The Optimal Strategy of China’s Plastic Drinking Straws Ban Based on Consumer Heterogeneity and Retailer Competition

Abstract

The Chinese government has issued a new “Plastic Restriction Ban” requiring that, by the end of 2020, the food and beverage industry across the country bans the use of single-use, nondegradable plastic drinking straws. The governance of plastic drinking straws is a multi-dimensional and complex process. Therefore, based on the heterogeneity of consumers, this paper constructs a tripartite game model (the government, retailers, and consumers) for the governance of plastic drinking straws in China. Under this model, this research derives an optimal strategy in both monopoly and competitive markets, assuming the government has access to two policy tools, fines and subsidies. The research results suggest the following. (1) In monopoly markets, when (a) the fine or subsidy fee is high or (b) the fine or subsidy fee is low and the number of environment-conscious consumers is high, retailers are more inclined to provide biodegradable drinking straws. (2) Consumer heterogeneity has a certain impact on policy results; when there are enough environment-conscious consumers, policy costs can be reduced. (3) For high-quality products, the policy costs in competitive markets is lower than in monopoly markets; for low-quality products, the policy costs in competitive markets is higher than in monopoly markets. Based on the conclusions, this work suggests the government should focus on cultivating consumers’ environmental awareness and tighter control of products quality, in addition to the two policy tools, i.e., fines and subsidies, because these can reduce policy costs. Consumers should be aware of their own importance to China’s Plastic Drinking Straws Ban and adopt a refusal to accept plastic drinking straws and reduce the consumption of disposable plastics to support the policy. Retailers should also realize that proactively catering to consumer and government expectations can bring higher benefits to themselves; this can be achieved by providing high-quality biodegradable straws to support China’s Plastic Drinking Straws Ban. The model of this work could be applied to other corporate activities related to sustainability, such as plastic bags, plastic bottles, etc., and their connection to government policies.

1. Introduction

What have we learned from pulling a straw out of a turtle’s nose [1]? Plastic waste has gained global attention due to growing concerns about its impact on human and environmental health [2]. In 2019, around 32.4 million straws were collected during natural environment cleaning operations, 90% of which were of the single-use plastic variety. Plastic drinking straws are the fifth largest category of items collected in trash, in the absolute number of items [3]. Single-use plastic products have become an indispensable part in our daily lives. The National Park Service reckons that an American uses an average of 1.6 straws daily, while U.S. citizens consume no fewer than 500 million plastic drinking straws every day [4]. The management of single-use nondegradable plastic drinking straws (referred to as ‘plastic drinking straws’ hereafter) is crucial to environmental protection because they are likely to leak into the environment [5] due to their small and light nature, at all stages of use and disposal; spillover can still occur during transportation even after they are placed in a garbage bin [6]. Among the sustainable development goals (SDGs) proposed by the United Nations in 2015 [7], clean water and sanitation (SDG 6), responsible consumption and production (SDG 12), climate action (SDG 13), life below water (SDG 14), and life on land (SDG 15) were all related to plastic drinking straws.

The Chinese government realized the severity of the environmental problem caused by plastic drinking straws and enacted a policy on 16 January 2020, which required that, by the end of 2020, plastic drinking straws should be banned in the food and beverage industry nationwide (referred to as ‘The Ban’ hereafter) [8]. For the government, it has adopted policy tools such as subsidies and fines. Under the fine strategy, retailers who continue to provide plastic drinking straws will be punished once found out. For example, on 18 June 2021, Shanghai Municipal Market Supervision Bureau imposed an administrative fine of CNY 10,000 on a catering retailer for continuing to provide disposable plastic drinking straws. Under the subsidy strategy, subsidies are given to firms that produce biodegradable drinking straws. For example, on 9 May 2021, the National Development and Reform Commission issued the “Pollution Control and Energy Conservation and Carbon Reduction Investment Special Management Measures within the Central Budget”, which clearly stated that it should focus on supporting biodegradable drinking plastic projects.

