Carbon Tariff vs. Emission Cap of North–South Countries in Response to Manufacturer’s Production

Abstract

Economy prosperity has concurrently caused severe emission damages worldwide, which calls for strong abatement efforts from both nations and manufacturers. In this paper, we establish a two-stage game to investigate the policy selections of a foreign developed country (North) and a domestic developing country (South), and the response of a Southern manufacturer. The welfare-maximizing governments in the two countries participate in an announcement game of environmental policies where the South decides on whether or not to enforce an emission cap and the North chooses either a carbon tariff or no policy, after which the profit-seeking manufacturer reacts to make production strategies and distribute differentiated products to the two countries. Our analysis shows that under an emission cap, the manufacturer shrinks product quantities in both markets, cuts emissions, and suffers profit losses. A carbon tariff has similar impacts on the manufacturer except for unaffected domestic sales. In addition, equilibrium policy selections for the two governments depend on the degree of emission damage in the South: A moderate level of damage generates an equilibrium in the scenario of the unilateral tariff policy where the Northern welfare peaks and the Southern well-being is not the worst; a severe damage leads to a prisoner’s dilemma, since the two governments would arrive at an equilibrium in the bilateral-policy scenario, but it is dominated by a no-policy scheme. What is more, we find that a negotiation between the two governments is able to help them out of the dilemma and achieve a Pareto-improving outcome.

1. Introduction

The world has witnessed runaway success of economic growth in developing countries over the past decades. Meanwhile, the increasingly prominent environmental issues have aroused significant concerns from the public, entrepreneurs, and nations all over the globe. Carbon pollution, in particular, has become one of the most urging problems to be tackled. Countering carbon emission issues asks for nationwide collaborations and joint efforts. Aside from regulation measures taken by governments, manufacturers worldwide are also embedding eco-friendly production activities and environmental management systems to improve the green features of products [1,2].

It is widely accepted that the developed countries are responsible for most historical greenhouse gas emissions [3], whereas developing countries are still topping economy prosperity in their agenda. The asymmetry between developed countries (the “North”) and the developing nations (the “South”) typically gives rise to a slate of environmental issues, which is termed as the “North–South” problem [4,5]. Foremost, industrialized nations have emphasized heavily on the environment protection to curb emission via various legislations, e.g., carbon tax, emission trading system, and serious punishments [6]. These rigorous policies in the North account for a phenomenon labeled “carbon leakage”, which has been spotted and attracted lots of research attention [7,8,9]. What is worse, such leakage largely leads to migration of polluting manufacturers to developing countries. Significant relocation of energy-intensive industries away from the OECD may occur, under certain market structures, with leakage rates as high as 130% [7]. Having observed the leakage, North countries have brought forward several means to prevent carbon leakage and to mitigate emission. One proposal points to the carbon tariff (also referred to Border Tax Adjustments (BTAs)), which levies a price or charge on exports from developing countries like China to industrialized nations such as the European nations and the US [10,11,12]. Practically, the passage of the US Clean Energy and Security Act in 2009, which allows the government to charge carbon tariff on imports by emission, signifies a pressing fact that carbon tariff implementation is about to effectuate in the short run around 2020. Based on the practical considerations, we assume that one manufacturer locates in the South but exports products to the North, and the latter charges a constant carbon tariff due to the embodied carbon emission.

Developing countries, especially China, have also voiced strong support in emission abatement and environment protection. As the largest emitter in the world, China has committed to a voluntary target of reducing 40–45% of its carbon emission per unit of GDP from the 2005 levels by the year 2020 [13,14]. To accomplish this goal, the Chinese central and local governments have strived to take legislations as well as market mechanisms [15,16]. Among the multiple policies enforced, the emission/carbon cap is one of the most commonly applied means, which is proved to be most effective in emission reduction. In reality, several local governments in China have mandatory emission allowances to manufacturers in their regions [17]. Compared with other measures, such as carbon tax and emission trading system, the emission cap is practically preferred by several environmental groups and governments in directly influencing the regulated manufacturers’ production activities, which bolsters its practical popularity [18]. Therefore, we reasonably focus the Southern policy option on an emission cap, which well captures the fact in developing countries like China.

Apart from the strengthening environmental policies in both developed and developing countries, the escalating green demand in public acts as another strong impelling force to call for greener products and manufacturing processes from producers. The ever-growing green demand in consumers has been captured by both empirical and theoretical researches [19,20]. However, it is noticed by many previous studies that the market demand driven by the consumer environmental awareness varies according to differences in many factors such as incomes, regions, political attitudes, educational levels, and demographics [20]. In industrialized nations, environmental standards on production are considerably higher than the counterparts in developing regions [21], and consumers are more willing to pay a premium on greener products [22]. To comply with such market differentiation, entrepreneurs usually adopt dual-mode production, with which two heterogeneous technologies are utilized to produce differentiated products. The technologies, namely, a traditional/conventional technology and a green one, differ in emission intensity (unit emission) and production cost [23]. Due to the different characteristics and valuation of the greenness of the production processes, the two types of products are assumed to be sold independently to the two markets. This fits into an independent market demand scenario, as discussed in [24]. Following the setting, we consider that the manufacturer in the South produces both conventional and green products, selling the former locally and exporting the latter to the North.

Based on the above-mentioned practical considerations, we intend to address the following research questions:

1. How do the emission cap of a developing country and the carbon tariff of a developed country affect a manufacturer’s production strategy and profit in the developing country?

2. How do the emission cap of the developing country and the carbon tariff of developed country affect their social welfare?

3. What are the interactions between the governments in both developed and developing countries in terms of policy selections?

To shed light on these questions, we develop a North–South framework and focus on the policy selection behaviors of two welfare-maximizing nations in terms of setting environment regulations, and a Southern manufacturer’s production strategies in response to different policy portfolios at home and abroad. One is a developing country where a manufacturer locates and operates production, and the other represents an industrialized one, which is the manufacturer’s foreign market. Each country has the option to announce its environmental policy. Specifically, the developing country can choose to implement an emission cap and the developed nation needs to determine whether or not to enforce a carbon tariff on exports from the manufacturer. In response, the manufacturer decides on its pricing strategy so as to maximize its own profit. We establish a two-stage game model: At first, the welfare-maximizing governments take part in an announcement game where each takes options of whether or not to implement the corresponding policy, namely, an emission cap in the South and a carbon tariff in the North; sequentially, the manufacturer reacts to make production strategy via pricing. Backward induction is applied to derive the equilibrium solutions of all the four possible subgames, and the subgame perfect equilibrium for the announcement game.

Our analysis yields the following interesting results. First, from the viewpoint of the regulated manufacturer, the implement of emission cap largely lowers its product sales in both markets, cuts total emission, pulls up domestic and foreign prices, and decreases its profits. The carbon tariff exhibits similar impacts on the manufacturer’s strategies and profits as well as the outcomes of total emission, except that it does not influence the price and demand in the South. Second, the Southern welfare peaks when the unilateral-policy of emission cap emerges. Likewise, the North finds its maximal welfare under the unilateral carbon tariff situation. Third, the degree of the environmental damage caused by the manufacturer’s production plays a critical role in the subgame perfect equilibrium of the announcement game the governments participate in: Under a comparatively small or moderate degree of emission damage, the governments arrives at an equilibrium under a tariff-only scheme where the North obtains the maximum welfare and the South is not the worst; when the damage becomes significant, the equilibrium points to the bilateral policy scenario, but it is dominated by the no-policy case, which brings about a prisoner’s dilemma for the two countries. An international negotiation process will perfectly help them out of the dilemma and achieve a Pareto-improving scenario in terms of welfare. Meanwhile, the negotiation mitigates the emission damage. Such results provide support to the international cooperation in emission mitigation via a game-theoretical approach.

