Comparing climate pledges and eco-taxation in a networked agricultural supply chain organisation

Abstract

1. Introduction

This study examines the roles of climate pledges and eco-taxation in addressing climate change within the agricultural sector, particularly evaluating the effectiveness of voluntary measures, such as climate pledges, in achieving carbon neutrality. This evaluation is conducted in light of the sector’s social acceptability challenges concerning environmental taxes and the absence of such taxes within the common agricultural policy (CAP) as highlighted by Deroubaix and Lévèque (2006). Agricultural systems, essential for human survival, face complex sustainability challenges across economic, social and environmental realms (Talukder et al., 2020). Accounting for nearly a quarter of global anthropogenic greenhouse gas (GHG) emissions, the agricultural sector is crucial in feeding a growing population, mitigating climate change and adapting to its impacts (Verschuuren, 2018). As a significant source of methane (CH₄) from livestock and nitrous oxide (N₂O) from fertilisers, its contribution to climate change is substantial (Lynch et al., 2021), with annual emissions from global agriculture at around 12 gigatons of CO₂-equivalent (Marechal, 2022). In the European Union (EU), agricultural emissions have increased by 1.5 per cent (Eurostat, 2022), underscoring the critical need for sustainable practices.

The EU has set an ambitious target of achieving climate neutrality by 2050 (European Commission, 2020). However, the existing measures in place for the agriculture sector face significant challenges in meeting this climate neutrality goal. Lóránt and Allen (2019) have explored various options for the sector, including improving production efficiency, modifying production methods and commodities and enhancing sequestration capacity. However, none of these individual approaches alone can achieve the required level of mitigation for a net-zero future. Combined, these options can only result in emission reductions of up to 46 per cent by 2050, assuming no substantial changes in land use (Aubert et al., 2019). Unlike sectors covered by the Emissions Trading System (ETS), the agricultural sector is regulated under the Effort Sharing Decision/Regulation, particularly regarding livestock emissions (OJ— Official Journal of the European Union, 2009). While European climate policy predominantly relies on the ETS, which addresses approximately half of the region’s emissions, discussions and policies regarding the pricing of agricultural emissions have received relatively limited attention so far (Dragicevic, 2021). To effectively achieve the EU’s long-term mitigation targets in a cost-effective manner, Grosjean et al. (2018) estimated that the agricultural sector should aim for emission reductions ranging from 42 to 49 per cent by 2050. The authors also recommend the use of market-based instruments as an effective means to achieve emission reductions in agriculture. The European Green Deal identifies the CAP as a tool to influence climate change policy-making (McEldowney, 2020). However, studies have found that CAP programmes are insufficient in addressing environmental challenges (Alliance Environment, 2019; Pe’er et al., 2019). Urgent restructuring of the European agricultural policy is therefore imperative, as there is currently no clear alignment of conditional payments with the goals of the Paris Agreement (Heyl et al., 2021).

Voluntary engagement in climate pledges involves active participation by individuals, organisations or governments in committing to specific actions and goals aimed at mitigating climate change. These pledges are made outside of formal legal obligations, driven by the recognition of the urgent need for collective action on climate change. At a global scale, motivations for voluntary commitments to climate pledges are shaped by a confluence of factors: collective stakes, international diplomacy, economic considerations and overarching anxieties regarding our planet’s future trajectory (Santos et al., 2022). Zooming into the microcosm of farming, the impetus for embracing climate pledges is multifaceted. Economic motivations are evident, with farmers anticipating future regulatory shifts, tapping into the increasing demand from eco-aware consumers and reaping cost benefits from sustainable practices (Ahmad et al., 2022). Environmental motivations are equally pressing, given that climatic aberrations directly influence crop yields, livestock well-being and the health of soil and water systems. Beyond these tangible drivers, intrinsic values play a pivotal role. Many in the agricultural community harbour a profound bond with the land they till and nurture, manifesting a sense of stewardship that extends to future generations (Raymond et al., 2016). This connection often translates into a moral imperative to act responsibly and sustainably.

Under the Paris Agreement, countries submit voluntary pledges known as nationally determined contributions (NDCs), which outline their intended climate actions and targets. However, it is important to note that the NDCs published by G20 countries lack clearly defined national targets specifically for food systems, including the agricultural sector. Despite the growing prominence of the Agricultural Sector Roadmap to limit global warming to 1.5°C (Coyne, 2022), which focuses on decoupling deforestation from the agrifood supply chains, the sector remains largely overlooked. This absence of specific targets poses challenges for investors who require clear objectives to align their investments accordingly (Coller, 2021).¹ The United Nations annually highlights the shortfall in achieving Paris Agreement goals. Sognnaes et al. (2021) found that even with full compliance with carbon pledges, global temperatures could exceed 2°C. The authors explored strategies for meeting these pledges, including emission reduction policies and gradually increasing carbon prices. Given agriculture’s current exemption from the ETS (Dragicevic, 2021), this study examines if carbon taxes could aid in achieving 2050 climate neutrality and whether ambitious pledges could rival binding fiscal policies, especially considering Europe’s goal of a 55 per cent emission reduction from 1990 levels by 2030 (European Council, 2023).

Our work augments the literature on voluntary commitments, like climate pledges, by focusing on a supply chain network including farmers, cooperatives, retailers and consumers. While many studies have explored farm sustainability, limited research has delved into the role of supply chain organisations in environmental sustainability (Dessart et al., 2019). We evaluate the efficacy of climate pledges in this supply chain, emphasising the interplay between cooperatives and individual farms in reducing agricultural GHG emissions. Agricultural cooperatives, due to their close connections with farmers, have the potential to drive sustainable practices by promoting the adoption of environmentally and socially responsible methods. They are voluntary organisations established by farmers to collectively address common challenges such as accessing credit, acquiring inputs, marketing products and sharing knowledge. Their cooperative model, characterised by democratic decision-making, equality and solidarity, distinguishes them from other enterprises and presents unique opportunities for advancing sustainability. Candemir et al. (2021) highlighted that cooperatives have the ability to motivate farmers to modify their practices by providing services, exerting market influence and collaborating on investments. This helps mitigate risks and facilitates the adoption of sustainable farming practices. The cooperatives hold significant market shares within the agrifood supply chains, particularly in Western countries. They represent 50 per cent of global agricultural production. In the EU, for instance, cooperatives accounted for 40 per cent of the agrifood sectors in 2010, with even higher shares in specific countries and sectors (Bijman et al., 2012; Bijman and Iliopoulos, 2014). In France, 75 per cent of farmers are affiliated with at least one cooperative (Coop de France, 2010).

Numerous studies have demonstrated the economic and social benefits of agricultural cooperatives (Albæ k and Schultz, 1998; Hovelaque et al., 2009; Fulton and Giannakas, 2013; Fulton and Pohler, 2015). Economically, they enable farmers to achieve economies of scale, enhance bargaining power, reduce transaction costs and access otherwise unavailable markets (Ménard and Valceschini, 2005; Van Herck, 2014; Wollni and Fischer, 2015; Liu et al., 2019; Omar, 2023). Cooperatives also deliver social benefits by fostering cohesion, empowering marginalised farmers and promoting community development (Mendoza et al., 2016). Furthermore, agricultural cooperatives play a vital role in ensuring the provision of high-quality products throughout the agrifood chain (Yu et al., 2022). Using network economics, we aim to determine the extent to which cooperatives can contribute to the overall carbon neutrality of the agrifood sector. Our postulation suggests that cooperatives have the capacity to contribute to climate change mitigation efforts, even in the absence of fiscal regulations, by consolidating revenue-sharing contracts from a collective of farmers (Rathbone, 1995). Individual farmers may face constraints in participating in collective mitigation efforts due to financial feasibility, whereas cooperatives utilise the collective assets of multiple farmers to overcome such limitations.

In our research, we blend in-depth analysis with computer-based simulations to explore how network economics can influence climate change solutions. Using insights from previous studies (Dragicevic and Barkaoui, 2016; Nagurney et al., 2002; Peng et al., 2023), we have developed a model that mirrors the flow of the agricultural supply chain from farmers to consumers. Our approach is anchored in the variational inequality theory, a proven technique to study equilibrium in systems (Mancino and Stampacchia, 1972). At the heart of our model are two main criteria that typically tug businesses in opposite directions. The first criterion is profit maximisation of farmers and retailers, which frequently stands as their sole goal. The second criterion focuses on minimising GHG emissions. Our model seeks to balance these two criteria. The underlying approach is like finding the best flow in a network. It ensures that everything runs optimally (Nagurney and Siokos, 2012). By including both criteria, our model becomes a valuable tool for businesses, especially in the agriculture sector, to understand the trade-offs and synergies between economic success and environmental sustainability.

The sections of this paper are structured as follows. Section 2 introduces the problem statement, where we employ a variational inequality model to analyse the equilibrium of the networked agricultural sector, considering climate pledges within a multi-objective optimisation framework. In Section 3, we introduce environmental taxes. To demonstrate the practical application of our approach, Section 4 presents simulation examples. Finally, Section 5 concludes the paper.

2. Model

One of the key areas of focus in the field of industrial organisation is the analysis of supply chains operating within networked structures. In a decentralised supply chain, multiple decision-makers are involved, and the behavior of each decision-maker needs to be characterised by a set of equilibrium conditions (Yang and Zhao, 2011). As described in Section 1, we utilise the variational inequality method to examine the equilibrium of our networked agricultural economy, which is organised across multiple tiers.