Disruptive technologies often have the potential of unleashing the full potential of environmental sustainability [9]. Unfortunately, biodegradable plastics (e.g., biodegradable straws) received a cold welcome. After the issue of The Ban, many retailers started to provide biodegradable drinking straws. However, this has caused a lot of controversy. While compared with plastic drinking straws, biodegradable drinking straws received negative feedback from lots of consumers due to their bad user experience (unstable properties [10], easy to dissolve [11], water sensitivity [12], etc.), and many intensive complaints about them were posted on Weibo (a Chinese website similar to Twitter). The tweets tagged under this topic were viewed as many as 100 million times [13]. For retailers, some of them actively respond to national policies and only provide biodegradable drinking straws, while others still provide plastic drinking straws in order to reduce costs and satisfy consumer experience of using straws. For consumers, consumers’ attitudes towards environmental protection are also heterogeneous. Many consumers support The Ban. According to the consumers survey (The authors conducted two surveys to gather the feedbacks from retailers and consumers on The Ban from April to June in 2021.) of 1984, among consumers in Zhejiang Province, 36.9% of them said they would expose retailers that still provide plastic drinking straws to the government. On the other hand, many consumers are unwilling to use them because of bad experiences using biodegradable drinking straws. Therefore, a tripartite game has evolved among consumers, retailers, and the government regarding The Ban. Considering consumer heterogeneity and monopoly and competitive retailer markets, how the government adopts the two policy tools of fines and subsidies to achieve the equilibrium strategy of the tripartite is of great significance to the realization of The Ban and the substitution of single-use plastic products in China.

Various studies have investigated the plastic problem. The literature examining this can generally be divided into three categories:

(1).

The environmental impact caused by drinking straws. For instance, Zanghelini et al. [14] used a comparative life cycle assessment (LCA) to assess the potential environmental impacts of six different types of drinking straws (plastic, stainless steel, glass, paper, bamboo, and jute). Lin and Chen [15] used the LCA to compare sustainability of plastic and stainless-steel straws and their results showed that plastic straws are more sustainable than stainless steel straws. Gregory [16] showed that plastic debris can harm or even kill an organism via entanglement, ingestion, or smothering. Roy et al. [2] studied the evolution of drinking straws and their environmental, economic, and societal implications. Chitaka et al. [17] compared the environmental impact of five straw material options in South Africa by LCA. However, those papers are in the environmental science field and focus on plastic drinking straws’ environmental impact. They ignore the social impact of environmental policies in the tripartite game behavior of the government, consumers, and retailers.

(2).

The use of game models to study environmental issues. For example, Mondal and Giri [18] discussed the investigating strategies of a green closed-loop supply chain for substitutable products under a government subsidy based on game theory. Barman et al. [19] studied the optimal pricing and greening strategy in a competitive green supply chain. Ma et al. [20] used a time-based pricing game in a competitive vehicle market regarding the intervention of carbon emission reduction. Ju et al. [21] used a tripartite evolutionary game to study the evolution of stakeholders’ behavioral strategies in the ecological compensation mechanism for poverty alleviation. Sun et al. [22] studied regional cooperation in the marine plastic waste cleanup initiative in the South Sea region. There are also studies that consider the heterogeneity of consumers. For instance, Meng et al. [23] considered consumer heterogeneity, and their results showed that the proportion of a green consumer increase can lead to the improvement of environmental and economic benefits, along with social welfare. Unfortunately, these studies did not consider the heterogeneity of consumers and competition among businesses while studying problems around the substitution of plastic products in China.

(3).

The governance of plastic drinking straws and other single-use plastic products. Fanini and Guittard [6] conducted an investigation into the discarding of disposable plastic straws before the ban on the tourist beaches of Crete. Neto et al. [24] analyzed 363 regulations enacted in 62.8% of American countries in terms of straw bans. Vince and Hardesty [25] analyzed local and global governance pertaining to plastic pollution around coastal environments. Wagner [26] examined 271 local government ordinances in the USA implemented to reduce single-use shopping bags. Nonetheless, none of them studied government policies and pollution control in relation to plastic drinking straws in China.

Therefore, this work establishes a tripartite game model, involving the government, retailers, and consumers, to explore the equilibrium strategy in both monopoly and competitive markets, assuming that the government has access to fines and subsidies as policy tools and that consumers are heterogeneous. In terms of current knowledge, this work makes the following contributions: (1) it presents a tripartite game model to analyze the equilibrium strategy of The Ban; (2) it includes consumer heterogeneity and retailer competition in deriving the equilibrium strategy of The Ban; and (3) to our best knowledge, this is the first work to discuss the impact of The Ban on consumers and retailers in China.