The paper is organized as follows. Section 2 gives a brief review of the related researches. In Section 3, we formulate a two-stage game model involving two governments and a manufacturer, and derive the equilibrium solutions. Numerical studies are given in Section 4, where the manufacturer’s production strategies and the governments’ policy selections are studied. Section 5 concludes this paper and provides future research directions.

2. Literature Review

The literature related to our research can be partitioned into two main streams: One investigates the operations of manufacturers under environmental regulations, in particular, the emission cap, and the other takes the perspectives of policy makers to study various legislations and their impacts on emission amount and social welfare.

As diverse environmental policies limit manufacturers on their production processes, many researchers have looked into the operational management problems for firms to give managerial hints on their production planning. The optimal product mix and outputs are investigated by modeling under various policy constraints, e.g., caps, taxes, penalties, and an emission trading system [25]. The dual-mode production strategies for a monopolist are developed under two types of emission constraints, namely, a mandatory emission cap and a cap-and-trade scheme [17]. The firm can choose either a conventional technology or a green one or both in its manufacturing process, in response to the given carbon policy. The authors design a dynamic programming algorithm to search for the optimal solution for the manufacturer. They indicate that a mixed technology option is preferred only when the given emission cap is binding. Although a low value of the emission cap greatly influences the firm’s strategy, the carbon price under a trading system does not exert significant impacts. By taking into account three main emission policies: taxation, carbon cap, and cap-and-trade regulations, an economic order quantity model is developed to study a retailer’s inventory replenishment and emission abatement investment strategies [26]. Numerical comparisons are provided to check the different impacts of policies on the retailer’s costs and emissions. Our work is closely related to Qi et al. [18]. They focus on a one-supplier-two-retailers supply chain under an emission cap, where the supplier sets wholesale prices and the retailers tag the products with retailing prices to meet end consumers. The authors show a proper range of the carbon cap, which can effectively reduce emission. However, all the above-mentioned researches set their backgrounds where the environmental regulations are exogenously given. Different from the previous researches, our work not only looks into the production strategy for a regulated manufacturer, but also involves the governments into the game, which better describes the fact that policy-setting is never an external decision process for regulators, but rather a reflection of how they evaluate the market and the objectives of the proposed regulations.

Several previous studies derive from the perspectives of governments to check their policy-setting behaviors and generate policy implications. For instance, using a game-theoretical approach, Krass et al. [27] investigate the technology choice for a monopolist as well as the policy decisions of a regulator. The monopolist firm maximizes its profit by choosing one technology from a series of green emission-mitigating technologies, whereas the regulator maximizes social welfare by determining tax, subsidy, or rebate rates to regulate the firm’s producing and emitting activities. Their results indicate that tax increment may exert different impacts on the firm’s technology choice; also, under a tax-only policy, the option of clean technology largely depends on the level of environmental concerns of the society. An empirical study aims, from the standpoint of a developed country, to check if a combination of a unilateral pollution control policy and a BTA scheme is able to tackle the carbon leakage problem [11]. The authors take the Canadian economy as an example to look into the impacts of the BTA on imports of energy-intensive products. Our work is closely related to the following two papers. The first one refers to Cai and Li [28], in which the “North–South” issue is also discussed. Their focus is on an international negotiation via a side payment from the North to the South. The goal is for the North to enlarge the South’s incentive to announce a tougher emission standard. The South guides its own firm’s abatement technology choice, and the North takes charge of a side payment to its counterpart. Under a Nash negotiation scheme, the two governments make joint decisions to maximize the joint social welfare. The second one is Eyland and Zaccour [29]. Their study provides a game-theoretical model of two nations, each with a firm producing products. Both regulators set their respective carbon taxs in either a non-cooperative or cooperative scenario and the two firms compete in a Cournot game in a single consumption market. The country where tax rate is comparatively tough can enforce a carbon tariff to adjust the taxes differences, whereas in another scenario, a third-party organization is introduced to announce the tariff rate at the outset. The conclusion points out that tax adjustment achieved by carbon tariff is able to maximize the total welfare and the BTA can be viewed as an effective measure to reach a cooperative outcome for the two regulators. Our paper distinguishes from the above-mentioned researches in two ways. First, we reasonably take practical consideration of carbon leakage so that merely the South bears a manufacturer due to the stringent policies in the North, whereas the manufacturer can still deal with international trading by exports. Second, both governments in two countries can choose their respective regulations, which well reflects the fact that developing countries are gaining more power in the world and have some flexibility in policy selections.

In sum, our research mainly differs from the previous studies in taking simultaneous consideration of the policy selections of the North and South as well as the firm’s reaction of production strategy. The model introduces more practical assumptions so that the location of the manufacturer falls in the South due to the North’s formidable regulations. Besides, we single out one typical environmental policy for each of the regulator, which is based on observations in reality. Also, we give some flexibility in terms of policy selections for both governments, and look into all the possible cases, i.e., the bilateral-policy scenario, the two unilateral-policy schemes, and a no-policy situation. Moreover, a negotiation process is introduced to give our theoretical support to the international cooperation in emission abatement.

3. Model and Equilibrium Analysis

3.1. Model Formulation

Consider a manufacturer (denoted as “m”), carrying out production operations in a South country (denoted as “s”) but selling its products both to the south country and to a North country (denoted as “n”). To prosper in economy, the South country, which is still at its developing stage, announces comparatively lax environmental policies to attract companies. On the contrary, the North country is much developed and gives priority to environmental issues, so that rigorous policies exist to strongly limit or simply forbid polluting manufacturing. As mentioned, this setting describes a “South–North” framework which is commonly discussed in the previous literature.

Under such backdrop, the manufacturer is assumed to differentiate its products by activating dual-mode production. Specifically, the manufacturer adopts two different technologies/innovations to produce conventional products by the traditional technology and green ones by the green production technology. This complies with realities of manufacturers in carbon-intensive industries who operate dual-mode production by two different technologies; several examples can be found in Gong and Zhou [23]. Considering the customers’ preferences and different characteristics of market demands in the two nations, the manufacturer is supposed to sell the conventional products in the South and export the green ones to the North.