Drawing on the modelling studies conducted by Nagurney (2006) and Dragicevic and Barkaoui (2016), we consider a three-layered agricultural industrial network as depicted in Figure 1. This network consists of a group of upstream agents or farmers, denoted as |$U_{i}=U_{1},{\ldots},U_{N}$|⁠, who supply their agricultural products to instream agents or cooperatives, denoted as |$I_{i}=I_{1},{\ldots},I_{N}$|⁠. The instream agents then distribute these agricultural products to downstream agents or retailers, denoted as |$D_{i}=D_{1},{\ldots},D_{N}$|⁠, who subsequently sell the products to final consumers, denoted as |$C_{i}=C_{1},{\ldots},C_{N}$|⁠. Retailers respond to consumer demand. It should be noted that the farmers also have the option to directly sell their products to retailers without involving the cooperatives. The utilisation of this structure adheres to the principle of atomicity in a well-functioning market.²

Fig. 1.

Agricultural industrial network

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Two key observations warrant special attention.

We exclude the manufacturing sector from our analysis, recognising that its functions are progressively integrated within the expanding roles of agricultural cooperatives and retail organisations. These entities have ventured into activities traditionally aligned with manufacturing. For instance, agricultural cooperatives extend their operations to include not only production and collection but also manufacturing and distribution (Wang et al., 2018; Zhang et al., 2021). This was the case in France, where in 2018, the country was home to |$1,416$| agricultural cooperatives (Statista, 2022). Among these, approximately |$1,400$| cooperatives were involved in various manufacturing activities, encompassing food processing, winemaking and biofuel production (French Ministry of Agriculture and Food, 2023). Similarly, retailers are encroaching on this domain, particularly through the development and marketing of private-label brands. These products compete with and often serve as perfect substitutes for those produced by traditional manufacturing firms (Sgroi and Salamone, 2022). This blurring of roles creates a complex overlap in the supply chain, making the inclusion of a distinct manufacturing sector in our model redundant.

It is important to note that our research framework does not explicitly include direct sales to consumers. According to Pipame (2017), a short distribution channel in the agrifood sector is defined by a marketing strategy that involves at most one intermediary between the producer and the final consumer. These channels can take various forms, ranging from direct sales from producer to consumer, to a model involving both a producer and a retailer before reaching the consumer. While our study covers short food supply chains, it is crucial to recognise that they account for approximately 20 per cent of agrifood trade (Renting et al., 2003; Renard and Chouin, 2017). Only about 3 per cent of sales are direct transactions with consumers, with the majority involving a single intermediary (Villard, 2008; Wattez, 2012). Dragicevic (2020) highlights that these short supply chains are unlikely to scale up sufficiently to capture a significant market share. Despite the potential advantages identified by Ademe (2017), these channels should not be seen as substitutes for longer distribution systems. They are better viewed as complementary choices, typically specialised in serving local markets. Including a model focused on direct consumer sales, which is a minor aspect in practice, would distort the overall analysis due to its relevance to a niche market with a limited product range.

2.1. Farmer’s multicriteria decision-making problem

Each farmer’s production process is evaluated on maximising profits and minimising GHG emissions from production and marketing activities, with marketing including shipping of products, denoted as |$q_{U_{i}}$| for farmer U_i and represented as a vector |$Q \in \mathbb{R}_{+}^{U_{N}}$|⁠. The production cost function for producer U_i is influenced by all outputs, expressed as |$f_{U_{i}}(q_{U_{i}})=f_{U_{i}}(Q)$|⁠, allowing operation within the Cournot competition framework. Farmers can engage in transactions with retailers either directly or through a cooperative, incurring transaction costs denoted as |$c_{U_{i}D_{i}}$| and |$c_{U_{i}I_{i}}$|⁠, respectively, and forming the vector |$Q \in \mathbb{R}_{+}^{U_{N}I_{N}}$|⁠. According to the conservation of the flow, the quantity produced by farmer U_i is equal to the sum of the quantities transacted by the farmer with all the retailers.

Let |$p_{1I_{i}}^{\star}$| represent the price set by farmer U_i for the product sold to retailer D_i through cooperative I_i, and let |$p_{1U_{i}}^{\star}$| denote the price directly charged by farmer U_i for the product sold to a retailer.³ The farmer and the cooperative have a revenue-sharing contract in place. The parameter ϕ, which takes values in the interval |$[0,1]$|⁠, represents the proportion retained by the cooperative, while |$1-\phi$| represents the allocation to the upstream agent (Dragicevic and Barkaoui, 2016; Dragicevic, 2023). This parameter is determined through collective negotiations between farmers and cooperatives, where cooperatives, competing for the same farmers, allocate a portion of income to sustain operations and implement development policies, rendering this process a form of collective bargaining.

In addition to the primary goal of maximising profits, we also consider the commitment of each farmer to reduce GHG emissions generated throughout the agricultural processing and delivery of crops and livestock. This commitment aligns with the business climate pledge initiatives, reflecting the farmers’ dedication to curbing climate change. Agriculture is both susceptible to the impacts of climate change and a contributor to GHG emissions. There is growing urgency for farmers to modify their agricultural practices to enhance resilience against fluctuating weather patterns and to mitigate GHG emissions as noted by Morton and Hobbs (2015). According to Sorvali et al. (2021), farmers exhibit a heightened awareness of climate change issues and possess a compelling sense of responsibility, believing that their proactive measures can effect meaningful change.

The emissions associated with the production of goods by farmer U_i are represented by the function |$e_{U_{i}}$|⁠, where |$e_{U_{i}}(q_{U_{i}})=h_{U_{i}}q_{U_{i}}$|⁠. The emissions produced by a farmer when their cooperative I_i engages in transactions with retailer D_i are given by the equation |$e_{U_{i}I_{i}}(q_{U_{i}I_{i}})=h_{U_{i}I_{i}}q_{U_{i}I_{i}}$|⁠. Furthermore, the function |$e_{U_{i}D_{i}}=e_{U_{i}D_{i}}(q_{U_{i}D_{i}})=h_{U_{i}D_{i}}q_{U_{i}D_{i}}$| represents the emissions generated during the transaction and the delivery of the product to retailer D_i. These emission functions are linear in quantities, where the nonnegative terms |$h_{U_{i}}$|⁠, |$h_{U_{i}I_{i}}$| and |$h_{U_{i}D_{i}}$| represent the amount of emissions generated per unit of product produced and traded, respectively.⁴

2.1.1. Farmer’s optimisation program

Farmer U_i prioritises profit maximisation as the primary objective and assigns a weight of one (numeraire) to this criterion. Additionally, the farmer assigns a non-negative weight α_i, which ranges from 0 to 1, to the emission-generated criterion. To incorporate both objectives, a constant additive weight value function is used to construct a value function for each farmer. The parameter α_i represents the level of commitment of each participant in the climate pledge. A value of α_i equal to 0 indicates that the farmer is indifferent towards their emissions and disregards emission reduction efforts. Conversely, an α_i value of 1 signifies that the farmer is fully committed to achieving carbon neutrality. For |$\alpha_{i}=0.5$|⁠, the farmer is willing to reduce their emissions by 50 per cent.⁵ Consequently, the multicriteria decision-making problem for farmer U_i can be reformulated as follows⁶

subject to |$q_{U_{i}I_{i}} \geq 0$| for all I_i and |$q_{U_{i}D_{i}} \geq 0$| for all D_i, where we maximise the function with respect to the quantities produced and transacted.

2.1.2. Farmer’s optimality conditions

In the context of Cournot–Nash competition, the farmers behave in a noncooperative manner. Each farmer aims to determine their optimal production quantity based on the choices made by their competitors. It is assumed that the production and transaction cost functions of each farmer are continuously differentiable and convex. Considering the optimal strategies of the competing farmers, each farmer independently determines their optimal production quantity and transactions. The simultaneous optimality criteria for all farmers can be expressed through an inequality, ensuring that each farmer’s decisions are optimised given the actions of their competitors. This mathematical formulation suggests that for each firm, the influence of its own actions on marginal profit takes precedence over the combined effects generated by the actions of all competing firms. In simpler terms, the sensitivity of a firm’s marginal profit is greater with respect to its own strategic choices than to the aggregate decisions of its competitors. This leads to a Cournot–Nash equilibrium point at which the farms realise positive profits (Leleno, 1993).

|$\forall Q$|  |$\in \mathbb{R}_{+}^{U_{N}(1+I_{N}+D_{N})}$|⁠.

In the cooperative-oriented scenario, the retailer’s price to the cooperative for the commodity must be at least as high as the sum of the marginal costs of production, transactions and the perceived marginal cost associated with emissions. If the total cost exceeds the proposed price, there will be no transaction volume. Similarly, in the second scenario where the farmer interacts directly with the retailer, the fundamental principle remains consistent. The price agreed upon between the farmer and the retailer must be at least equal to the combined marginal costs.

2.2. Retailer’s multicriteria decision-making problem

Retailers are responsible for covering handling costs, which include expenses related to processing, storing, packing and shipping orders. These costs are represented by |$c_{D_{i}}$|⁠. The handling costs are influenced by the quantity of the product acquired from multiple farmers through both cooperative and direct transactions.⁷ We express |$c_{D_{i}}$| as |$c_{D_{i}}(Q)$|⁠. This formulation places the retailer within a Cournot competition framework, where the market price depends on the total quantity produced by all farmers.⁸ When a farmer’s production, facilitated by the cooperative, is assumed to be sold to the retailer, we establish |$q_{I_{i}D_{i}}=q_{U_{i}I_{i}}$|⁠. We denote the transaction costs associated with retailer D_i as |$\hat{c}_{U_{i}D_{i}}(q_{U_{i}D_{i}})$| and |$\hat{c}_{U_{i}I_{i}}(q_{U_{i}I_{i}})$| for all D_i and all I_i.

