipe technology supplier. From this point of view, there is an overinvestment in R&D which lowers the total welfare. Facing this situation, the regulator must adjust its policy. The regulator may sustain the level of taxation and undergo a loss equal to R&D cost ($W_{eop}^*(t) - r$) or to set the tax $\underline{t} < t^*$ such that $\pi_{eop/\theta}(\underline{t}) \ge \max(\pi_{eop/c}(\underline{t}), \pi_c(t))$. The regulator prevents thus the monopoly from R&D investment. In this case, the regulator certainly avoids the deadweight loss $r$ but, on the other side it loses on environmental quality (as tax gets lower and so does abatement). The resulting welfare is equal to $W_{eop/\theta}(\underline{t})$.

Following this logic, the optimal range of taxation can be proposed.

**Proposition 6.** In a case of over-investment, where the end-of-pipe regime dominates the clean regime in terms of welfare at optimum, $W_c(t_c^{opt}) < W_{eop/\theta}(t_{eop}^{opt})$, and a polluter wants to innovate just to leverage the bargaining power ($\pi_{eop/c}^*(t_{eop}^{opt}) > \max\{\pi_{eop/\theta}^*(t_{eop}^{opt}), \pi_c(t_{eop}^{opt})\}$), the welfare goes down. This forces the regulator to either support the loss of useless innovation, or to change the level of taxation to discourage the firm from innovating. Unusually, the option to develop a clean technology may make the regulator laxer when it comes to taxation.

If, on the contrary, for a given tax $\tau$ the regulator prefers the clean technology a region of underinvestment arises, where a firm decides to use end-of-pipe technology. Two possibilities may happen. Interests of regulator and private firm may be well aligned, resulting in the proposition below.
**Proposition 7.** In a case where the clean regime dominates the end-of-pipe regime in terms of welfare, $W_c(t_{clean}^{opt}) > W_{eop/\emptyset}(t_{eop}^{opt})$, and interests of a polluter and a regulator are aligned ($\pi_c^*(t_{clean}^{opt}) > \max\{\pi_{eop/c}((t_{clean}^{opt})^*), \pi_{eop/\emptyset}^*((t_{clean}^{opt})^*)\}$), the optimal tax maximizes the welfare.

If the interests are not aligned, a region of forced investment in stage 2 appear, where the monopoly profit with clean technology is lower than the one with end-of-pipe technology, ($\pi_c^*(t_{clean}^{opt}) \le \min\{\pi_{eop/c}^*(t_{clean}^{opt})^*, \pi_{eop/\emptyset}^*(t_{clean}^{opt})^*\}$). The underinvestment may stem either from no innovation or from no adoption.

In a case of no innovation, the regulator must increase the tax and force the innovation. As can be seen on Fig. 2(a) this can sometimes lead to consequent innovation and adoption. However, in some cases, a stringer regulation may not lead to innovation, or even in extreme cases lead the polluter to innovate but not to adopt. It may be in the interest of regulator instead to keep the tax on lower level and accept the lower welfare as well. This leads us to the following proposition for the optimal tax.

**Proposition 8.** In a case where the end-of-pipe regime is dominated by the clean regime in terms of welfare ($W_c(t_{clean}^{opt}) > W_{eop/\emptyset}(t_{eop}^{opt})$), but the polluter does not want to innovate at all or to adopt innovation, the regulator may encourage the firm to innovate and adopt, i.e. choose a tax such that $\pi_c^*(t) > \max\{\pi_{eop/c}((t)), \pi_{eop/\emptyset}^*((t))\}$.

If on the other hand the underinvestment stems from lack of adoption only with useless R&D spending, for already strong regulation, lesser levels of tax may be called upon and end-of-pipe solution may be advocated.

To sum up, the regulator compares each time the welfare functions at given tax and chooses if tax changes are worthwhile or the lower welfare should be tolerated. Some parameters are crucial in decision process as market size, emission efficiency of technologies and bargaining powers of parties.

## 9. Financial aspects of investment

The financial position of an innovating company plays a central role in shaping its innovation activities. Research and development (R&D) decisions are influenced by corporate financial factors such as the availability of internal funds and levels of corporate debt. Profitability and liquidity, in particular, are two key determinants of R&D intensity. Financial constraints may nevertheless hamper the investment strategies to upgrade the position in negotiation process. Different policies and actions help to overcome these constraints.