The traditional technology is superior in terms of cost-efficiency by consuming lower unit production cost, and meanwhile generates more unit emission during manufacturing process. In contrast, the green technology expends a higher unit production cost, but achieves a greener process performance which renders less unit emission during production. Denote $c_i$ and $e_i$ ($i=s,n$) as the unit production cost and the unit emission during production for the traditional and green technologies, respectively. As such, $c_s<c_n$ and $e_s>e_n$ stand to capture the difference between the two production processes. In addition, we take the conventional unit emission $e_s$ as a reference and measure the process performance of the green products by $e_s-e_n$, so that the larger the difference between the two unit emissions, the more superior performance the green products exhibit. With the two types of production activities available, the manufacturer places sales of the two sorts of products to meet both market demands $q_s$ and $q_n$, which are given by

$$\begin{array}{cc}\hfill q_s& ={\alpha }_s-{\beta }_s{p}_s,\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill q_n& ={\alpha }_n-{\beta }_n{p}_n+\gamma (e_s-e_n),\hfill \end{array}$$

(2)

where ${\alpha }_s$ and ${\alpha }_n$ denote the market potentials in the South and the North, respectively; ${\beta }_s$ and ${\beta }_n$ represent the price sensitivities; $p_s$ and $p_s$ are the retail prices in both nations. Parameter $\gamma$ denotes the consumer environmental awareness in the North so that the term $\gamma (e_s-e_n)$ describes the demand-enhancing effect of the green process performance. We assume that the Southern consumers are less concerned about the green features, so that the process performance of products will not impact the local demand. To better approximate the fact that the North is much industrialized and its consumers care less about price, we assume ${\beta }_n<{\beta }_s$. Such assumptions describe a North market where consumers are less price-sensitive but care more about the green feature (process performance) of the products. The manufacturer, observing the differentiation between consumers in the two nations, arranges its production activity according to each market’s needs and adopts different prices to the conventional and green products [24]. As the manufacturer deals with both manufacturing and sales of products, for simplicity, we exclude demand uncertainty and take a make-to-order scheme for the manufacturer where its production volumes are equal to the market demands [18].

The sequence of events is described as follows. In the first stage, the two countries/governments play a Nash game of policy announcement to maximize their respective social welfare:

$$\begin{array}{cc}\hfill W_s=& {\displaystyle {\pi }_m+\frac{1}{2{\beta }_s}{({\alpha }_s-{\beta }_s{p}_s)}^2-hE,}\hfill \end{array}$$

(3)

$$\begin{array}{cc}\hfill W_n=& {\displaystyle \omega e_n({\alpha }_n-{\beta }_n{p}_n+\gamma (e_s-e_n))+\frac{1}{2{\beta }_n}{({\alpha }_n-{\beta }_n{p}_n+\gamma (e_s-e_n))}^2,}\hfill \end{array}$$

(4)

where ${\pi }_m$ is the profit of the regulated manufacturer, h presents the degree of emission damage to the South, and E denotes the manufacturer’s total emission, i.e., $E=e_s{q}_s+e_n{q}_n$. The second term in each equation represents the consumer surplus in each country. The well-being of the South compromises of three components: the manufacturer’s profit, the consumer surplus, and the environmental damage which is related to the total amount of emission. Following Eyland and Zaccour [29], we assume that a constant carbon tariff rate $\omega$ is imposed to tax exports by emission and the manufacturer is forced to submit for each unit of export from the South to the North a tariff of $\omega e_n$. Therefore, the Northern social welfare consists of the tax income brought by the carbon tariff and the Northern consumer surplus. To be specific, the South makes choice of whether or not to ratify an effective emission cap Q; simultaneously, the Northern regulator decides to either announce a positive carbon tariff rate $\omega$ or take no tariff act. The two governments make announcement movements simultaneously and non-cooperatively. In the second stage, the manufacturer reacts to set the two products’ prices $p_s$ and $p_n$ to maximize its profit:

$$\begin{array}{cc}\hfill {\pi }_m=& {\displaystyle (p_s-c_s)q_s+\left(p_n-c_n-\omega e_n\right)q_n.}\hfill \end{array}$$

(5)

In this phase, both governments are regarded as Stackleberg leaders and the manufacturer acts as the follower.

3.2. Equilibrium Solutions

In this subsection, we derive the equilibrium solutions. Applying the backward induction method, we first look at the second stage where the manufacturer produces two kinds of products and determines their prices $p_s$ and $p_n$. With an effective emission cap Q, the manufacturer’s total emission is strictly constrained by the emission cap in the South, i.e., $E\le Q$. Therefore, the manufacturer’s profit maximization problem is given by

$$\begin{array}{cc}\hfill & \underset{p_s,p_n}{max}{\pi }_m,\hfill \\ \hfill & \mathrm{s}.\mathrm{t}.E\le Q.\hfill \end{array}$$

(6)

In particular, there arise two possible scenarios with the effectiveness of the emission cap. If the emission cap goes into effect to strictly limit total emission, the manufacturer’s best response must point to a full utilization of the given emission quotas so as to maximize its profit. Therefore, an effective emission cap actually functions such that the condition $E=Q$ satisfies. If not, the cap is too lax to impact the manufacturer’s production activities, which can be regarded as a cap-free or no-cap scheme.

In the first stage, the two countries take part in an announcement game by simultaneously making policy selections to maximize their respective social welfare. The optimization problems for the two governments are given by

$$\begin{array}{cc}\hfill & \underset{Q}{max}{W}_s,\hfill \end{array}$$

(7)

$$\begin{array}{cc}\hfill & \underset{\omega }{max}{W}_n.\hfill \end{array}$$

(8)

In the announcement game, each government faces two options with regard to its policy enforcement. Specifically, the South needs to decide whether or not to implement an emission cap. As mentioned, the manufacturer will fully utilize the given emission quotas if the emission cap is effective to upper-bound the total emission. Otherwise, a too lax emission cap can be equally regarded as a cap-free situation. Simultaneously, the North decides on whether or not to impose a carbon tariff. If it determines to tax the manufacturer’s exports, the tariff rate $\omega$ is positive; otherwise, a zero tariff rate actually means a tariff free policy, which can be equivalently translated as the North announcing no carbon tariff. As a result, there arise four cases in the announcement game, depending on each player’s policy selection behavior. For clarity and simplicity, we resort to the first superscript “C” or “$\overline{C}$” to present the South’s choice of enacting an emission cap or a cap-free policy, respectively; likewise, we apply the second superscript “T” or “$\overline{T}$” to state that the North sets a positive or free carbon tariff rate, respectively.

Table 1. Announcement Game for the Governments.

Policies	Carbon Tariff (T)	Tariff Free ($\overline{\mathit{T}}$)
Emission Cap ($\mathit{C}$)	($W_s^{CT},W_n^{CT}$)	($W_s^{C\overline{T}},W_n^{C\overline{T}}$)
Cap Free ($\overline{\mathit{C}}$)	($W_s^{\overline{C}T},W_n^{\overline{C}T}$)	($W_s^{\overline{C}\overline{T}},W_n^{\overline{C}\overline{T}}$)

gives a schematic representation of the announcement game between the two governments. In the following, we first analyze each of the four cases and then give the corresponding equilibrium solutions. All proofs are relegated to the Appendix A.

(1) Case $CT$: This subgame refers to the bilateral policy situation where both countries enforce their respective regulations. In particular, the manufacturer uses up the emission allowances given by the emission cap, and submits a positive carbon tariff. In Case $CT$, the sequence of events is as follows. In the first stage, the Southern regulator decides a value of the emission cap Q and the North sets a carbon tariff rate $\omega$. In the second stage, the manufacturer reacts to produce the two differentiated products, set their prices, and sell them to end consumers in the two markets. Solving first the manufacturer’s optimization problem (6), and then those of the two governments shown in (7) and (8), we obtain the equilibrium solutions in the following proposition.

Proposition 1.