Let |$q_{D_{i}C_{i}}$| denote the quantity of the product consumed by customers. We assume that the transaction cost associated with retailer D_i and customer C_i is represented by |$c_{D_{i}C_{i}}=c_{D_{i}C_{i}}(q_{D_{i}C_{i}})$|⁠.⁹ The price set by retailer D_i for the goods at their retail outlet is denoted by |$p_{2D_{i}}^{\star}$|⁠. In the model, the price is determined endogenously. The objective function is designed to maximise the difference between the payouts to farmers and the revenues while considering the handling and transaction costs. To accurately reflect real-world dynamics, a constraint is introduced that requires customers to purchase larger quantities of products from cooperatives compared to individual farms. This constraint is based on empirical evidence indicating that cooperatives have a significant market share in the distribution of agricultural products from farms to final consumers (Deller et al., 2009; Agbo et al., 2015).

In addition to the primary objective of maximising profits, we recognise the commitment of each retailer to reduce GHG emissions associated with the processing, storing, packing and shipping processes. This commitment aligns with the business climate pledge, reflecting the retailers’ dedication to mitigating the environmental impact of their operations. By integrating sustainability practices into their supply chain, the retailers aim to contribute to the collective effort of addressing climate change within the agricultural sector.¹⁰ Several scholars assert that corporate social responsibility (CSR) involves voluntary commitments by companies, like pledges for sustainable resource use and climate change mitigation, aiming to preserve resources for future generations and impact society positively (Allen and Craig, 2016; Vasquez, 2021). The food sector is increasingly integrating CSR into core strategies due to pressures and its interaction with corporate financial performance (CFP) (Hartmann, 2011; Lu and Taylor, 2016). Our framework explores the indirect interrelation between CSR and CFP in this context.

2.2.1. Retailer’s optimisation program

Retailer D_i assigns a non-negative weight β_i to the emissions generation requirement and a weight of one to the objective of maximising profits. The parameter β_i reflects the level of commitment of each retailer to the climate pledge. A value of β_i equal to 0 indicates that the retailer is indifferent towards their emissions and does not prioritise emission reduction. Conversely, a β_i value of 1 signifies that the retailer is fully committed to achieving carbon neutrality. For |$\beta_{i}=0.5$|⁠, the retailer is willing to reduce their emissions by 50 per cent. This gives rise to a multicriteria decision-making problem, which can be formulated as follows

subject to |$\sum \limits_{D_{i}=D_{1}}^{D_{N}} q_{U_{i}D_{i}} \leq \sum \limits_{I_{i}=I_{1}}^{I_{N}} q_{U_{i}I_{i}}$|⁠, |$\sum \limits_{C_{i}=C_{1}}^{C_{N}} q_{D_{i}C_{i}} \leq q_{U_{i}}$| and the nonnegativity constraints, where we maximise the function with respect to the quantities transacted.

2.2.2. Retailer’s optimality conditions

In consideration of the actions taken by other retailers, each retailer behaves in a noncooperative manner, following the Cournot–Nash framework. To achieve an equilibrium state, all transactions among the decision-makers within the network must align and coincide.

|$\forall (Q,\gamma)\in\mathbb{R}_+^{U_N(1+I_N+D_N)+D_iC_i}$|⁠.

Note that γ_i is the Lagrange multiplier associated with constraint |$q_{U_{i}}^{\star} \geq \sum \limits_{C_{i}=C_{1}}^{C_{N}} q_{D_{i}C_{i}}^{\star}$| for retailer D_i. The equilibrium model endogenises the prices the farmers and retailers set.

The price set by retailer D_i, denoted as |$p_{2D_{i}}^{\star}$|⁠, is precisely equal to |$\gamma_{i}^{\star}$| plus the marginal cost associated with this transaction, when |$q_{U_{i}D_{i}}^{\star} \geq 0$|⁠. Similarly, when a farmer conducts a transaction with a retailer through a cooperative, the price |$\gamma_{i}^{\star}$| is exactly equal to retailer D_i’s indirect payment to the farmer |$(1-\phi)p_{1I_{i}}^{\star}$|⁠, in addition to the marginal cost of handling the product, the retailer’s marginal transaction cost and the marginal cost of emissions.

2.3. The behaviour of the consumers

Beyond the prices determined by retailers and farmers, consumers also consider transaction costs associated with acquiring the commodity, as well as the emissions generated during those transactions, when determining the quantity to purchase. Let |$p_{3C_{i}}$| represent the willingness to pay of the market consumers. The demand for the product, denoted as |$d_{D_{i}}$|⁠, is assumed to be governed by a continuous demand function |$d_{D_{i}}=d_{D_{i}}(p_{3C_{i}})$|⁠.¹¹ Consumers factor in the unit transaction cost associated with obtaining the product (⁠|$\hat{c}_{U_{i}D_{i}}$|⁠), adding it to the price set by retailers (⁠|$p_{2D_{i}}^{\star}$|⁠). Additionally, consumers take into account the pricing determined by the producer |$(1-\phi)p_{1I_{i}}^{\star}$|⁠, making them sensitive to the fair remuneration of the farmers (Taylor and Boasson, 2014), along with the associated transaction cost (⁠|$\hat{c}_{U_{i}I_{i}}$|⁠). The GHG emissions related to transactions and purchases are weighted, reflecting the assumption that consumers make multicriteria decisions.

2.3.1. Consumer’s multicriteria equilibrium conditions for the demand markets

The nonnegative weight parameter, denoted as |$\eta_{i} \in [0,1]$|⁠, indicates the importance attributed to the overall emissions produced through consumer transactions. It quantifies the degree to which consumers are conscious of their consumption patterns within a demand-driven market economy and their role in contributing to climate change. A higher value of η_i indicates a greater level of sensitivity among consumers towards the environmental impact of their consumption choices. By incorporating this weight into the analysis, we acknowledge the consumers’ awareness of their responsibility in addressing climate change and their willingness to prioritise sustainable consumption practices (Hartmann, 2011). Consequently, the equilibrium conditions for consumers in a demand market can be expressed as follows.

For all retailers

For all farmers¹²

and

Customers will choose to purchase the product from retailer D_i if the total price charged by the retailer, including transaction costs and the marginal cost of emissions associated with the transaction, does not exceed the price customers are willing to pay. In equilibrium, all the conditions are satisfied, and the demand markets can be formulated as a variational inequality problem. We seek to determine |$(Q, p_{3C_{i}}) \in \mathbb{R}_{+}^{U_{N}}$|⁠, representing the optimal quantities and prices in the demand markets.

|$\textstyle\forall(Q,p_{3C})\in\mathbb{R}_+^{U_N(1+I_N+D_N)}$|⁠.

2.4. The equilibrium of the supply chain

For the supply chain to achieve equilibrium, the quantity of goods sold by farmers to retailers must match the quantity of products purchased by retailers from farmers. Additionally, the quantities of goods bought by customers must correspond to the quantities supplied by the retailers. To formalise the agreements and interactions among the different tiers of the supply chain network while considering environmental considerations, the equilibrium transaction and price patterns must satisfy both the sum of optimality conditions and the equilibrium conditions for the demand markets. The supply chain attains an equilibrium state when the flows between its tiers align, and when the transactions, prices and GHG emissions of the products fulfil both the optimality and equilibrium conditions.¹³

The proof is located in  Appendix B.

After solving the variational inequality to determine the prices, the supply-chain network reaches an equilibrium state based on the following condition.

|$\forall Q\in\mathbb{R}_+^{U_N(1+I_N+D_N)}$|⁠.

The proof is located in  Appendix C.

3. Environmental taxation

Let us now consider a scenario in which the government introduces an environmental tax, denoted as τ, specifically targeting GHG emissions. This policy aligns with the concept of internalising negative externalities. It is important to note that the tax will impact the entire supply chain regardless of whether it is imposed on producers or consumers. Considering the economic tax incidence, which may differ from the legal tax incidence, it is necessary to acknowledge that the implementation of such a tax by public authorities is likely to reduce farmers’ spontaneous willingness to voluntarily mitigate GHG emissions. This can be attributed to the fact that the tax acts as a disincentive for farmers to engage in proactive reduction measures.

3.1. Taxing the top tier

Let |$\tau_{U_{i}}h_{U_{i}}(q_{U_{i}}) \Leftrightarrow \tau_{U_{i}}h_{U_{i}I_{i}}(q_{U_{i}I_{i}})+\tau_{U_{i}}h_{U_{i}D_{i}}(q_{U_{i}D_{i}})$| represent the unit environmental tax associated with the GHG emissions produced by farmer U_i during production and trade activities. This indicates that the top tier, the farmers, contributes to the collective effort to reduce emissions. In this case, the decision-making framework shifts from multicriteria to the farmer’s updated profit function, which now includes an additional cost. Consequently, the variational inequality can be expressed as follows

|$\forall Q$|  |$\in \mathbb{R}_{+}^{U_{N}(1+I_{N}+D_{N})}$|⁠.

The following proposition can be stated regarding the adjusted equilibrium prices.

|$\forall Q\in\mathbb{R}_+^{U_N(1+I_N+D_N)}$|⁠.

The proof is located in  Appendix D.

At the juncture of supply chain equilibrium—where the quantity supplied aligns with the quantity demanded—the formulation for the price elasticity of supply can be articulated as |$\epsilon_{S} = \frac{\frac{Q^{\star}(\tau_{U_{i}})}{Q^{\star}} - 1}{\frac{p_{{1I_{i}},{1U_{i}}}^{\star}(\tau_{U_{i}})}{p_{{1I_{i}},{1U_{i}}}^{\star}} - 1}$|⁠, where |$Q^{\star}(\tau_{U_{i}})$| and |$p_{{1I_{i}},{1U_{i}}}^{\star}(\tau_{U_{i}})$| denote the equilibrium quantity supplied and the equilibrium selling price, respectively, after the enactment of the ecological tax on producers |$\tau_{U_{i}}$|⁠.