This paper makes several useful arguments. First, it provides a game model to study the effects of consumers type on government policy under different markets and then addresses the issue of what straws—plastic drinking straws or biodegradable drinking straws—retailers should provide to maximize their profits under different policies. The results show that the government’s subsidy strategy is always more beneficial for retailers than the fine strategy. This means that retailers are more willing to cooperate with the policy implementation, thus enabling the government to achieve its policy goals under the subsidy strategy.

Second, what straws the retailer would provide depends on the policy fee and consumer types. Specifically, retailers are more inclined to provide biodegradable drinking straws when (a) policy fees are high enough for monopoly markets and competitive markets or (b) policy fees are low but there are enough environment-conscious consumers for a monopoly market. Therefore, the government can increase subsidies and fines and/or educate consumers to increase their environmental awareness. In other words, the number of environment-conscious consumers and government policy measures are complementary.

Third, this study also shows the robustness of the model in this paper and finds that, when the quality of a product is high, the fine and subsidy costs in competitive markets are lower than those in monopoly markets. This means that, for high-quality products, competitive markets replace government policies to a certain extent. Consequently, in order to cut expenditure on policy implementation, the government should advocate competition among retailers for high-quality products.

The rest of the paper is organized as follows. Section 2 introduces a problem description. A tripartite game model is built in Section 3. Section 4 shows the results and discussion. The paper is concluded in Section 5.

2. Statement of the Problem and Formulation

2.1. Strategies of Players

Around The Ban, there are three players in the game: the government, retailers, and consumers (Figure 1).

First, the government decided to adopt two policy tools, subsidies and fines. That is, subsidies are provided to producers that produce biodegradable drinking straws and then reduce retailers’ purchasing cost of biodegradable drinking straws, while fines are imposed on retailers that provide plastic drinking straws. Government policy will directly affect retailers’ decisions and indirectly affect consumer decisions.

Second, in monopoly or competitive markets, retailers decide which kind of straws to use and inform consumers of the corresponding product price when providing different types of straws. Retailers’ decisions will affect the policy results and the consumers’ decisions.

Finally, consumers with different environmental preferences decide whether to buy products with different types of straws. Consumers’ decisions will affect policy results and retailers’ profits.

2.2. Government’s Strategies

The government should consider the lower cost of plastic drinking straws before implementing The Ban. Therefore, the government adopts policy tools to push forward using biodegradable drinking straws. This model considers the impact of two policy tools of government policy on plastic and biodegradable drinking straws. The two policy tools are advocated for by providing biodegradable drinking straws. One is a fine, $f\ge 0$, which a retailer will be issued for providing plastic drinking straws, a fine that they must pay to the government. Let $\mu \in \left[0,1\right]$ be the probability of detection for retailers using plastic drinking straws. Another is a subsidy, $s\ge 0$, on biodegradable drinking straw production. This subsidy policy would affect the purchasing cost of biodegradable drinking straws for retailers.

2.3. Retailers’ Strategies

This model considers monopoly and competitive markets. Two retailers, 1 and 2, provide horizontally differentiated products with quality $v$ at price $p_{ijk}$, where $i=\left\{1,2\right\}$, $j=\left\{B,P\right\}$, $k=\left\{f,s\right\}$. Let the cost of the product be $c$. It is worth noting that the constant product costs do not affect retailer decisions when choosing straws. Thus, we normalize $c=0$ to simplify our model. Because the products of two retailers have different brand characteristics, consumers are heterogeneous in their product preferences. Consumers’ product preference $x$ is uniformly distributed along a unit line [27], with retailer 1 located at 0 and retailer 2 located at 1. A continuum of consumers of measure 1 is uniformly distributed along the line. The products all need to be sold with drinking straws, such as pearl milk tee, a very popular beverage in China.

After The Ban, retailers would choose to provide plastic drinking straws or biodegradable drinking straws. The quality of one plastic drinking straw and that of one biodegradable drinking straw is denoted as 1 and $q$, respectively, where $q<1$. The reason for this is that consumers have better experiences using plastic drinking straws. This is why the tag “the reason I hate paper straws” was read over 100 million time [12]. The cost of one plastic drinking straw and that of one biodegradable drinking straw is denoted as $c_2$ and $c_1$, respectively, where $c_2<c_1$. This assumption is identical to the realistic market. According to Chinese official media reports, the cost of biodegradable drinking straws is 3–5 times higher than that of plastic drinking straws [28].