When the South decides to announce an emission cap and the North determines to enforce a carbon tariff, the equilibrium emission cap and carbon tariff rate are, respectively, given by

$$\begin{array}{cc}\hfill Q^{\ast }=& \frac{2{\beta }_n{e}_s{e}_n^2({\alpha }_s{\beta }_n{e}_n^2-{\beta }_s{k}_1)-{\beta }_s^2{e}_s^3\left(3{\beta }_s{e}_s^2(e_{s}h+c_s)+k_2\right)+5{\beta }_n{\beta }_s{e}_s{e}_n^2(e_{s}h+c_s)(2{\beta }_n{e}_n^2-{\beta }_s{e}_s^2)}{({\beta }_s{e}_s^2+2{\beta }_n{e}_n^2)(3{\beta }_s{e}_s^2+2{\beta }_n{e}_n^2)},\hfill \end{array}$$

(9)

$$\begin{array}{cc}\hfill {\omega }^{\ast }=& {\displaystyle \frac{({\beta }_s{e}_s^2+2{\beta }_n{e}_n^2)\left({\alpha }_n-{\beta }_n{c}_n+\gamma (e_s-e_n)\right)-{\beta }_n{e}_n\left(2{\beta }_n{e}_n^{2}h-{\alpha }_s{e}_s+{\beta }_s{e}_s(2e_{s}h+c_s)\right)}{e_n{\beta }_n(3{\beta }_s{e}_s^2+2{\beta }_n{e}_n^2)},}\hfill \end{array}$$

(10)

and the equilibrium prices for the manufacturer are given by

$$\begin{array}{cc}\hfill p_s^{\ast }& =\frac{e_s^2(e_n\gamma +2{\alpha }_s)+e_s\left(e_n{k}_3-e_n^2{\beta }_n{\omega }^{\ast }-2Q^{\ast }\right)+e_n^2{\beta }_n{c}_s}{2({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)}+\frac{{\alpha }_s{e}_n^2{\beta }_n}{2{\beta }_s({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)},\hfill \end{array}$$

(11)

$$\begin{array}{cc}\hfill p_n^{\ast }& =\frac{{\beta }_s{e}_s^2(e_n{\omega }^{\ast }+c_n)+e_s{e}_n{k}_4-2e_n\left(e_n(e_n\gamma -{\alpha }_n)+Q^{\ast }\right)}{2({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)}+\frac{{\beta }_s{e}_s^2\left({\alpha }_n+\gamma (e_s-e_n)\right)}{2{\beta }_n({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)},\hfill \end{array}$$

(12)

where $k_i$ ($i=1-4$) can be found in the Appendix A.

Eventually, we can compute the manufacturer’s production quantities and profit, as well as the consumer surplus and social welfare in each country.

(2) Case $\overline{C}T$: This unilateral policy case indicates a tariff-only regulation for the manufacturer. Particularly, in the first stage, when announcement game occurs, the North acts to announce a positive carbon tariff rate, whereas the South determines not to ratify an emission cap. In the second stage, the manufacturer faces no emission limit, and sets its prices in response to the tax policy in the North. The following proposition concludes the equilibrium solutions under Case $\overline{C}T$.

Proposition 2.

When the South chooses not to enact an emission cap but the North decides to stick to a carbon tariff policy, the equilibrium carbon tariff rate is given by

$$\begin{array}{c}\hfill {\displaystyle {\omega }^{\ast }=\frac{{\alpha }_n-{\beta }_n{c}_n+\gamma (e_s-e_n)}{3e_n{\beta }_n},}\end{array}$$

(13)

and the equilibrium prices for the manufacturer are given by

$$\begin{array}{cc}\hfill p_s^{\ast }& {\displaystyle =\frac{{\alpha }_s+{\beta }_s{c}_s}{2{\beta }_s},}\hfill \end{array}$$

(14)

$$\begin{array}{cc}\hfill p_n^{\ast }& {\displaystyle =\frac{2{\alpha }_n+{\beta }_n{c}_n+2\gamma (e_s-e_n)}{3{\beta }_n}.}\hfill \end{array}$$

(15)

Accordingly, the equilibrium profit for the manufacturer and the social welfare for the two countries can be obtained.

(3) Case $C\overline{T}$: This subgame names another unilateral policy case under which the South effectuates an emission cap but the North determines to give up the carbon tariff. Therefore, in the stage of announcement game, only the South needs to set an effective emission cap which will be fully utilized by the manufacturer. Sequentially, the manufacturer in the second stage is merely constrained by the emission cap when maximizing its profit. We give the equilibrium emission cap for the South and the manufacturer’s pricing strategies in Proposition 3.

Proposition 3.

When the South enforces an effective emission cap and the North announces no carbon tariff, the equilibrium emission cap is given by

$$\begin{array}{cc}\hfill Q^{\ast }=& {\displaystyle \frac{2{\beta }_n{e}_n^3{k}_5-e_s{e}_n\left(e_n{k}_6-e_s{\beta }_s({\alpha }_n-{\beta }_n{c}_n+\gamma e_s)\right)+2{\beta }_s{e}_s^3\left({\alpha }_s-{\beta }_s(e_{s}h+c_s)\right)}{2({\beta }_s{e}_s^2+2{\beta }_n{e}_n^2)},}\hfill \end{array}$$

(16)

and the equilibrium prices are given by

$$\begin{array}{cc}\hfill p_s^{\ast }=& \frac{e_s^2(e_n\gamma +2{\alpha }_s)+e_s\left(e_n({\alpha }_n-{\beta }_n{c}_n-e_n\gamma )-2Q^{\ast }\right)}{2({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)}+\frac{e_n^2{\beta }_n({\alpha }_s+{\beta }_s{c}_s)}{2{\beta }_s({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)},\hfill \end{array}$$

(17)

$$\begin{array}{cc}\hfill p_n^{\ast }=& \frac{2e_n^2({\alpha }_n-e_n\gamma )+e_n\left(e_s({\alpha }_s-{\beta }_s{c}_s+2e_n\gamma )-2Q^{\ast }\right)}{2({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)}+\frac{{\beta }_s{e}_s^2\left({\alpha }_n+{\beta }_n{c}_n+\gamma (e_s-e_n)\right)}{2{\beta }_n({\beta }_s{e}_s^2+{\beta }_n{e}_n^2)},\hfill \end{array}$$

(18)

where $k_5$ and $k_6$ can be found in the Appendix A.

Consequently, the corresponding profit and production output for the manufacturer can be calculated, and the social welfare in both countries can be obtained.

(4) Case $\overline{C}\overline{T}$: This is a no-policy case, meaning that the two governments do not enforce policies in the announcement game. As such, the manufacturer faces neither a emission constraint nor a carbon tariff rate. This situation resembles Case $\overline{C}T$ except for a zero tariff rate. Therefore, the corresponding pricing strategies for the manufacturer can be derived from Proposition 2 by setting $\omega =0$.

Proposition 4.

When neither of the two governments determines to announce the environmental policies, the pricing strategies for the manufacturer are given by

$$\begin{array}{cc}\hfill p_s^{\ast }& =\frac{{\alpha }_s+{\beta }_s{c}_s}{2{\beta }_s},\hfill \end{array}$$

(19)

$$\begin{array}{cc}\hfill p_n^{\ast }& =\frac{{\alpha }_n+{\beta }_n{c}_n+\gamma (e_s-e_n)}{2{\beta }_n}.\hfill \end{array}$$

(20)

Therefore, we are able to obtain the profit for the manufacturer and the social welfare for the two governments.