3.2. Taxing the bottom tier

Let |$\tau_{C_{i}}h_{C_{i}}(q_{C_{i}}) \Leftrightarrow \tau_{C_{i}}h_{U_{i}I_{i}}(q_{U_{i}I_{i}})+\tau_{C_{i}}h_{U_{i}D_{i}}(q_{U_{i}D_{i}})$| represent the unit environmental tax associated with the emissions generated through the consumption of agricultural products. This implies that the bottom tier, the consumers, plays a role in reducing emissions. In this case, the decision-making process shifts from multicriteria to a modified demand function that incorporates internalised negative externalities. As a result, the variational inequality is transformed into

|$\textstyle\forall(Q,p_{3C})\in\mathbb{R}_+^{U_N(1+I_N+D_N)}$|⁠.

The following proposition can be stated regarding the revised equilibrium prices.

|$\forall Q\in\mathbb{R}_+^{U_N(1+I_N+D_N)}$|⁠.

The proof is located in  Appendix E.

At the juncture of supply chain equilibrium—where the quantity supplied aligns with the quantity demanded—the formulation for the price elasticity of demand can be articulated as |$\epsilon_{D} = \frac{\frac{d_{D_{i}}(p_{3C_{i}}^{\star}, \tau_{C_{i}})}{d_{D_{i}}(p_{3C_{i}}^{\star})} - 1}{\frac{p_{3C_{i}}^{\star}(\tau_{C_{i}})}{p_{3C_{i}}^{\star}} - 1}$|⁠, where |$d_{D_{i}}(p_{3C_{i}}^{\star}, \tau_{C_{i}})$| and |$p_{3C_{i}}^{\star}(\tau_{C_{i}})$| denote the equilibrium quantity demanded and the equilibrium willingness to pay, respectively, after the enactment of the ecological tax on customers |$\tau_{C_{i}}$|⁠.

Two general remarks arise regarding these results.

4. Simulations

This section presents the outcomes and properties that were established through numerical simulations conducted using Python 3.11. The objective is to provide a comprehensive overview of the results obtained from these simulations. A detailed description of the algorithm, enhanced by machine learning techniques, is available in  Appendix F.

In the context of our study, we made certain assumptions. We assumed that the sum of |$q_{U_{i}I_{i}}$| from I₁ to I_N was equal to |$50q_{U_{i}I_{i}}$|⁠, and similarly, the sum of |$q_{U_{i}D_{i}}$| was equal to |$50q_{U_{i}D_{i}}$|⁠. This assumption was based on the fact that half of the world’s farms were grouped into cooperatives (Candemir et al., 2021). Consequently, the total number of farms considered in this example was 100. It was observed that farms belonging to cooperatives had higher production compared to individual farms, leading to |$q_{U_{i}I_{i}} \geq q_{U_{i}D_{i}}$|⁠. Additionally, in our analysis, we considered the presence of 100 retailers, and the total production was fixed at |$Q=1,000$|⁠.

In the initial phase of our analysis, we adopted an emission intensity ratio of 1 to 1, indicating that the production of one unit of output is associated with the emission of one unit of GHGs. As a result of this assumption, the initial global emission levels reached |$1,000$| units. Utilising multicriteria optimisation, our aim is to maximise profit while simultaneously reducing the emission intensity associated with agricultural activities. This entails seeking an optimal solution that achieves both a higher level of profitability and a lower level of emission intensity within the agricultural sector.

The explicit functions are as follows:

• Farmer’s production cost function: |$f_{U_{i}}(Q)=50q_{U_{i}I_{i}}+50q_{U_{i}D_{i}}$|⁠.

• Farmer’s transaction cost function via the cooperative: |$c_{U_{i}I_{i}}(q_{U_{i}I_{i}})=10q_{U_{i}I_{i}}^2$|⁠.

• Farmer’s direct transaction cost function: |$c_{U_{i}D_{i}}(q_{U_{i}D_{i}})=10q_{U_{i}D_{i}}^2$|⁠.

• Retailer’s handling cost function: |$c_{D_{i}}(Q)=50q_{U_{i}I_{i}}+50q_{U_{i}D_{i}}$|⁠.

• Retailer’s transaction cost function via the cooperative: |$\hat{c}_{U_{i}I_{i}}(q_{U_{i}I_{i}})=10q_{U_{i}I_{i}}$|⁠.

• Retailer’s direct transaction cost function: |$\hat{c}_{U_{i}D_{i}}(q_{U_{i}D_{i}})=10q_{U_{i}D_{i}}$|⁠.

• Final demand function: |$d(p_{3C_{i}})= 1,000-p_{3C_{i}}$|⁠.

We assume that the transaction costs incurred by farmers, whether selling their products to the cooperative or directly to the retailers, are equivalent. Likewise, we assume that retailers face equal transaction costs in both scenarios. To account for the interplay between trade and GHG emissions, the transaction costs are formulated as quadratic, following the approach proposed by Cordoni and Lillo (2022). These foundational assumptions form the basis of our investigation into the interconnectedness of production and GHG emissions in the agricultural sector.

Next, we will present the simulation results obtained from the climate pledge scenario and the environmental taxation scenario, followed by sensitivity analyses focusing on the most influential variables.

4.1. The algorithm outputs

The optimal values from the climate pledge obtained by running the iterative algorithm are presented in Table 1. Among the results, it is important to note that the algorithm searched for optimal values of α_i, β_i and η_i to facilitate the attainment of multiobjective decision-making.

In the context of the environmental tax |$\tau_{U_{i}, C_{i}}$|⁠, the minimisation function for emissions and the coefficients α_i, β_i and η_i become irrelevant. The tax rate has been set at 0.5 to maintain the overall production level consistent with the previous scenario and ensure a minimum reduction of 50 per cent in global emissions compared to the initial situation. The optimal values obtained using this approach are presented in Table 2.

4.1.1. The analysis of the optimal values from the climate pledge

The optimal production quantity, denoted as Q, is determined to be 981.65. The optimal ratios between cooperative and individual farms remain unchanged, with cooperative farms producing 497.06 and individual farms producing 484.59, representing nearly half of the total production. This optimal quantity takes into account the GHG emissions associated with production, which are addressed through the implementation of the climate pledge, resulting in emissions of 794.09 units. This represents a reduction of 20.59 per cent compared to the initial state. The model thus successfully minimises GHG emissions, with one unit of production generating only 0.81 units of emissions. The optimal price for final demand, denoted as |$p_{3C_{i}}$|⁠, is determined to be 2.39, which can be considered a reasonable price within the market context. This price enables farmers to adequately cover their costs, which is currently not being achieved (Dragicevic, 2023).

The shadow price γ_i that enables clearing the markets along the supply chain is 2.23, which is close to the consumer’s price but still a bit lower. When the shadow price is close to the consumer’s price, it suggests that the market is efficient, and the supply chain is operating optimally. In cases where the shadow price is found to be lower than the consumer’s price, it suggests the presence of excess supply or inefficiencies within the supply chain. These inefficiencies could arise from various factors, including market frictions resulting from information asymmetry or excessive transaction costs.

The coefficients α_i, β_i and η_i symbolise the weights assigned by economic agents to minimise GHG emissions. These weights reflect the level of importance each agent places on reducing emissions. For instance, a weight of 0.5 indicates that an agent is willing to decrease GHG emissions by up to 50 per cent but not more. In the context of climate change, risk-averse behavior would manifest as a higher weight placed on reducing GHG emissions. Conversely, risk neutrality or slight risk-taking behavior suggests a relatively lower emphasis on emission reduction, indicating a different set of priorities or considerations for these firms. The results demonstrate that, at the network equilibrium and the social optimum, characterised by the simultaneous achievement of profit maximisation and GHG emissions’ minimisation, consumers exhibit risk-averse behaviour concerning climate change. This is evidenced by their relatively high weight of 0.68 assigned to the reduction of GHG emissions. On the other hand, firms engaged in agricultural production (0.46) and distribution (0.45) display a somewhat risk-neutral or slightly risk-taking attitude.¹⁴

4.1.2. The analysis of the optimal values from the environmental tax

The optimal production quantity Q represents the socially acceptable level of production considering the negative externalities that need to be internalised through emissions’ taxation. The calculated value is 947.86, indicating a small decrease of 3.44 per cent compared to the production level under the climate pledge scenario. The optimal proportions of cooperative and individual farms are similar to those obtained with emissions’ minimisation, with cooperative farms producing 500.16 and individual farms producing 447.70, the latter representing a 7.61 per cent decrease from the previous case. It is noteworthy that production from cooperatives increases, while production from individual farmers decreases compared to the climate pledge scenario. This optimal quantity incorporates the GHG emissions associated with production, totaling 421.27 units, resulting in a reduction of 57.87 per cent compared to the initial state. The model not only brings GHG emissions to the social optimum, but it also performs better than in the case of emissions’ minimisation with 1 unit of production generating only 0.44 units of emissions. It is important to highlight that the Pigouvian tax, commonly employed to address negative externalities, typically achieves internalisation by reducing production. However, our framework demonstrates that through the implementation of fiscal policies, it is possible to achieve a substantial enhancement in emission intensity while keeping production levels constant. This finding makes such policies compatible with the constraints imposed by a growing population that needs to be fed and the imperative of land sparing (OECD, 2022). The optimal final demand price |$p_{3C_{i}}$| is 2.44, which is slightly higher but similar to the price obtained under the climate pledge scenario, allowing farmers to cover their costs (Dragicevic, 2023).