2.4. Consumers’ Strategies

Consumers are one of the important players in environmental policy [29]. The model assumes two segments of consumers. The first segment is environment-conscious consumers, and the fraction of such consumers is $1-\alpha$. This segment agrees with The Ban and considers the use of plastic drinking straws to be morally unacceptable. Therefore, these consumers absolutely do not buy product with plastic drinking straws. According to the consumers survey, 36.6% and 30.5% of consumers chose the “relatively support” and “very support categories”, respectively. The environment-conscious consumers believe that environmental awareness needs to start from themselves, and plastic drinking straws should not be used because they cause environmental problems. The other segment of consumers is environment-oblivious consumers who may buy products with plastic drinking straws. The fraction of this segment is $\alpha$. There are 3.6%, 4.1%, and 29.9% of consumers who chose “not support at all”, “not very support”, and “general support” categories, respectively. This segment of consumers does not agree with The Ban, and their environmental awareness is not strong. Each consumer uses at most one unit of product. Particularly, in this model, the straws only affect the consumer experience but do not affect the consumer preferences for a retailer’s product.

3. Research Model

This model focuses on the optimal strategy of The Ban based on consumers’ experience and environmental awareness. This paper analyzes consumer behavior under different retailer strategies. The utility that a consumer derives from a product is the product of the quality plus the experience from the straw net products price net product misfit cost. This misfit cost depends on the distance between consumer location and the given retailer, and let $t$ be the unit misfit cost.

Table 1. Notations.

Notations	Explanations
$v$	Product valuation
1	Quality of one plastic drinking straw
$q$	Quality of one biodegradable drinking straw
$\alpha$	Fraction of environment-oblivious consumers
$s$	Subsidy fee of one biodegradable drinking straw
$\mu$	Probability of being detected for using plastic drinking straws
$f$	Fine fee for using plastic drinking straws when the retailer has been detected
$t$	Unit misfit cost
$c_1$	Cost of one biodegradable drinking straw for retailer
$c_2$	Cost of one plastic drinking straw for retailer
$p_{ijk}$	The product price for retailer $i$ with straw $j$ under policy $k$
$D_{ijk}$	The product demand for retailer $i$ with straw $j$ under policy $k$
${\pi }_{ijk}$	The profit for retailer $i$ with straw $j$ under policy $k$

shows the notations and explanations in this model.

3.1. Optimal Pricing Decision in Monopoly Markets

The consumer utility in terms of buying a product with biodegradable drinking straws from retailers 1 is

$$U_1=v+q-t{\mathrm{x}}_{1B}-{\mathrm{p}}_{1B}$$

(1)

The consumer utility of buying a product with plastic drinking straws from retailers 1 is

$$U_2=v+1-t{\mathrm{x}}_{1P}-{\mathrm{p}}_{1P}$$

(2)

The consumer will purchase a product that generates a net utility no less than a certain reservation value, which is normalized to zero. By calculating $U_1\ge 0$ and $U_2\ge 0$, it derives that $x_{1B}^{\ast }\le \left(v+q-p_{1B}\right)/t$ and $x_{1P}^{\ast }\le \left(v+1-p_{1P}\right)/t$. Because the fraction of environment-conscious consumers is $1-\alpha$, the fraction of environment-oblivious consumers is $\alpha$. That is, the demand of retailer 1 with biodegradable drinking straws is $\left(v+q-p_1\right)/t$, while the demand of retailer 1 with plastic drinking straws is $\alpha \left(v+1-p_2\right)/t$.

3.1.1. Optimal Pricing Strategy under Fine Policy

Under the fine policy, retailer 1′s profit with biodegradable drinking straws is

$${\pi }_{1Bf}=\left(p_{1Bf}-c_1\right)D_{1Bf}$$

(3)

Retailer 1′s profit with plastic drinking straws is

$${\pi }_{1Pf}=\left(p_{1Pf}-c_2\right)D_{1Pf}-\mu f$$

(4)

Solving the prices $p_{1Bf}$ and $p_{1Pf}$ maximizes the retailer’s profits, respectively. Based on the best response functions, it derives the equilibrium prices. Then, it derives the equilibrium profits by substituting the equilibrium prices into the profit functions. The equilibrium results are stated as follows: the equilibrium prices:

$$p_{1Bf}^{\ast }=\left(v+q+c_1\right)/2, p_{1Pf}^{\ast }=\left(v+1+c_2\right)/2$$

the equilibrium demands:

$$D_{1Bf}^{\ast }=\left(v+q-c_1\right)/2t,D_{1Pf}^{\ast }=\alpha \left(v+1-c_2\right)/2t$$

the equilibrium profits:

$${\pi }_{1Bf}^{\ast }=\frac{{\left(v+q-c_1\right)}^2}{4t},{\pi }_{1Pf}^{\ast }=\frac{\alpha {\left(v+1-c_2\right)}^2}{4t}-\mu f$$