Various mechanisms to scale up credit for environmental investments include subsidized and guaranteed loans for climate-related projects, direct investments via private equity, green infrastructure funds, and green bonds. Generally, large incumbent firms tend to focus on innovations that enhance existing products, while startups are more inclined towards radical product innovations (Oltra, 2008). For companies that cannot or prefer not to use internal resources, external financing is a plausible strategy for driving innovation within supply chains. Schiller (2018) demonstrates that within supply chains, customer firms are, on average, ten times larger in terms of book value of assets and five times larger in terms of market capitalization compared to the average supplier, positioning them as strong candidates for driving innovation. Innovation is typically financed through debt or equity (Kerr and Nanda, 2015). Bank financing is more suitable for large, mature firms, where investments are less risky due to the presence of operational cash flows and fixed assets, such as patents, which can serve as collateral for debt financing (Mann, 2018). Firms with significant patent activity also tend to secure cheaper bank loans (Kerr and Nanda, 2015).

Leveraging external knowledge is another way to reducing the costs associated with the innovation process (Pihlajamaa et al., 2017). External collaboration activities can serve as substitutes for internal R&D efforts. Marchi and V (2012) empirically demonstrates that cooperation with external partners, such as universities, compensate for limited internal resources in Spanish industries. For environmental innovators, external information, knowledge, and collaboration are particularly valuable, suggesting that networking can offset resource constraints. Additionally, access to accelerators, cost-effective software and hardware, open-source platforms, and artificial intelligence significantly reduces the costs of experimentation.

Given the substantial capital investments required for environmental innovation, firms with stronger financial viability are more likely to engage in such activities. Policies to support equity show up very important. Environmental policies, such as carbon taxes and research subsidies, play a key role in triggering clean investments (Acemoglu et al., 2016) and help firms overcome financial constraints, particularly when these policies are not conditional on specific outcomes. The critical role of regulation, especially subsidies, in fostering eco-innovation is widely recognized (Marchi and V, 2012; Del Río et al., 2015). Green investments respond to credit supply in presence of government subsidies, suggesting that subsidies may be the most effective to induce firms to undertake clean investments (Accetturo et al., 2022). Howell (2017) demonstrates that public grants for innovation significantly enhance innovative success, as measured by the number of patents, and also increase company revenues. This finding is particularly relevant to our framework, as Howell's (2017) study shows that the grant programs are not necessarily enforced ex post. Grants allow companies to retain more equity and alleviate liquidity constraints in capital-intensive sectors, especially when the grant is provided as a lump sum.

An interesting point is suggested by behavioral finance literature that highlights two important biases for financial decision: optimism and overconfidence. A sense of power leads negotiators to perceive greater control over negotiation outcomes, resulting in overconfident decisions that can lead to financial losses (Fast et al., 2009) and cause them to underweight other environmental factors in decision-making (Galinsky et al., 2008). Zavertiaeva et al. (2018) show how behavioral biases influence the innovation policy and that managerial overconfidence influences positively corporate R&D. Financial determinants of R&D like liquidity and profitability are amplified when managers are overconfident. However, their study also indicates that these investments may become inefficient, potentially harming firm value. Similarly, Galasso and Simcoe (2011) demonstrate that overconfidence can drive
significant shifts in a firm's innovation strategy, resulting in a change in direction rather than merely increasing R&D spending and productivity. Malmendier and Tate (2005) argue that overconfident managers overestimate the firm's equity and the cost of external funding.

However, overconfidence typically applies to individual managers rather than organizations as a whole. When managers' sense of power is derived from the stronger bargaining position of their organization in negotiations, these behavioral tendencies could help explain why companies pursue investments, including those that do not lead to technology deployment, even when they face credit constraints. The impact of bargaining power on psychology of negotiation have already been studied in the context of delay cost effect. Gago-Rodríguez et al. (2021) show that initial offers inform negotiators of their counterparts' aspirations and that bargaining power moderates the "delay costs effect" (profit losses derived from the length of the negotiation) in supply chain context. Behavioral considerations thus offer an alternative explanation for why investments occur even in financially constrained environments.