The shadow price γ_i required for clearing the markets along the supply chain is 2.70, a little higher than the consumer’s price. A shadow price close to the consumer’s price indicates an efficient market and optimal supply chain operations. However, a shadow price exceeding the consumer’s price suggests an inefficient allocation of resources, pointing out opportunities for policy interventions, such as subsidies, to align the market price with a social cost. This implies that public authorities should provide subsidies to consumers affected by environmental taxes up to the point where both costs align.

Given that the coefficients α_i, β_i and η_i hold no significance in the context of taxation, we have set the tax level at 0.5 to ensure the overall production level remains consistent with the previous scenario. This means that each unit of production incurs an additional cost of 0.25, resulting in a corresponding increase in prices for consumers. The primary objective in this situation is to achieve a reduction in emissions of at least 50 per cent. By comparing this approach to the previous case, we observe that this level of internalisation reflects the perspective of a risk-neutral agent towards climate change. With all parameters hovering around 0.5, the outcomes highlight the effectiveness of environmental taxation in comparison to alternative tools such as voluntary commitments for climate action.

The price elasticity of demand, represented as ϵ_D, serves to quantify the responsiveness of consumer demand to alterations in price, while the elasticity of supply, ϵ_S, evaluates the responsiveness of the quantity supplied to fluctuations in price. Within a variational inequality framework that is divergent from conventional economic models, a meticulous comparative analysis of equilibrium states that pre- and post-eco-tax implementation was undertaken to ascertain price elasticity. The results reveal that the price elasticity of demand is |$\epsilon_{D}=0.42$| with intermediaries and |$\epsilon_{D}=0.20$| for direct sales, indicating a moderate decrease in quantity demanded with an infinitesimal unit price increase. For both sales contexts, the supply side is nearly completely inelastic at |$\epsilon_{S}=0.01$|⁠, showing negligible responsiveness to price increases post-eco-tax, suggesting that suppliers predominantly bear the tax burden. For a more profound understanding of tax incidence, the concept of tax pass-through (Weyl and Fabinger, 2013; Miravete et al., 2018; Miravete et al., 2023) is scrutinised, elucidating the degree to which the ramifications of tax imposition are transferred from the initial bearers to other economic entities. This concept is portrayed as the alteration in consumer prices attributable to a per-infinitesimal-unit tax on the product, represented as |$\rho = 1 / (1 + (\epsilon_{D}/\epsilon_{S}))$|⁠. In the given scenario, a value of 0.05 denotes a restrained pass-through, corroborating the insights acquired through elasticity examinations and indicating that consumers incur a marginal fraction of the tax burden, while a substantial proportion is assimilated by the suppliers.

4.2. The sensitivity analysis

A sensitivity analysis is conducted to assess how changes in variables affect various outputs of the model. This analysis helps identify the variables that have the most significant impact on the optimality and equilibrium outcomes.

In the displayed plots, the blue lines function as graphical depictions of linear regression models, characterising the optimal linear association between the independent (x-axes) and dependent variables (y-axes). Situated alongside these blue lines, light grey bands outline the 95 per cent confidence intervals for the linear regression estimates. These confidence bands serve as quantifiable indicators of the uncertainty inherent in the linear models; a narrower band suggests a higher degree of confidence that the true best-fit line would reside within the shaded region. Specifically, the light grey bands delineate the interval in which the true underlying linear relationship is expected to lie 95 per cent of the time, thereby providing a robust measure of the reliability of the blue regression lines.

Despite displaying moderate goodness-of-fit metrics, the models should be evaluated considering the high degree of randomness introduced by the algorithmic framework.

4.2.1. The sensitivity analysis of the climate pledge

Figure 2 illustrates the linear relationships between the levels of trade via cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) and direct trade with retailers (⁠|$ q_{U_{i}D_{i}} $|⁠) in Figure 2(a), as well as the relationship between the revenue-sharing factor (ϕ) and trade via cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) in Figure 2(b). In these analyses, |$ q_{U_{i}D_{i}} $| and |$ q_{U_{i}I_{i}} $| are treated as dependent variables to understand how they are influenced by the independent variables, namely the levels of trade conducted through cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) and the revenue-sharing factor (ϕ).

Fig. 2.

Levels of (a) |$q_{U_{i}D_{i}}$| with respect to |$q_{U_{i}I_{i}}$| and levels of (b) |$q_{U_{i}I_{i}}$| with respect to ϕ, all within 95 per cent confidence intervals. The levels of |$q_{U_{i}I_{i}}$| and ϕ are depicted on the x-axes, while the corresponding levels of |$q_{U_{i}D_{i}}$| and |$q_{U_{i}I_{i}}$| are represented on the y-axes.

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The left-side plot unveils a relationship between |$ q_{U_{i}I_{i}} $| and |$ q_{U_{i}D_{i}} $| that demonstrates weak dependence. The linear regression equation, |$ q_{U_{i}D_{i}} = 641.80 - 0.15q_{U_{i}I_{i}} $|⁠, suggests a negative relationship between these two variables. Specifically, a unit increase in |$ q_{U_{i}I_{i}} $| corresponds to a decrease of 0.15 units in |$ q_{U_{i}D_{i}} $|⁠. This indicates a substitutability effect. As indicated by its standard error of 0.19, this effect is not significantly different from zero, which could be due to random variation in the data. The R² value of the model is 0.02, indicating that only about 2.53 per cent of the variability in the production levels of individual farms (⁠|$ q_{U_{i}D_{i}} $|⁠) is explained by the production levels within cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠). This low R² value implies that other factors play a significant role in determining the production levels within cooperatives. It should be mentioned that the model incorporates the constraint |$ q_{U_{i}I_{i}} + q_{U_{i}D_{i}} \leq 1,000 $|⁠, which reflects the maximum combined production limit for the two channels of commercialisation. This constraint allows for a range of potential relationships between individual farm production and cooperative production.

The right-side plot reveals a relationship between ϕ and |$ q_{U_{i}I_{i}} $| that exhibits strong dependence. The linear regression equation, |$ q_{U_{i}I_{i}} = 578.06 - 160.71\phi $|⁠, suggests a negative relationship between these two variables. Specifically, an increase of 1 unit in ϕ corresponds to a decrease of approximately 160.71 units in |$ q_{U_{i}I_{i}} $|⁠. This illustrates that lower revenue shares obtained by farmers are associated with a reduction in the production levels. However, the standard error of the coefficient is large at 213.08, expressing a high level of uncertainty in the estimate. The R² value of the model is 0.02, implying that only about 2.41 per cent of the variability in the production levels within cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) is explained by the revenue-sharing factor (ϕ).

Figure 3 illustrates the linear relationships between the levels of trade via cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) and the corresponding GHG emissions (⁠|$ e_{U_{i}I_{i}} $|⁠) in Figure 3(a), as well as between the levels of direct trade with retailers (⁠|$ q_{U_{i}D_{i}} $|⁠) and their associated GHG emissions (⁠|$ e_{U_{i}D_{i}} $|⁠) in Figure 3(b). In these analyses, the levels of trade via cooperatives and direct trade with retailers are treated as independent variables against which the respective GHG emissions from each trade type are regressed.

Fig. 3.

Levels of (a) |$e_{U_{i}I_{i}}$| with respect to |$q_{U_{i}I_{i}}$| and levels of (b) |$e_{U_{i}D_{i}}$| with respect to |$q_{U_{i}D_{i}}$|⁠, all within 95 per cent confidence intervals. The levels of |$q_{U_{i}I_{i}}$| and |$q_{U_{i}D_{i}}$| are depicted on the x-axes, while the corresponding levels of |$e_{U_{i}I_{i}}$| and |$e_{U_{i}D_{i}}$| are represented on the y-axes.

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The analysis of the left-side plot reveals a pronounced increasing trend in the relationship between |$ q_{U_{i}I_{i}} $| and |$ e_{U_{i}I_{i}} $|⁠. Specifically, for every 1 unit increase in |$ q_{U_{i}I_{i}} $|⁠, there is a corresponding increase in GHG emissions of approximately 0.34 units. This relationship is captured by the linear regression equation |$ e_{U_{i}I_{i}} = 48.45 + 0.34q_{U_{i}I_{i}} $|⁠. The coefficient, exhibiting a standard error of 0.04, denotes a statistically significant correlation between production levels and GHG emissions. The R² value of the model is 0.72, announcing that approximately 72.02 per cent of the variability in the level of GHG emissions (⁠|$ e_{U_{i}I_{i}} $|⁠) can be explained by the production levels of the cooperative farms (⁠|$ q_{U_{i}I_{i}} $|⁠).

The right-side plot depicting the relationship between |$ q_{U_{i}D_{i}} $| and |$ e_{U_{i}D_{i}} $| reveals a robust increasing trend, characterised by a high level of confidence. This pattern indicates that increases in GHG emissions are proportionate to the production levels of individual farms. Specifically, for every 1 unit increase in |$ q_{U_{i}D_{i}} $|⁠, there is an increase in GHG emissions of approximately 0.24 units. This relationship is captured by the linear regression equation |$ e_{U_{i}D_{i}} = 119.93 + 0.24q_{U_{i}D_{i}} $|⁠. The coefficient, with a notably low standard error of 0.07, expresses a statistically significant relationship between production levels and GHG emissions. The R² value of the model is 0.33, specifying that approximately 33.25 per cent of the variability in the level of GHG emissions (⁠|$ e_{U_{i}D_{i}} $|⁠) can be explained by the production levels of the individual farms (⁠|$ q_{U_{i}D_{i}} $|⁠).