Currently, an increasing number of governments and nations make collaborative efforts to abate emission, as one’s polluting behavior impacts the well-being of all nations. In the four cases above, Case $CT$ describes a bilateral policy situation where both governments enforce their respective policies, whereas others state either a unilateral environmental regulation (Case $\overline{C}T$ and Case $C\overline{T}$) or a no-policy scheme (Case $\overline{C}\overline{T}$). Under the bilateral scheme, we intend to check if the mechanism of international negotiation between the two nations is able to benefit both sides. In doing so, we follow the Nash bargaining process [30] to formulate a negotiation model as follows:

$$\begin{array}{c}\hfill \underset{\omega ,Q}{max}\{W={(W_s-W_s^{CT})}^{\rho }{(W_n-W_n^{CT})}^{1-\rho }\},\end{array}$$

(21)

where the positive parameter $\rho <1$ presents the bargaining power of the South, and $1-\rho$ stands for that of the North. The optimization problem above describes that, instead of non-cooperative movements, the South and the North collaborate to determine the policies so as to maximize the welfare product W. Note that the negotiation is based on a voluntary participation principle. That is, both governments are willing to ink a collaboration only when such an action results in well-being enhancement for each player compared with the benefits under the originally non-negotiated Case $CT$. Otherwise, any possible welfare loss for either or both sides tolerates no space for negotiation.

In a bid to check the efficiency of each subgame as well as the negotiation case, we introduce a benchmark of complete centralized scheme where the two governments and the manufacturer are assumed to be integrated as one central regulator. As a result, the total social welfare under the centralized condition, which we denote by $W_t$, sums up the social welfare from the South and the North, i.e., $W_t=W_s+W_n$. The central regulator, therefore, faces the following policy-making problem:

$$\begin{array}{c}\hfill \underset{Q,p_s,p_n}{max}{W}_t.\end{array}$$

(22)

In particular, the tax income by the carbon tariff is taken from the manufacturer’s profit to the Northern social welfare. For the central regulator, this monetary transformation occurs internally from one pocket (South) to another (North). Thus, the tariff rate becomes an exogenous parameter and will not affect the total social welfare $W_t$. On the contrary, the emission cap remains an endogenous factor to be determined by the regulator. We conclude the strategies under the centralized case in the following proposition.

Proposition 5.

Under the benchmark case where a centralized regulator maximizes total social welfare, the optimal emission cap is given by

$$\begin{array}{cc}\hfill Q^{\ast }=& e_n\left({\alpha }_n-{\beta }_n(e_{n}h+c_n)+\gamma (e_s-e_n)\right)+e_s\left({\alpha }_s-{\beta }_s(e_{s}h+c_s)\right),\hfill \end{array}$$

(23)

and the optimal prices are given by

$$\begin{array}{cc}\hfill p_s^{\ast }& =e_{s}h+c_s,\hfill \end{array}$$

(24)

$$\begin{array}{cc}\hfill p_n^{\ast }& =e_{n}h+c_n.\hfill \end{array}$$

(25)

Accordingly, the total social welfare under the centralized case can be calculated.

4. Numerical Studies

As shown in the previous section, it is difficult for us to obtain analytical analysis due to the complex expressions. Hence, we resort to numerical studies to give clear comparisons of the results. In this section, we first investigate the manufacturer’s pricing strategies and key outcomes under all the cases to provide firm-level suggestions. Sequentially, we discuss the subgame perfect Nash equilibrium (SPNE) for the announcement game, aiming to reveal the policy selection behaviors of the governments. The results contribute to give policy-setting implications. We also check the efficiency of each case and the key outcomes such as welfare and emission amount. Finally, we study whether a bilateral negotiation scheme can improve the social welfare of the two nations.

The benchmark parameter set is given as follows:

Market potentials: ${\alpha }_s=30,{\alpha }_n=25$;

Price sensitivities: ${\beta }_s=2,{\beta }_n=1.5$;

Green preference parameters: $\gamma =2$;

Unit emissions: $e_s=3$, $e_n=2$;

Unit production costs: $c_s=1$, $c_n=2$;

Emission damage degree: $h=3$;

Bargaining power: $\rho =0.4$.

This parameter set can ensure positive prices, demands, profit for the manufacturer, and social welfare for the governments.

4.1. Equilibrium Outcomes of Subgames for the Manufacturer and Governments

In this subsection, we carry out comparisons among the four cases for the manufacturer with regard to its pricing and production strategies, profits and total emissions. We also give the equilibrium solutions for the two governments to investigate their specific policy-settings.

Under the benchmark parameter setting,

Table 2. Equilibrium Outcomes for the Four Subgames.

Cases	${\mathit{p}}_{\mathit{s}}^{\ast }$	${\mathit{p}}_{\mathit{n}}^{\ast }$	${\mathit{q}}_{\mathit{s}}^{\ast }$	${\mathit{q}}_{\mathit{n}}^{\ast }$	${\mathit{\pi }}_{\mathit{m}}^{\ast }$	E	${\mathit{\omega }}^{\ast }$	${\mathit{Q}}^{\ast }$
$\mathit{CT}$	11.00	14.73	8.00	4.91	115.70	33.82	2.73	33.82
$\overline{\mathit{C}}\mathit{T}$	8.00	12.67	14.00	8.00	140.67	58.00	2.67	N/A
$\mathit{C}\overline{\mathit{T}}$	11.00	12.00	8.00	9.00	170.00	42.00	0	42.00
$\overline{\mathit{C}}\overline{\mathit{T}}$	8.00	10.00	14.00	12.00	194.00	66.00	0	N/A

summarizes the equilibrium outcomes under various environmental policy portfolios of the governments, i.e., bilateral, unilateral, or no policy cases. From Table 2, we can obtain the following results.

For one thing, imposing an emission cap in the South pulls up the two prices, shrinks demands in both markets, decreases the total emission, and eventually leads to profit loss for the manufacturer. As mentioned, given an effectively strict emission cap, which directly lowers the total emission, the profit-seeking manufacturer would always decrease the emission quotas. The total emission limitation by the cap translates to a constraint of the total production output for the manufacturer, as unit emissions of the conventional and green manufacturing are exogenous constants. Therefore, compared with a cap-free situation where the manufacturer is free to produce and emit, the manufacturer is forced to comply with the given emission cap and reduce its total production output accordingly. Note that the emission quotas generated to the manufacturer can be regarded as a limited resource to be carefully distributed to the two operating productions. Different from a cap-free scenario, an emission cap scheme gives inadequate emission allowances to the manufacturer who is best to allocate less quotas to both productions in order to achieve profit maximization. As indicated by the comparisons in the case pair ($CT$, $\overline{C}T$) or ($C\overline{T}$, $\overline{C}\overline{T}$), the manufacturer reduces sales in both markets so that the demands decrease. Correspondingly, the manufacturer has to price higher the products at home and abroad to keep its profit margins. The profit for the manufacturer, consistent with common sense, decreases as the total production output declines.