## 10. Conclusions

The primary goal of environmental regulation is to correct the market failures due to negative externalities. Today, the effectiveness of such regulations is often measured by the incentives they provide to encourage both R&D and the adoption of improved abatement technologies. In this article, we examine the role that environmental taxation can play in reducing environmental pollution and prompting a profit-maximizing monopoly to choose cleaner technologies. We show that, the strategic interaction between a monopoly and an upstream industry can alter the adoption of the best available abatement technology. Specifically, after the introduction of an emission tax, a polluter may, under certain conditions, invest in R&D to develop cleaner technologies—not to use them directly, but only to have a better outside option while bargaining with the end-of-pipe technology supplier. In such a way he obtains a more profitable contract. This effect may give rise to conflicts between regulators and innovators. The conflict arises from the division of industry profits, which may become more advantageous for the polluter if he innovates solely to enhance its bargaining power. From the regulator's perspective, the profit division is irrelevant, as total industry profit remains unchanged. Our paper highlights the importance of considering the contracting process with technology providers when designing effective environmental regulations.

In the event of a conflict, the regulator is left with no option but to adjust the environmental tax to ensure the polluter adopts the technology preferred by the policy maker. This, however, leads to a reduction in overall welfare, as the tax must be altered to influence the polluter's adoption decisions. Consequently, environmental damages increase beyond what could have been achieved if the regulator's and polluter's preferences were aligned. Additionally, we demonstrate that in some cases, the regulator may be unable to influence the polluter's innovation and adoption choices, resulting in an unavoidable welfare loss.

Our model suggests that merely patenting, as noted by Calel (2020), may not be an encouraging indicator for the future; it could simply reflect that firms are enhancing their bargaining power relative to technology providers. Stricter regulations in the future may not lead to technology adoption if the share of industry profits from contracts favoring the polluter remains significantly more attractive. Furthermore, if we alter the technology provision framework—where the upstream firm proposes clean technology and the polluter develops an end-of-pipe solution—the qualitative results hold. The key element lies in a trade-off between the portion of profits that can be secured by the innovator and the costs associated with innovation.

Several questions remain unaddressed in this paper and merit some further study. First, we assume that the two technologies are substitutable. Recent research Hammar and Löfgren (2010) shows however, that companies that use end-of-pipe equipment engage as well in clean (in-house) innovation. Unfortunately, this research does not clarify the timing of technology adoption or identify who developed these technologies. This alternative assumption can be incorporated in our framework as well. The complementarity of technologies might be attributed to the enhanced capabilities of the polluter to conduct research or to perceive other opportunities as a result of getting accustomed to environmental technology. In-house research could lead to a reduced reliance on end-of-pipe equipment, enabling the renegotiation of existing contracts with upstream suppliers. A potential example can be found in the metallurgy industry, where substantial amounts of water are used in production process. Historically, quenching<fnref n="6" /> was associated with the use of oils in hardening process. Production of ball bearing for automobile and aerospace industry requires fast cooling of steel. In certain industries until the 1980s, it was done using oil as coolant. However, the steel afterwards had to be quenched in water, giving need to waste water purifying station to filter out inter alia the oil. In subsequent years, significant research was conducted by the polluting industry resulting in the direct replacement of oil with water as a coolant. Empirical validation of this hypothesis would necessitate a close study of contracts between polluters and the associated independent end-of-pipe producers.

Second, our results indicate potential tensions between a regulator focused on maximizing welfare and one aimed at minimizing environmental damage. If there are two principals—each responsible for industrial and environmental policy—their efforts must be coordinated. Industrial policy may advocate for increased innovation efforts that could be deemed excessive from the perspective of the other principal. These issues remain open for further research.

<footnote n="6">⁶ In materials science, quenching is the rapid cooling of a workpiece to obtain certain material properties. Many variables influence the quality and mechanical properties of hardened steel and they are all important to control: the quenching temperature; the soaking time; the cooling rate (cooling rate); the chemical composition of the material.</footnote>
CRediT authorship contribution statement

Oliwia Kurtyka: Formal analysis. Rania Mabrouk: Formal analysis.

Declaration of Generative AI and AI-assisted technologies in the writing process

During the preparation of this work the author(s) used ChatGPT in order to correct the english language of introduction, literature review, financial aspects of investments and conclusion part. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

We would like to thank two anonymous referees for precious comments and suggestions that have improved the paper significantly.

Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.reseneeco.2025.101514.

Data availability

No data was used for the research described in the article.

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