Figure 4 showcases linear regression analyses examining the relationships between the shadow price for market clearance (γ_i) and the consumer’s willingness to pay (⁠|$ p_{3C_{i}} $|⁠) in Figure 4(a), as well as between the consumer’s willingness to pay (⁠|$ p_{3C_{i}} $|⁠) and the revenue-sharing factor (ϕ) in Figure 4(b). In these analyses, the shadow price for market clearance and the consumer’s willingness to pay are treated as independent variables against which the consumer’s willingness to pay and the revenue-sharing factor are regressed, respectively.

Fig. 4.

Levels of (a) |$p_{3C_{i}}$| with respect to γ_i and levels of (b) ϕ with respect to |$p_{3C_{i}}$|⁠, all within 95 per cent confidence intervals. The levels of γ_i and |$p_{3C_{i}}$| are depicted on the x-axes, while the corresponding levels of |$p_{3C_{i}}$| and ϕ are represented on the y-axes.

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The linear regression analysis of the left-side plot examining the relationship between γ_i and |$ p_{3C_{i}} $| reveals a decreasing pattern, illustrating a degree of substitutability between these variables. Specifically, the regression equation |$ p_{3C_{i}} = 2.96 - 0.23\gamma_{i} $| suggests that for every 1 unit increase in γ_i, there is a decrease in |$ p_{3C_{i}} $| of approximately 0.23 units. The standard error of the coefficient is 0.24, pinpointing some uncertainty in the estimate. The R² value of the model is 0.03, conveying that only about 3.87 per cent of the variability in the consumer’s willingness to pay (⁠|$ p_{3C_{i}} $|⁠) is explained by the shadow price (γ_i).

The right-side plot depicting the relationship between |$ p_{3C_{i}} $| and ϕ reveals a pattern that is distinct from the previously analysed relationships. The linear regression analysis, represented by the equation |$ \phi = 0.30 + 0.05p_{3C_{i}} $|⁠, indicates a slight positive relationship between these variables. Specifically, for every 1 unit increase in |$ p_{3C_{i}} $|⁠, there is an increase in ϕ of 0.05 units. This suggests that the revenue-sharing factor evolves modestly with changes in the consumer’s purchasing price. The standard error of the coefficient is 0.04, denoting a moderate level of uncertainty in the estimate. The R² value of the model is 0.08, marking that only about 8.44 per cent of the variability in the revenue-sharing factor (ϕ) is explained by the consumer’s price (⁠|$ p_{3C_{i}} $|⁠).

4.2.2. The sensitivity analysis of the environmental tax

Figure 5 presents a comprehensive representation of the linear relationships between the levels of trade via cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) and their dependencies on the levels of direct trade with retailers (⁠|$ q_{U_{i}D_{i}} $|⁠) in Figure 5(a), as well as on the eco-tax (⁠|$ \tau_{U_{i}, C_{i}} $|⁠) in Figure 5(b). In these analyses, the levels of trade via cooperatives and the eco-tax are treated as the independent variables against which the levels of direct trade with retailers and the levels of trade via cooperatives are regressed, respectively.

Fig. 5.

Levels of (a) |$q_{U_{i}D_{i}}$| with respect to |$\textstyle q_{U_iI_i}$| and levels of (b) |$\textstyle q_{U_iI_i}$| with respect to |$\tau_{U_i,C_i}$|⁠, all within 95 per cent confidence intervals. The levels of |$q_{U_{i}I_{i}}$| and |$\tau_{U_{i}, C_{i}}$| are depicted on the x-axes, while the corresponding levels of |$q_{U_{i}D_{i}}$| and |$q_{U_{i}I_{i}}$| are represented on the y-axes.

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The analysis of the left-side plot examining the relationship between |$ q_{U_{i}I_{i}} $| and |$ q_{U_{i}D_{i}} $| reveals a nuanced trend. The linear regression equation, |$ q_{U_{i}D_{i}} = 608.99 - 0.12q_{U_{i}I_{i}} $|⁠, suggests a slight negative relationship between these variables. Specifically, an increase of 1 unit in |$ q_{U_{i}I_{i}} $| corresponds to a decrease of 0.12 units in |$ q_{U_{i}D_{i}} $|⁠. This indicates a near independence or, at most, a very slight degree of substitutability between the production levels within cooperatives and those of individual farms. The standard error of the coefficient is 0.20, expressing a high level of uncertainty in the estimate. The R² value of the model is a mere 0.01, demonstrating that only about 1.47 per cent of the variability in the production levels of individual farms (⁠|$ q_{U_{i}D_{i}} $|⁠) is explained by the production levels within cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠).

The right-side plot analysis reveals a notable trend in the relationship between |$ \tau_{U_{i}, C_{i}} $| and |$ q_{U_{i}I_{i}} $|⁠. The linear regression equation, |$ q_{U_{i}I_{i}} = 625.24 - 195.35\tau_{U_{i}, C_{i}} $|⁠, suggests a significant negative relationship between these variables. Specifically, an increase of 1 unit in |$ \tau_{U_{i}, C_{i}} $| leads to a decrease of approximately 195.35 units in |$ q_{U_{i}I_{i}} $|⁠. This indicates strong substitutability between the tax and production levels, reflecting the internalisation of negative externalities and the movement towards a socially optimal level of agricultural production. The standard error of the coefficient is 198.16, marking a considerable level of uncertainty in the estimate. The R² value of the model is 0.04, announcing that approximately 4.05 per cent of the variability in the production levels within cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) is explained by the tax level (⁠|$ \tau_{U_{i}, C_{i}} $|⁠).

Figure 6 depicts the linear relationships between the levels of trade via cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠) and the corresponding GHG emissions (⁠|$ e_{U_{i}I_{i}} $|⁠) in Figure 6(a), as well as between the levels of direct trade with retailers (⁠|$ q_{U_{i}D_{i}} $|⁠) and their associated GHG emissions (⁠|$ e_{U_{i}D_{i}} $|⁠) in Figure 6(b). In these analyses, the levels of trade via cooperatives and direct trade with retailers are treated as independent variables against which the respective GHG emissions from each trade type are regressed.

Fig. 6.

Levels of (a) |$e_{U_{i}I_{i}}$| with respect to |$q_{U_{i}I_{i}}$| and levels of (b) |$e_{U_{i}D_{i}}$| with respect to |$q_{U_{i}D_{i}}$|⁠, all within 95 per cent confidence intervals. The levels of |$q_{U_{i}I_{i}}$| and |$q_{U_{i}D_{i}}$| are depicted on the x-axes, while the corresponding levels of |$e_{U_{i}I_{i}}$| and |$e_{U_{i}D_{i}}$| are represented on the y-axes.

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The analysis of the left-side plot examining the relationship between |$ q_{U_{i}I_{i}} $| and |$ e_{U_{i}I_{i}} $| reveals a moderately increasing trend. The linear regression equation, |$ e_{U_{i}I_{i}} = 60.27 + 0.19q_{U_{i}I_{i}} $|⁠, shows that an increase of 1 unit in |$ q_{U_{i}I_{i}} $| leads to an increase of only 0.19 units in |$ e_{U_{i}I_{i}} $|⁠. This observation suggests a decoupling phenomenon between production and GHG emissions, where higher levels of production result in less than proportionate increases in emissions. The very low standard error of 0.03 means that the relationship between production levels and GHG emissions is statistically significant. The R² value of the model is 0.52, signalling that approximately 51.90 per cent of the variability in GHG emissions (⁠|$ e_{U_{i}I_{i}} $|⁠) can be explained by the production levels within cooperatives (⁠|$ q_{U_{i}I_{i}} $|⁠).

The right-side plot, depicting the relationship between |$ q_{U_{i}D_{i}} $| and |$ e_{U_{i}D_{i}} $|⁠, shows a moderately increasing trend. The linear regression equation, |$ e_{U_{i}D_{i}} = 68.15 + 0.18q_{U_{i}D_{i}} $|⁠, expresses that an increase of 1 unit in |$ q_{U_{i}D_{i}} $| leads to an increase of only 0.18 units in |$ e_{U_{i}D_{i}} $|⁠. This suggests a positive relationship between the production levels of individual farms and GHG emissions, where higher production levels are associated with an increase in emissions albeit at a rate that is far less than proportionate. The standard error of 0.04 testifies a statistically significant relationship. The R² value of the model is 0.48, denoting that approximately 47.87 per cent of the variability in GHG emissions (⁠|$ e_{U_{i}D_{i}} $|⁠) can be explained by the production levels of individual farms (⁠|$ q_{U_{i}D_{i}} $|⁠).

These findings suggest that taxation measures are likely to have a similar impact on both individual farms and cooperatives. However, it is crucial to acknowledge that cooperatives have a distinct advantage in terms of resource availability. By pooling revenue-sharing contracts from a collective of farmers, cooperatives can actively participate in climate change mitigation initiatives even in the absence of fiscal policies. While individual farmers may face challenges in engaging in such initiatives due to the limited economic viability, cooperatives benefit from the combined resources of a group of farmers. This discrepancy in impact between individual farms and cooperatives can be attributed to the varying levels of resources at their disposal. Indeed, in certain iterations, individual farms with low profitability exerted a moderate influence on the minimisation of emissions. In such instances, cooperatives benefited from the aggregation of revenue generated by all participating farmers.