3.1.2. Optimal Pricing Strategy under Subsidy Policy

Under subsidy policy, retailer 1′s profit with biodegradable drinking straws is

$${\pi }_{1Bs}=\left(p_{1Bs}-c_1+s\right)D_{1Bs}$$

(5)

Retailer 1′s profit with plastic drinking straws is

$${\pi }_{1Ps}=\left(p_{1Ps}-c_2\right)D_{1Ps}$$

(6)

By solving the profit maximization, it derives the equilibrium results as follows:

the equilibrium prices:

$$p_{1BS}^{\ast }=\left(v+q+c_1-s\right)/2,p_{1PS}^{\ast }=\left(v+1+c_2\right)/2$$

the equilibrium demands:

$$D_{1BS}^{\ast }=\left(v+q-c_1+s\right)/2t,D_{1PS}^{\ast }=\alpha \left(v+1-c_2\right)/2t$$

the equilibrium profits:

$${\pi }_{1BS}^{\ast }=\frac{{\left(v+q-c_1+s\right)}^2}{4t},{\pi }_{1PS}^{\ast }=\frac{\alpha {\left(v+1-c_2\right)}^2}{4t}$$

3.2. Optimal Pricing Strategies in Competitive Markets

In competitive markets, this model analyzes the fully covered market of how one retailer responds to another retailer who obeys The Ban. Without a loss of generality, the model assumes retailer 1 obeys the policy that only provides biodegradable drinking straws, and retailer 2 chooses to provide biodegradable drinking straws or plastic drinking straws. In this case, the consumer utility of buying a product with biodegradable drinking straws from retailer 1 is

$$U_1=v+q-tx-{\mathrm{p}}_{1B}$$

(7)

The consumer utility of buying a product from retailer 2 is

$$U_2=\{\begin{array}{c}v+1-t\left(1-x\right)-p_{2P, }providing plastic straws\\ v+q-t\left(1-x\right)-p_{2B}, providing biodegradable drinking straws\end{array}$$

(8)

In this case, if only one retailer provides biodegradable drinking straws and the other provides plastic drinking straws, environment-conscious consumers purchase the product with providing biodegradable drinking straws. For environment-oblivious consumers, it derives the indifference point $x^{\ast }=\left(t-\Delta v-p_{1B}+p_{2P}\right)/2t$ by calculating $U_1=U_2$, where $\Delta v=1-q$. Therefore, the product demands for two retailers are

$$\{\begin{array}{c}{D}_{1B}=\alpha \left(\left(\mathrm{t}-\Delta \mathrm{v}-{\mathrm{p}}_{1B}+{\mathrm{p}}_{2P}\right)/2\mathrm{t}\right)+1-\alpha \\ D_{2P}=\alpha \left(1-\left(\mathrm{t}-\Delta \mathrm{v}-{\mathrm{p}}_{1B}+{\mathrm{p}}_{2P}\right)/2\mathrm{t}\right)\end{array}$$

(9)

If two retailers provide biodegradable drinking straws for consumers, it derives the indifference point $x^{\ast }=\left(\mathrm{t}-{\mathrm{p}}_{1B}+{\mathrm{p}}_{2B}\right)/2\mathrm{t}$ by calculating $U_1=U_2$. Therefore, the product demands for two retailers are

$$\{\begin{array}{c}{D}_{1B}=\left(t-{\mathrm{p}}_{1B}+{\mathrm{p}}_{2B}\right)/2t\\ D_{2B}=1-\left(t-{\mathrm{p}}_{1B}+{\mathrm{p}}_{2B}\right)/2t\end{array}$$

(10)

3.2.1. Optimal Pricing Strategies under Fine Policy

(1) When the two retailers provide different straws under the fine policy, the two retailers profits are

$$\{\begin{array}{c}{\pi }_{1Bf}=\left(p_{1Bf}-c_1\right)D_{1Bf}\\ {\pi }_{2Pf}=\left(p_{2Pf}-c_2\right)D_{2Pf}-\mu f\end{array}$$

(11)