For another example, enforcing a carbon tariff in the North exerts no impact on the domestic price and sales, but pulls up the foreign price, decreases exports to North, lowers the total emission, and the manufacturer’s profit. The carbon tariff, unlike the emission cap, which directly limits the total emission and production output, functions to add monetary burden to each unit of export from the South to the North. This dampens the manufacturer’s interest of exportation and eventually shrinks the amount of exports. With fewer products distributed in the North, the manufacturer needs to tag the products at a higher foreign price to keep its profit margin. Case pair comparison ($CT$, $C\overline{T}$) or ($\overline{C}T,\overline{C}\overline{T}$) show that whether or not the North implements a carbon tariff does not unilaterally alter the manufacturer’s domestic price of the conventional products, or equivalently, demand in the local market. This suggests that the manufacturer’s best response to a carbon tariff enforcement is to constrain the negative impact on the foreign demand for the green products, while keeping domestic sales of the conventional products unaffected. As such, the manufacturer is able to at least keep profit from the local market and only suffer profit loss from exports. The corresponding domestic price stays independent to the policy selection of the North. The total emission amount, therefore, declines as total product quantity decreases.

Taking the no-policy scheme ($\overline{C}\overline{T}$) as a reference case, we aim to investigate the respective impacts of the two unilateral cases, namely, cap-only ($C\overline{T}$) and tariff-only ($\overline{C}T$) scenarios. Results show that the emission cap and carbon tariff function differently on the manufacturer. It is easy to check that a cap-only backdrop leads to less total production output, compared with a tariff-only regulation. As shown in Table 2, a no-policy environment allows the manufacturer to take a production allocation strategy $(14.00,12.00)$. When merely an emission cap comes into effect, that figure alters to $(8.00,9.00)$, revealing that the manufacturer has to lower both production quantities so as to comply with the cap policy. Specifically, the sales drops more in the South than in the North. The rationale behind this result is that given smaller emission quotas which pull down both volumes, the manufacturer prefers to cut to a greater extent the conventional output whose production process generates more emissions rather than the green manufacturing. In contrast, the tariff-only case gives rise to the product distribution of $(14.00,8.00)$. As discussed, the tariff policy will not influence the domestic sales, but merely decreases the exports. Despite that the emission cap shrinks the domestic demand greatly and pulls down the foreign sales, the manufacturer responses to tag the conventional products in the South with a higher price, that is, $p_s^{\ast }=11.00$ under $C\overline{T}$ compared with the domestic price $8.00$ under $\overline{C}T$. Therefore, the manufacturer is able to reap more profit under a unilateral cap policy. In sum, compared with a tariff-only scheme, the manufacturer’s total production volumes and emission amount decline more under a cap-only case. Accordingly, the total emission under a cap-only situation is less than its counterpart with a tariff-only scheme. The manufacturer’s profit, on another front, is higher under an emission cap policy merely.

From the perspective of the North government, the carbon tariff rate steps up if both governments decide to ratify the policies, in comparison with a tariff-only case. As seen from Cases $CT$ (bilateral policy) and $\overline{C}T$ (tariff-only policy), the equilibrium tariff rate rises from $2.67$ to $2.73$ if the South changes from a cap-free decision to an effective cap policy. As indicated in Table 2, under a bilateral case compared with a tariff-only condition, the manufacturer would sell much fewer products in the South and also lower the sales in the North. Consequently, the consumer surplus in the North decreases. As the negative effect of emission cap is considerably significant, the decrements of Northern sales and consumer surplus become obvious. Under such conditions, the best response of the North whose social welfare sums up the consumer surplus and the tariff income is to raise the tariff rate which leads to a higher margin of each export.

The standpoint of South government shows that with an effective emission cap, the South would stick to a stricter cap policy if the North ratifies a carbon tariff. Note that, as mentioned above, implementing a carbon tariff in the North will not change the domestic price and sales quantity, but merely pulls down the foreign demand. As the consumer surplus and the manufacturer’s domestic revenue are not affected, the South only needs to make a trade-off between the manufacturer’s profit from exports and the environmental damage. Our result shows that the South’s welfare-maximizing response is to tighten the emission cap so as to mitigate the emission damage.

In summary, (1) both policies increase the foreign price, and decrease exports amount, the manufacturer’s revenue, and total emission; (2) the emission cap negatively affects the domestic sales and pulls up the price in the South, however, the carbon tariff does not alter the price and product volumes in the South; (3) compared with the carbon tariff, the emission cap exerts more significant impacts on the manufacturer’s total production output while enabling the manufacturer to suffer smaller profit losses; (4) the North should legislate a tougher tariff rate once the South decides to enforce an emission cap rather than a cap-free option, and the South is advised to implement a stricter emission cap if the North moves from a tariff-free policy to a carbon tariff scheme.

4.2. Policy Selections in the Announcement Game

Until now, we have used numerical studies to derive the equilibrium solution in each subgame and make comparisons of the strategies for the manufacturer and the policy-setting for the regulators. In this subsection, we focus on the policy selections for the two welfare-maximizing governments who participate in an announcement game in the first stage. One major factor influencing the welfare of the governments points to the degree of emission damage, which is captured by parameter h. We search for the equilibrium policy selection (or the SPNE) for the two players under various values of h to measure the corresponding impacts. Besides, we introduce a negotiation scheme which is commonly seen in practice and theoretical researches to check if it is able to achieve welfare improvements for both players.

The impacts of emission damage on the Southern social welfare can be translated into multiple meanings [27]. First, it spells how the South government weighs environmental damage in its social welfare. Second, it stands for the monetary losses for the manufacturer in terms of emission during its manufacturing processes. Third, it reflects the public concern in the South about emission issues. We also provide an additional explanation that interprets h as the capability of the Southern environment to naturally absorb the carbon emitted by the manufacturer’s production activities. It is commonsense that different regions have various levels of ability to capture and decompose carbon pollution, due to the diverse geographic and environment characteristics. Therefore, we regard a higher h as a less absorptive environment in the South to deal with carbon emission. In sum, a larger value of h in the South stands for a greater weighting the government measures the emission damage in welfare, a larger amount of monetary lose for the manufacturer caused by emission, more green-sensitive consumers in the South, or a worse natural environment in terms of carbon absorption. In this subsection, we vary $h\ge 2.0$ to cover a broader range of emission damage, ceteris paribus in the benchmark setting. The reason is twofold: first, although the weighting values of other contributors in Southern welfare are normalized to 1, as shown in welfare function (3), a greater value of $h\ge 2.0$ describes the fact that developing countries are increasingly emphasizing the importance of environmental protection and emission mitigation; second, instead of a fixed $h=3.0$, as in the benchmark set of parameters, varying the value of h is able to better approximate the fact that different regions have various levels of public green awareness and natural absorption capabilities of carbon pollution.

Table 3. Social Welfare ($W_s^{\ast },W_n^{\ast }$) of the Four Cases under Different h.

Weighting	Policies	Carbon Tariff	Tariff Free
$\mathit{h}=\mathbf{2.0}$	Emission Cap Cap Free	$(67.32,55.85)$ $(73.67,64.00){}^{\ast }$	$(111.60,43.32)$ $(111.00,48.00)$
$\mathit{h}=\mathbf{2.5}$	Emission Cap Cap Free	$(46.73,44.71){}^{\ast }$ $(44.67,64.00)$	$(83.40,34.68)$ $(78.00,48.00)$
$\mathit{h}=\mathbf{3.0}$	Emission Cap Cap Free	$(30.25,34.81){}^{\ast }$ $(15.67,64.00)$	$(60.00,27.00)$ $(45.00,48.00)$

concludes the social welfare for the two governments under different policy selections in the announcement game. For each value of h, there exists a unique equilibrium selection pair (SPNE). For clarity, we mark in each example the subgame equilibrium with an asterisk from now on.