Figure 7 presents the results of linear and polynomial regression analyses exploring the relationships between the consumer’s willingness to pay (⁠|$ p_{3C_{i}} $|⁠) and the shadow price for market clearance (γ_i) in Figure 7(a), as well as between the consumer’s willingness to pay (⁠|$ p_{3C_{i}} $|⁠) and the eco-tax (⁠|$ \tau_{U_{i}, C_{i}} $|⁠) in Figure 7(b). In these analyses, the shadow price for market clearance and the consumer’s willingness to pay are treated as independent variables against which the consumer’s willingness to pay and the eco-tax are regressed, respectively.

Fig. 7.

Levels of (a) |$p_{3C_{i}}$| with respect to γ_i and levels of (b) |$\tau_{U_{i}, C_{i}}$| with respect to |$p_{3C_{i}}$|⁠, all within 95 per cent confidence intervals. The levels of γ_i and |$p_{3C_{i}}$| are depicted on the x-axes, while the corresponding levels of |$p_{3C_{i}}$| and |$\tau_{U_{i}, C_{i}}$| are represented on the y-axes.

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The analysis of the left-side plot examining the relationship between γ_i and |$ p_{3C_{i}} $| reveals a declining trend. The linear regression equation, |$ p_{3C_{i}} = 3.37 - 0.30\gamma_{i} $|⁠, suggests that an increase of 1 unit in γ_i corresponds to a decrease of approximately 0.30 units in |$ p_{3C_{i}} $|⁠. This shows a substitutability relationship between the shadow price and the consumer’s price. The standard error of the coefficient is 0.23, hinting some level of uncertainty in the estimate. The R² value of the model is 0.06, manifesting that approximately 6.55 per cent of the variability in the consumer’s price (⁠|$ p_{3C_{i}} $|⁠) is explained by the shadow price (γ_i).

The analysis of the right-side plot, informed by linear regression, reveals a nuanced trend in the relationship between |$ p_{3C_{i}} $| and τ. The linear regression equation, |$ \tau = 0.58 - 0.03p_{3C_{i}} $|⁠, implies a slight negative relationship between these variables. Specifically, an increase of 1 unit in |$ p_{3C_{i}} $| corresponds to a decrease in τ of 0.03 units. This implies that changes in the consumer’s price have an almost imperceptible impact on the level of the environmental tax akin to the implementation of a flat tax. The standard error of the coefficient of 0.04 designates a moderate level of uncertainty in the estimate. The R² value of the model is 0.01, signalling that only about 1.83 per cent of the variability in the environmental tax (τ) is explained by the consumer’s price (⁠|$ p_{3C_{i}} $|⁠).

5. Conclusion

This study provides valuable insights into the complex sustainability challenges faced by the agricultural sector, particularly in relation to mitigating climate change. The findings underscore the critical role of environmental taxation as the most effective strategy for addressing climate change. The implementation of taxation measures demonstrates comparable impacts on both individual farms and cooperatives, surpassing the performance of climate-pledged initiatives in achieving significant reductions in GHG emissions. Eco-taxation achieves a substantial reduction in global emissions, amounting to 57.87 per cent, while climate pledges only account for a 20.59 per cent reduction at the same production level. Moreover, the adoption of taxation measures leads to more favorable outcomes in terms of emission intensity. Specifically, our findings demonstrate a significant decoupling between emissions and output when implementing eco-taxes, resulting in an emission intensity of 0.44. This emission intensity is considerably lower than the intensity of 0.81 observed under a climate pledge. Therefore, eco-taxation achieves a greater reduction in emission intensity, with a difference of 45.68 per cent compared to climate pledges. These findings align with the imperative of accommodating a growing population and the necessity of land sparing (OECD, 2022). All in all, an eco-fiscal policy proves to be more effective than climate commitments in achieving the established objectives of the EU.

Designing effective environmental policies for the agricultural sector, whether through economic instruments or other options, poses challenges due to the diffuse nature of pollution emissions. Research by Weersink et al. (1998) and Dragicevic and Sinclair-Desgagné (2010) suggests that environmental taxation is the most effective approach to internalise pollution from diffuse sources. However, Weersink et al. (1998) highlighted the complexity of addressing environmental issues in agriculture, which involve multiple diffuse pollution sources with unobservable abatement practices, making it difficult to achieve cost-effective pollution control with a single instrument. They proposed that technological advancements and business-led initiatives may be the most effective means of addressing diffuse-source pollution in agriculture. On the other hand, our findings indicate that business-led initiatives, such as climate pledges, are inadequate in achieving significant reductions in GHG emissions. Empirical evidence strengthens our findings, underscoring the necessity of implementing environmental taxes even in situations where specific abatement costs are unknown (Ambec and Coria, 2021).

Expanding upon the understanding derived from the equivalence in impact on the supply chain between the climate pledge and the fiscal policy—conditioned by the equality of the marginal cost of production-related GHG emissions to the marginal cost of trade-related net GHG emissions—the conundrum surrounding the choice between the adoption of climate pledges and the implementation of eco-taxation as mechanisms to internalise environmental externalities gains enhanced clarity. In this context, eco-taxation emerges as a probable superior strategy for achieving cost-effective environmental internalisation. The preference for eco-taxation is rooted in the improbable scenario that direct trading with retailers could ever be consistently less GHG-intensive than trading through cooperatives. Cooperatives often have the institutional capabilities to invest in emission-reducing technologies and practices, particularly in the agrifood sector, thereby lowering their own environmental footprint. As a result of these dynamics, the introduction of an eco-tax could potentially undermine the viability and attractiveness of voluntary climate pledges made by businesses. However, there exists a caveat: if businesses can leverage their climate pledges for market differentiation, by attaining near-climate-neutral production, for instance, they could still capture increased market shares (Lash and Wellington, 2007). This could make voluntary commitments a viable supplement to eco-taxation under specific conditions.

Both climate pledges and eco-fiscal policies yield a notable outcome: the achievement of economic decoupling between production and GHG emissions. To manifest this decoupling and reduce emission intensity in the agricultural sector, it is essential to undertake a series of strategic interventions. These interventions encompass the adoption of precision agriculture methodologies, enhanced nutrient management to curtail fertiliser consumption and its associated emissions, the encouragement of agroforestry systems that amalgamate trees with crops and livestock operations, and the deployment of sustainable livestock management practices aimed at mitigating CH₄ emissions (FAO, 2017). Relying solely on climate pledges to achieve these necessary measures comes with inherent risks. However, in the event that widespread implementation of eco-taxes fails to materialise, cooperatives, with their enhanced resource capacities resulting from the aggregation of revenue-sharing contracts among a collective body of farmers, remain well-positioned to actively engage in climate change mitigation efforts. Therefore, cooperatives are expected to play a significant role in collective endeavors aimed at combating climate change (Candemir et al., 2021), particularly within the framework of climate-pledged initiatives.

It is pertinent to highlight that supply contracts emerge as a compelling auxiliary route for curbing emissions, especially when the limitations of cooperative frameworks—both in terms of duration and scale—become apparent. A substantial body of scholarly work lends credence to the efficacy of supply contracts as a cornerstone for optimised coordination within supply chains (Cachon and Lariviere, 2005; Yang and Zhao, 2011; Bouamra-Mechemache et al., 2015; Barkaoui and Dragicevic, 2016; Dragicevic, 2023). These contracts are multidimensional, encompassing not only volume obligations and product quality criteria but also extending to nuanced aspects such as pricing algorithms, payment modalities and the terms for contract dissolution (CGAAER, 2012). In line with transaction cost theory, the institutionalisation of such agreements tends to attenuate transaction expenses, thereby fortifying the likelihood of successful interactions between parties (Peteraf, 1993). In contexts where the expansion of cooperative memberships is impracticable, particularly within fragmented bioeconomic sectors confronted with the complexities of holistic emission mitigation, supply contracts hold promise. They confer the benefit of introducing structured vertical coordination, facilitating more surgically targeted and actionable environmental intervention strategies. Therefore, supply contracts stand as a viable alternative or supplement to cooperative arrangements.

Advocating for the cooperative model within the supply chain system emphasises the significance of transaction costs in achieving equilibrium. Considering all layers of the system simultaneously underscores the need for coordination among these layers to attain network equilibrium, which emerges from the integration of multiple tiers. Efficient coordination is facilitated by reduced transaction costs (Banerjee et al., 2017). Conversely, elevated transaction costs can hinder effective decision-making and collaboration within cooperatives, leading to inefficiencies and decreased overall performance (Castañer and Oliveira, 2020). Cooperatives tend to foster market competitiveness, resulting in improved profitability and meeting demand (Liang and Wang, 2020). Accordingly, individual farms are obligated, due to the competitive yardstick effect (Liang and Hendrikse, 2016), to align their prices with those of cooperatives. This necessitates harmonising their transaction costs with those of cooperatives, leading to potential benefits for the entire sector. Hence, the properties of network equilibrium, characterised by appropriate price and quantity levels, are strongly influenced by the impact of transaction costs, which is duly recognised in the study of supply chain equilibrium.

Given the significant role of cooperatives, combating climate change in the agrifood sector necessitates the establishment of binding commitments (Hochstetler and Viola, 2012) and stringent monitoring of annual progress (Boiral et al., 2012). Moreover, it is crucial to raise public awareness about the importance of environmental taxes, particularly in the context of the EU’s implementation of a carbon tax through the Carbon Border Adjustment Mechanism (European Parliament, 2022), which can address concerns about competitiveness. However, the acceptance of environmental taxes hinges on clearly linking them to the damages they address, to avoid perceptions of them being mere pretexts for additional taxation. A gradual implementation of environmental measures can soften the immediate financial impact and encourage firms to transition towards eco-friendly practices (OECD, 2007; Dragicevic and Sinclair-Desgagné, 2010).