By solving the profit maximization problem, it derives the equilibrium results as follows:

The equilibrium prices are

$$\{\begin{array}{c}{p}_{1Bf}^{\ast }=\frac{2\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t}{3\alpha }\\ p_{2Pf}^{\ast }=\frac{\alpha c_1+2\alpha c_2+\alpha t+\alpha \Delta v+2t}{3\alpha }\end{array}$$

(12)

The equilibrium demands are

$$\{\begin{array}{c}{D}_{1Bf}^{\ast }=\frac{-\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t}{6t}\\ D_{2Pf}^{\ast }=\frac{\alpha c_1-\alpha c_2+\alpha t+\alpha \Delta v+2t}{6t}\end{array}$$

(13)

The equilibrium profits are

$$\{\begin{array}{c}{\pi }_{1Bf}^{\ast }=\frac{{(-\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t)}^2}{18\alpha t}\\ {\pi }_{2Pf}^{\ast }=\frac{{(\alpha c_1-\alpha c_2+\alpha t+\alpha \Delta v+2t)}^2}{18\alpha t}-\mu f\end{array}$$

(14)

(2) When the two retailers provide biodegradable drinking straws under the fine policy, the two retailers’ profits are

$$\{\begin{array}{c}{\pi }_{1Bf}=\left(p_{1Bf}-c_1\right)D_{1Bf}\\ {\pi }_{2Bf}=\left(p_{2Bf}-c_1\right)D_{2Bf}\end{array}$$

(15)

By solving the profit maximization problem, it derives the equilibrium results as follows:

The equilibrium prices are

$$\{\begin{array}{c}{p}_{1Bf}^{\ast }=v+q-t/2\\ p_{2Bf}^{\ast }=v+q-t/2\end{array}$$

(16)

The equilibrium demands are

$$\{\begin{array}{c}{D}_{1Bf}^{\ast }=1/2\\ D_{2Bf}^{\ast }=1/2\end{array}$$

(17)

The equilibrium profits are

$$\{\begin{array}{c}{\pi }_{1Bf}^{\ast }=\left(2v+2q-2c_1-t\right)/4\\ {\pi }_{2Bf}^{\ast }=\left(2v+2q-2c_1-t\right)/4\end{array}$$

(18)

3.2.2. Optimal Pricing Strategies under Subsidy Policy

(1) When the two retailers provide different straws under the subsidy policy, the two retailers profits are

$$\{\begin{array}{c}{\pi }_{1Bs}=\left(p_{1Bs}-c_1+s\right)D_{1Bs}\\ {\pi }_{2Ps}=\left(p_{2Ps}-c_2\right)D_{2Ps}\end{array}$$

(19)

By solving the profit maximization problem, it derives the equilibrium results as follows:

The equilibrium prices are

$$\{\begin{array}{c}{p}_{1Bs}^{\ast }=\frac{2\alpha c_1+\alpha c_2-2\alpha s-\alpha t-\alpha \Delta v+4t}{3\alpha }\\ p_{2Ps}^{\ast }=\frac{\alpha c_1+2\alpha c_2-\alpha s+\alpha t+\alpha \Delta v+2t}{3\alpha }\end{array}$$

(20)

The equilibrium demands are

$$\{\begin{array}{c}{D}_{1Bs}^{\ast }=\frac{\alpha s-\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t}{6t}\\ D_{2Ps}^{\ast }=\frac{\alpha c_1-\alpha c_2-\alpha s+\alpha t+\alpha \Delta v+2t}{6t}\end{array}$$

(21)

The equilibrium profits are

$$\{\begin{array}{c}{\pi }_{1Bs}^{\ast }=\frac{{(\alpha s-\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t)}^2}{18\alpha t}\\ {\pi }_{2Ps}^{\ast }=\frac{{(\alpha c_1-\alpha s-\alpha c_2+\alpha t+\alpha \Delta v+2t)}^2}{18\alpha t}\end{array}$$

(22)

(2) When the two retailers provide biodegradable drinking straws under the subsidy policy, the two retailers profits are

$$\{\begin{array}{c}{\pi }_{1Bs}=\left(p_{1Bs}-c_1+s\right)D_{1Bs}\\ {\pi }_{2Bs}=\left(p_{2Bs}-c_1+s\right)D_{2Bs}\end{array}$$

(23)

By solving the profit maximization problem, it derives the equilibrium results as follows:

The equilibrium prices are

$$\{\begin{array}{c}{p}_{1Bs}^{\ast }=v+q-t/2\\ p_{2Bs}^{\ast }=v+q-t/2\end{array}$$

(24)

The equilibrium demands are

$$\{\begin{array}{c}{D}_{1Bs}^{\ast }=1/2\\ D_{2Bs}^{\ast }=1/2\end{array}$$

(25)

The equilibrium profits are

$$\{\begin{array}{c}{\pi }_{1Bs}^{\ast }=\left(2v+2q-2c_1+2s-t\right)/4\\ {\pi }_{2Bs}^{\ast }=\left(2v+2q-2c_1+2s-t\right)/4\end{array}$$

(26)

The equilibrium payoff matrix in fully covered market is summarized in

Table 2. Equilibrium payoff matrix in competitive markets.

Fine Policy/Subsidy Policy	Retailer 2
Retailer 1 with biodegradable drinking straws	Biodegradable Drinking Straws	Plastic Drinking Straws
	$\{\begin{array}{c}{\pi }_{1Bf}^{\ast }=\left(2v+2q-2c_1-t\right)/4\\ {\pi }_{2Bf}^{\ast }=\left(2v+2q-2c_1-t\right)/4\end{array}$	$\{\begin{array}{c}{\pi }_{1Bf}^{\ast }=\frac{{(-\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t)}^2}{18\alpha t}\\ {\pi }_{2Pf}^{\ast }=\frac{{(\alpha c_1-\alpha c_2+\alpha t+\alpha \Delta v+2t)}^2}{18\alpha t}-\mu f\end{array}$
	$\{\begin{array}{c}{\pi }_{1Bs}^{\ast }=\left(2v+2q-2c_1+2s-t\right)/4\\ {\pi }_{2Bs}^{\ast }=\left(2v+2q-2c_1+2s-t\right)/4\end{array}$	$\{\begin{array}{c}{\pi }_{1Bs}^{\ast }=\frac{{(\alpha s-\alpha c_1+\alpha c_2-\alpha t-\alpha \Delta v+4t)}^2}{18\alpha t}\\ {\pi }_{2Ps}^{\ast }=\frac{{(\alpha c_1-\alpha s-\alpha c_2+\alpha t+\alpha \Delta v+2t)}^2}{18\alpha t}\end{array}$

.

4. Results and Discussion

4.1. Equilibrium Results in Monopoly Markets

Proposition 1.

The optimal price when using biodegradable drinking straws decreases as the subsidy fee increases but is invariant to the change in fine fee. In addition, the product price decreases more slowly than the subsidy fee, in the sense that$\frac{dp}{ds}>-1$.

All proofs are available in the Appendix A. Proposition 1 shows that the subsidy policy would affect a product’s price, but the fine policy does not. Specifically, when the subsidy fee rises by USD 1, the retailer decreases the price, but by less than USD 1. The subsidy policy reduces product price and then encourages potential consumers to switch from buying nothing to buying, thus increasing the retailer’s profit.

Proposition 2.

In the monopoly setting, providing a subsidy strategy is more beneficial for the retailer than providing a fine strategy in terms of whether the retailer provides biodegradable or plastic drinking straws.

Proposition 2 compares the equilibrium profit under the subsidy strategy and the fine strategy. The intuitive result shows that providing a fine strategy would make the retailer obtain less profit. In fact, the subsidy strategy is an incentive policy, while the fine strategy is a penalty policy. This means that the retailer prefers the incentive policy rather than penalty policy.

Proposition 3.

In the monopoly setting, the profit differentiation between subsidy policy and fine policy from providing biodegradable drinking straws is higher than that from providing plastic drinking straws if and only if the quality of biodegradable drinking straws is high (i.e.,$q>\frac{4t\mu f-s^2}{2s}-v+c_1$) and the subsidy fee is high (i.e.,$s>\sqrt{{(v+1-c_1)}^2+4t\mu f}-v-1+c_1$ ).