One result reveals that if the environmental damage exerts relatively moderate social impact, e.g., $h=2.0$, the social welfare of the South under the four cases is compared as $W_s^{C\overline{T}}>W_s^{\overline{C}\overline{T}}>W_s^{\overline{C}T}>W_s^{CT}$, and that of the North follows $W_n^{\overline{C}T}>W_n^{CT}>W_n^{\overline{C}\overline{T}}>W_n^{C\overline{T}}$. Under a comparatively moderate level of emission damage, the Southern welfare reaches its peak under the cap-only unilateral situation, whereas is the worst under a bilateral case. In contrast, the North enjoys highest well-being when the two governments choose a tariff-only scheme, and its lowest social welfare emerges if the South takes an emission cap but the North holds no tariff regulation. In general, each government would welcome a corresponding unilateral case where itself sticks to a policy and its partner gives up legislation. Table 3 shows the equilibrium for the announcement game, which points to a cap-free and tariff-only scenario (Case $\overline{C}T$). Notice that the equilibrium case dominates the bilateral one in terms of each participant’s benefit. In other words, the equilibrium case $\overline{C}T$ is Pareto-improving than the bilateral one for the two parties. Specifically, the North achieves its maximal welfare at the equilibrium among the four cases. Therefore, we conclude that the equilibrium of tariff-only scheme is satisfactory for both sides as the Northern social welfare peaks and the South is not the worst.

An interesting observation points to a switch of equilibrium case when the emission damage mounts to a more significant level, e.g., $h\ge 2.5$. As shown in the second and third rows in Table 3, the equilibrium of the announcement game refers to the bilateral condition where both regulators implement their respective policy. It is easy to check that for the South, the welfare is compared as $W_s^{C\overline{T}}>W_s^{\overline{C}\overline{T}}>W_s^{CT}>W_s^{\overline{C}T}$, and the Northern welfare shows $W_n^{\overline{C}T}>W_n^{\overline{C}\overline{T}}>W_n^{CT}>W_n^{C\overline{T}}$. Such results reflect the policy selection from each government’s perspective. For the South, it is always better to ratify an emission cap, regardless of what the North’s choice is. That is, effectuating an emission cap is always a dominant decision for the South. The Southern benefit drops to the lowest if it gives up the cap while the North taxes exports. By the same token, the North is always wise to choose a carbon tariff, whether the South legislates an emission cap or not. The least-wanted case for the North is that no tariff is imposed but its partner implements an emission cap. Also, the no-policy scheme is the second-best for both regulators. Therefore, we conclude that the dominate strategy or policy for the South points to always enacting an emission cap, and the best move for the North is to insist a carbon tariff. As a result, both parties are wise enough to make policy selections according to best interest of themselves, which comes to the bilateral case.

However, notice that the case of no-policy ($\overline{C}\overline{T}$) actually dominates the equilibrium bilateral one ($CT$) in terms of social welfare for both sides. In other words, the two are able to achieve Pareto improvement of welfare if they both decide to announce no policy in the game. This leads to a prisoner’s dilemma for the participants of the announcement game. Besides,

Table 4. Total Welfare under All the Subgames.

Weighting	$\mathit{CT}$	$\overline{\mathit{C}}\mathit{T}$	$\mathit{C}\overline{\mathit{T}}$	$\overline{\mathit{C}}\overline{\mathit{T}}$	Centralized Case
$\mathit{h}=\mathbf{2.0}$	$123.17$	$137.67{}^{\ast }$	$154.92$	$159.00$	$172.00$
$\mathit{h}=\mathbf{2.5}$	$91.44{}^{\ast }$	$108.67$	$118.08$	$126.00$	$133.00$
$\mathit{h}=\mathbf{3.0}$	$65.06{}^{\ast }$	$79.67$	$87.00$	$93.00$	$100.00$

shows that the total welfare under the four cases follows the order $W_t^{\overline{C}\overline{T}}>W_t^{C\overline{T}}>W_t^{\overline{C}T}>W_t^{CT}$, indicating that the no-policy accomplishes a greatest efficiency of welfare, whereas the equilibrium case is least ideal. As a result, the two governments, although trying to make their respective best selection, miss the goal of reaching a satisfactory situation for both sides. We emphasize that such prisoner’s dilemma would emerge when the emission damage becomes relatively significant (that is, $h\ge 2.5$). Also, note that we set our backdrop of the announcement game under a non-cooperative manner that the two players act simultaneously without collaboration or negotiation. In addition, comparing the total welfare under the four cases with that of the centralized case reflects the efficiency of each subgame. As seen, the efficiency decreases with increasing h. This result emphasizes the importance of cooperation between the nations, since a greater environmental damage largely hinders the efficiency of all the non-cooperative subgames in terms of welfare.

From the perspective of emission abatement, we see from

Table 5. Total Emission under the Four Subgames.

Weighting	$\mathit{CT}$	$\overline{\mathit{C}}\mathit{T}$	$\mathit{C}\overline{\mathit{T}}$	$\overline{\mathit{C}}\overline{\mathit{T}}$
$\mathit{h}=\mathbf{2.0}$	$50.84$	$58.00{}^{\ast }$	$61.20$	$66.00$
$\mathit{h}=\mathbf{2.5}$	$42.33{}^{\ast }$	$58.00$	$51.60$	$66.00$
$\mathit{h}=\mathbf{3.0}$	$33.82{}^{\ast }$	$58.00$	$42.00$	$66.00$

that total emission for the manufacturer is compared as $E^{\overline{C}\overline{T}}>E^{\overline{C}T}>E^{C\overline{T}}>E^{CT}$ if the emission damage is severe; whereas $E^{\overline{C}\overline{T}}>E^{C\overline{T}}>E^{\overline{C}T}>E^{CT}$ if the environmental impact is comparatively moderate. Notice that in the absence of an emission cap, the manufacturer’s total emission is not limited and thus is not impacted by the degree of emission damage. In other words, as shown in Table 5, the emission under $\overline{C}T$ and that under $\overline{C}\overline{T}$ remain independent to the change of h. It is easy to check that the total emission is always highest under a no-policy situation and lowest when bilateral-policy emerges. Under a no-policy scheme, the manufacturer is neither limited by emission constraint nor burdened by tariff cost. Compared with other cases, this is a most lax regulation environment for the manufacturer who will gear up to carry out manufacturing activities and outputs at greatest production quantity. Along with peak product volumes, the total emission also mounts to a highest level. On the contrary, under a bilateral case where the manufacturer has to pay tariff for exports and is forced to obey the emission cap, the production volume is smallest among all cases, which leads to a least amount of emission for the manufacturer. When the emission damage is significant, the effect of cap on emission mitigation gets more obvious so that a unilateral cap policy cuts more emission than a tariff-only regulation does. If the environmental damage is measured to be relatively moderate, e.g., $h=2$, the cap becomes less strict and the tariff exerts greater impacts on emission cut so that $E^{C\overline{T}}>E^{\overline{C}T}$ holds.