Our study highlights the potential of network-based frameworks in investigating emissions reductions in agriculture. Using variational inequality techniques and advanced simulations, we gained insights into the effectiveness of voluntary commitments and eco-taxation for mitigating climate change. However, we acknowledge the limitations of our approach. We did not consider heterogeneity among model players, cautioning against generalising the results. To address this, we conducted |$1,000$| iterations with diverse initial values, capturing a range of contexts and providing realistic averages. While we account for uncertainty through randomness, our model lacks explicit consideration of decision-making under uncertainty, which warrants future research, as emphasised by Just (2001). Furthermore, applying this methodology to the agroforestry sector could be significant, particularly given its potential to mitigate polluting agricultural production through simultaneous carbon sequestration (Ramachandran Nair, 2010).

Acknowledgements

The authors express their gratitude to Serge Garcia (INRAE—French National Research Institute for Agriculture, Food and Environment, AgroParisTech—Paris-Saclay University, University of Lorraine) and Marc Leandri (UVSQ—University of Versailles – Saint-Quentin-en-Yvelines—Paris-Saclay University, Paris-Nanterre University—Paris-Lumières University) for their valuable comments and insightful suggestions, which greatly contributed to improving this work. They also convey their high appreciation to the discussants from Waseda University (AAERE) and the University of Graz (Wegener Center for Climate and Global Change). Finally, the authors are grateful to the editor and to the anonymous referees for their thorough comments and suggestions, which significantly contributed in elevating the overall quality of the paper.

Funding

This project received funding from Chulalongkorn University (grants nos. 0325/2566 and 0589/2566).

Conflict of interest

The authors have no conflicts of interest to declare.

Data availability

Data sharing does not apply to this article as no new data were created or analysed in this study.

Footnotes

References

The variational inequality problem was solved using an algorithm that employs mathematical optimisation and fixed-point iteration to determine the equilibrium in the agricultural network system. The algorithm updated the variables iteratively, guided by the model’s constraints and the objective function’s derivatives, until convergence was achieved. To incorporate machine learning in the iterative optimisation process, a hyperparameter known as the learning rate was utilised. The learning rate, which was set to 0.01, determined the magnitude of parameter updates at each iteration during the model training. Specifically, the learning rate was multiplied by the gradient of the objective function concerning the model parameters, which controlled the size of the parameter update. By setting a low learning rate, the magnitude of updates was decreased, leading to a slower optimisation process but enabling more precise convergence of the model.

In the algorithmic framework, the variational inequality was addressed through a fixed-point iteration procedure that ensured the equilibrium point satisfied the model’s requirements. This was achieved by imposing constraints on the production decisions (⁠|$q_{U_{i}I_{i}}$|⁠, |$q_{U_{i}D_{i}}$|⁠) and prices (γ_i, |$p_{3C_{i}}$|⁠). The primary fixed-point iteration loop computed updated variables by utilising the current variable values and the derivatives of the objective function. The loop ran until convergence was achieved, defined as the point where the difference between the updated and previous variables was less than the specified tolerance. The variational inequality is essential to the algorithm since it guarantees that the equilibrium point meets the model’s conditions, representing a stable state. The optimal values derived from the algorithm enabled the maximisation of profits while minimising emissions across the supply chain.

The algorithm incorporated randomness to enhance its versatility, efficiency and performance. Firstly, it leveraged the random initialisation of variables, scaled by corresponding factors, allowing for the exploration of multiple starting points in the machine learning process. This stochasticity facilitated the algorithm in traversing diverse regions of the solution space, thereby increasing the probability of discovering the global optimum. As a result, the algorithm was able to converge rapidly to an acceptable solution, even when faced with a large number of iterations, in this case, |$1,000$|⁠.¹⁵Moreover, its resilience to fluctuations and uncertainties in the input data was enhanced, rendering it highly suitable for real-world case studies, as the process of aggregating a substantial number of measurements leads to a more precise estimation.

This section presents a summary of a model that focuses on bilateral negotiations between farmers and retailers to determine quantities and prices, disregarding the involvement of cooperatives and consumers. Two extreme scenarios are considered. In the first case, either a single farmer or a group of farmers denoted as U engages in simultaneous bilateral negotiations with multiple retailers D_N. In the second case, a group of farmers denoted as U_N negotiates collectively with a single retailer D. The quantities exchanged and the corresponding prices are subject to negotiation.

To conduct the negotiations, we adopt the Nash-in-Nash method,¹⁶wherein one negotiator engages in multiple separate bilateral negotiations simultaneously (Collard-Wexler et al., 2019). A Nash equilibrium is derived from the Nash bargaining solutions (NBS) between the farmers and retailers as part of the Nash-in-Nash procedure. These solutions differ from the outcomes obtained through variational inequality, as they reflect the optimisation of individual benefits by both farmers and retailers.

• Nash bargaining between one farmer and N retailers

We first studied the negotiation between one farmer and N retailers. The payoff for the individual farmer denoted as U, is determined by Equation (2), which represents the production quantity as the sum of quantities |$q_{UD_{i}}$| sold to each model-retailer D_i within the range from D₁ to D_N. On the other hand, the payoff for the model-retailer D_i purchasing the quantity |$q_{UD_{i}}$| is determined by Equation (4).¹⁷The NBS can be written as

with |$\Delta f_{U}=f_{U}(Q)-f_{U}\left( Q-q_{UD_{i}}\right)$| and |$\Delta c_{D_{i}}=c_{D_{i}}(Q)-c_{D_{i}}(Q-q_{UD_{i}})$|⁠. First-order conditions over |$p_{1U}$| give

Maximising with respect to |$q_{UD_{i}}$| yields

The equation offers an implicit determination of the value for |$q_{UD_{i}}$|⁠, which can subsequently be substituted to calculate the corresponding price |$p_{1U}$|⁠.

We have derived the expression for the price |$p_{2D_{i}}$| that retailers will charge customers. In the given scenario, where farmer U and retailers D_N optimise their payoffs, the negotiated prices |$p_{1U}$| and |$p_{2D_{i}}$| can be compared with the prices obtained from Equations (16) and (18). As a consequence of this bargaining process, the allocation of the surplus generated in the agricultural context is expected to differ.

• Nash bargaining between N farmers and one retailer

We then looked that the negotiation between a model-farmer U_i and a retailer D, where U_i sells to D for |$p_{1U_{i}}$|⁠.¹⁸Using the same method as before, we calculated the |$NBS_{U_{i}D}$| and obtained

Maximising with respect to |$q_{U_{i}D}$| gave

The equation (G16) provides an implicit value for |$q_{U_{i}D}$|⁠, which can be substituted into equation (G15) to determine the price |$p_{1U_{i}}$|⁠.

• Simulation outputs

By employing iterative numerical simulations, we embarked on solving a system of equations comprising three unknown variables (⁠|$p_{1U}$|⁠, |$p_{2D_i}$| and |$q_{UD_i}$|⁠). This system represents the interactions between a single farmer (U) and a group of N retailers (D_i). At each iteration, the algorithm substituted the value of |$q_{UD_i}$| and solved the resulting system of equations. Constraints were then defined for the solutions |$p_{1U}$|⁠, |$p_{2D_i}$| and |$q_{UD_i}$|⁠, which were appended at the end of the loop.

To achieve emissions reduction equivalent to the standard voluntary initiatives case, where |$e_{UD_{i}}=383.35$|⁠, we examined a scenario adjusting parameters α and β to 0.21. This represents agents in upper and middle tiers with higher risk tolerance and less consideration for GHG emissions impact. The prices are then |$p_{1U}=1.36$| for the farmer and |$p_{2D_{i}}=2.73$| for the retailer. However, this leads to a trade level |$q_{UD_i}=200$|⁠, causing underproduction and shortages due to its insufficiency. Additionally, each unit of production generates 1.92 units of emissions in this scenario, a rise from the standard case, attributed to using the same infrastructure for reduced production levels. Thus, the Nash bilateral bargaining solution between a single farmer and multiple retailers is deemed suboptimal due to these discrepancies.

Iterative numerical simulations were then employed to solve a system of equations with three unknowns (⁠|$p_{1U}$|⁠, |$p_{2D_i}$| and |$q_{U_{i}D}$|⁠), which represented a group of N farmers (U_i) and one retailer (D). At each iteration, the algorithm substituted the value of |$q_{UD_i}$| and solved the resulting system of equations. Finally, after defining the constraints, the solutions for |$p_{1U}$|⁠, |$p_{2D_i}$| and |$q_{U_{i}D}$| were appended at the end of the loop.

To match the emissions reduction in the standard case, |$e_{UD_{i}}=383.35$|⁠, we adjusted α and β to |$5.23 \times 10^{-4}$| and |$1.80 \times 10^{-3}$|⁠, respectively, representing agents in the top and middle tiers with higher risk tolerance and lesser emphasis on GHG emissions. This results in prices |$p_{1U}=1.66$| and |$p_{2D_{i}}=2.73$|⁠, but the trade level |$q_{UD_i}=200$| is insufficient, causing underproduction and shortages. Additionally, each unit of production now generates 1.92 units of emissions due to the consistent use of the same infrastructure and delivery systems despite reduced production, marking an increase from the standard case. Thus, the Nash bilateral bargaining solution involving multiple farmers and a single retailer is suboptimal due to these elevated emission levels.

In conclusion, the suboptimal outcomes delineated earlier underscore the prevailing dominance of network games compared to bilateral bargaining games. In instances where the Nash bargaining model is implemented, it is discerned that when a monopolistic cooperative, embodying the comprehensive inter-branch organisation, partakes in transactions with numerous retailers, consensus is more feasibly attained.