As mentioned in Section 3, there exist a variety of international environmental agreements in practice, under the framework of which several nations work together as cooperative partners to set the environmental policies [4,8,28]. In a bid to investigate a possible way out of the prisoner’s dilemma, the two governments confront when the emission damage is significant, and we follow the Nash negotiation process as in optimization problem (21).

Table 6. Equilibrium Solutions and Social Welfare under Case $CT$ and Negotiation.

Cases	${\mathit{\omega }}^{\ast }$	${\mathit{Q}}^{\ast }$	${\mathit{W}}_{\mathit{s}}^{\ast }$	${\mathit{W}}_{\mathit{n}}^{\ast }$
Without Negotiation	$2.73$	$33.82$	$30.25$	$34.81$
With Negotiation	$0.13$	$65.87$	$42.75$	$49.79$

gives the equilibrium solutions under the original bilateral and the negotiation scenarios as well as the social welfare of the governments.

Table 7. Social Welfare in Four Cases after Negotiation of $CT$.

Policies	Carbon Tariff	Tariff Free
Emission Cap	$(42.75,49.79){}^{\ast }$	$(60.00,27.00)$
Cap Free	$(15.67,64.00)$	$(45.00,48.00)$

replaces the proceeding bilateral case with the one after negotiation, aiming to check the possible impact of negotiation on the policy selections of the governments.

As shown in Table 6, the tariff rate after negotiation largely drops from $2.73$ to $0.13$, whereas the emission cap significantly jumps from $33.82$ to $65.87$. Recall that in the preceding analysis, each government should tighten its policy if the partner determines to impose the respective policy. However, we show that the negotiation actually asks both sides to take a step back so as to ink a cooperation. Put differently, the South lifts up its emission cap and the North enforces light tariff. The two governments achieve a Pareto improvement, that is, a win–win situation in terms of welfare under the negotiation framework. Further, the negotiation not only enhances the benefits of both sides compared with the original bilateral case, but also enlarges the Northern welfare to an extent that outperforms that in the no-policy scheme, as indicated in Table 7. Moreover, the efficiency of the bilateral case after negotiation increases to $92.54\%$, which approaches the highest efficiency ($93\%$ under the no-policy scenario) among those of all the subgames. Besides, the total emission ($E=65.87$) is less than that under a no-policy condition ($E=66.00$). We conclude that the negotiation is able to help the governments out of the prisoner’s dilemma, achieve Pareto improvement in welfare and slightly mitigate total emission. This result serves to voice our theoretical supports to the prevalent application of international environmental cooperation.

To sum up, we conclude, first of all, that equilibrium policy selection of the governments depends on the degree of emission damage in the South: A moderate level of damage generates equilibrium of the unilateral tariff policy where the Northern welfare peaks and Southern well-being is not worst; a high level of damage leads to a prisoner’s dilemma as the two regulators would arrive at a bilateral-policy scenario, which is dominated by a no-policy scheme. Second, a negotiation between the two regulators is able to help out of the dilemma and achieve welfare Pareto-improvement.

5. Conclusions

Rapid industrial development in developing countries has contributed to a significant surge the social economy; meanwhile, it also causes serious damage to the global environment that lower the well-being of societies. The transboundary nature of pollution, carbon emission in particular, calls for joint efforts to abate emission, which involve activities from both the developing and developed nations as well as the polluting manufacturers. In this paper, we base the research backdrop on a typical “North–South” framework, which includes a developed nation (North), a developing country (South), and a manufacturer in the South. Market preferences are differentiated by consumers: the ones in the North are more green conscious and less price-sensitive than those in the South. Accordingly, the manufacturer carries out dual-mode operation so that conventional products are distributed locally and green products are exported to the North.

We establish a two-stage game between the governments and the manufacturer. The governments are Nash game players at first, and act as Stackleberg leaders to regulate the manufacturer’s production activity in a later stage. In the first phase, the two welfare-maximizing governments participate in an announcement game where each decides on whether or not to enforce the respective environmental policy, namely, an emission cap in the South and a carbon tariff on exports in the North. In the second stage, the manufacturer as a Stackleberg follower reacts to set prices of the products which reflect its production allocation strategy. There emerge four possible subgames in the announcement game, depending on the governments’ policy selections. We derive the equilibrium solution for each subgame by applying backward induction. Sequentially, we search for the subgame perfect Nash equilibrium for the announcement game. Several main conclusions are drawn from numerical examples to give firm-level suggestions and policy-setting implications.

First, the emission cap and carbon tariff both decrease the manufacturer’s production output, emission, and profit. Relative to the carbon tariff, the emission cap has great negative impacts on the manufacturer’s total output but it enables the manufacturer to suffer smaller profit losses. Also, the emission cap makes the output of the conventional products drop more than that of the green products, whereas the carbon tariff has no impact on production output of the conventional products. These results bring some inspiring ideas for the governments about how to control manufacturers’ output for the conventional products. They should enforce an emission cap and encourage manufacturers to carry out product innovation and produce greener products.

Second, the North should legislate a tougher tariff rate once the South enforces an emission cap rather than a cap-free option, and the South is advised to implement a stricter emission cap if the North moves from a tariff-free policy to a carbon tariff scheme. This result indicates that the governments in different countries should enforce rigorous policies simultaneously; if one government, as an exception, adopts lax regulations, its social welfare would be greatly hurt.

Third, the degree of emission damage plays a paramount role in the policy selection behaviors of the regulators. With a moderate environmental damage caused by emission, the subgame equilibrium falls into the cap-free and tariff-only case, where the North is able to notch up its maximal welfare and the Southern welfare is not the worst. The total emission in equilibrium is less than those under the cap-only and no-policy scenarios. However, when the emission damage is severe, the equilibrium refers to the bilateral case where both governments stick to their policies. Under such conditions where the total emission is the least, the two governments are confronted with a prisoner’s dilemma, as a no-policy scheme dominates the equilibrium of bilateral-policy situation. One way out of the dilemma is to utilize a negotiation mechanism, which enables the two governments to decide the policies in a cooperative manner and to accomplish Pareto-improvement in terms of welfare. These results imply that the government who is responsible for firms’ emissions should investigate the degree of emission damage for each firm, differentiate the firms according to the corresponding degree of emission damage, and choose a reasonable emission policy. What is more, our results highlight the importance of international cooperation in emissions reduction. It is advisable for more countries to join collaborative efforts to protect environment, as done in practice.

Our research is mainly based on several assumptions. Relaxing some of these assumptions provides the foundation for some directions for future researches. First, this work sets its background to be in a short-term and static policy environment where both the emission cap and the carbon tariff rate are fixed. In the long run, however, we observe that governments are strengthening the regulations so that emission cap becomes more stringent periodically and the tariff rate is also subject to change. One future work may point to study the impacts of policy updates on the manufacturer’s production activities. Second, we assume, in this paper, that the manufacturer has already held two mature manufacturing technologies and product lines. However, for some of producers in developing countries, this is not always the case, as they usually lack of technology advantage. Initiating green technology asks for a comprehensive consideration of set-up cost, risk of innovation failure, and so on. Therefore, it would be interesting to check if the manufacturer has the option to pick merely one technology or to adopt a mix production strategy. Last but not least, the demand in both market is known for the manufacturer so that a make-to-order scheme applies. Practically, the demands for green products in a foreign market sometimes remain unclear for the manufacturer. This points to one of the future works for us to involve demand uncertainty in our model to better approximate reality.