Proposition 3 investigates the condition under which the retailer with the subsidy strategy prefers biodegradable drinking straws more than the retailer with the fine strategy. The condition is that the subsidy fee is high and consumers prefer high-quality biodegradable drinking straws. In the consumer survey, consumers are asked for their preference among four kinds of straws: PLA (biodegradable), plastic, paper (biodegradable), and others. In the results, 46.6% picked PLA as the top choice, compared with 19.9 (plastic), 16.8% (paper), and others (16.9%). To intuitively understand proposition 3, notice that more users would buy the product with biodegradable drinking straws if the quality of biodegradable drinking straws is higher, which is true under both government strategies. The higher quality of biodegradable drinking straws then leads to a higher profit for the monopoly retailer because more users buy their products. The subsidy strategy differs critically from the fine strategy in that the fine strategy affects a retailer’s profit directly. As the subsidy fee increases, the retailer with biodegradable drinking straws has the incentive to charge a lower product price to take advantage of the higher demand, which benefits the retailer. Therefore, the retailer under the subsidy strategy benefits more from the quality of biodegradable drinking straws when the quality of biodegradable drinking straws and the subsidy fee are high. If the fine fee is high, it is intuitive that the fine strategy results in more profit differentiation between providing biodegradable drinking straws and providing plastic drinking straws. When the quality of biodegradable drinking straws is low, the demand of users sharply decreases even though the government provides the subsidy policy. In this case, the fine strategy with more deterrent power is more beneficial for the retailer to provide biodegradable drinking straws because the positive effect of subsidy fee is dominated by the negative effect of the loss of user demand.

Proposition 4.

In the fine strategy, the monopoly retailer prefers to provide biodegradable drinking straws rather than plastic drinking straws if and only if one of the following conditions is satisfied:

(a)

The fine fee is high (i.e.,$\mu f>\mu f_1=\left(2v+q+1-c_1-c_2\right)\left(1-q+c_1-c_2\right)/4t$);

(b)

The fine fee is low (i.e.,$\mu f<\left(2v+q+1-c_1-c_2\right)\left(1-q+c_1-c_2\right)/4t$) and the number of environment-conscious consumers is high (i.e.,$\alpha <({\left(v+q-c_1\right)}^2+4t\mu f)/{\left(v+1-c_2\right)}^2$.

Proposition 4 states the conditions under which a retailer has the incentives to provide biodegradable drinking straws with a fine strategy, as shown in Figure 2. This proposition also means that the monopoly retailer prefers to provide plastic drinking straws under the fine strategy if and only if the fine fee is low and the number of environment-conscious consumers is low. It is an intuitive condition that the monopoly retailer prefers to provide biodegradable drinking straws when the fine fee is high. When the fine fee is low, the retailer has incentive to provide biodegradable drinking straws if and only if the number of environment-conscious consumers is high. The reason for this is that environment-conscious consumers only use biodegradable drinking straws and never use plastic drinking straws. Because consumer experience of quality plastic drinking straws is higher than that for biodegradable drinking straws, consumers are more likely to use a plastic drinking straw without considering whether consumers are environmentally conscious. Therefore, only when the number of environment-conscious consumers is high, more consumers do not buy products with plastic drinking straws, thus reducing retailer profit when providing plastic drinking straws.

Proposition 5.

In the subsidy strategy, the monopoly retailer prefers to provide biodegradable drinking straws rather than plastic drinking straws if and only if one of the following conditions is satisfied:

(a)

The subsidy fee is high (i.e.,$s>s_1=1+c_1-q-c_2$);

(b)

The subsidy fee is low (i.e.,$s<1+c_1-q-c_2$) and the number of environment-conscious consumers is high (i.e.,$\alpha <{\left(v+q-c_1+s\right)}^2/{\left(v+1-c_2\right)}^2$).

Similar to proposition 4, proposition 5 also states the conditions under which a retailer has incentive to provide biodegradable drinking straws with the subsidy strategy (Figure 3). The monopoly retailer prefers to provide biodegradable drinking straws when the subsidy fee is high. The high subsidy fee not only makes the retailer obtain more profit but also responds to the government policy positively, which is consistent with the existing literature [18]. When the subsidy fee is low, the retailer has incentive to provide biodegradable drinking straws if and only if the majority consumers are environmentally conscious. This is because a low subsidy fee would increase the product price, thereby reducing the user demand. Recall from proposition 4 that only when the number of environment-conscious consumers is high, fewer consumers buy the product with plastic drinking straws, thus reducing retailer profits when providing plastic drinking straws. In fact, whether the retailer provides biodegradable drinking straws depends on the negative effect from the quality differentiation between biodegradable drinking straws and plastic drinking straws, as well as the positive effect from the number of environment-conscious consumers. Providing biodegradable drinking straws benefits retailers more if and only if a high number of environment-conscious consumers has a positive effect. In other words, the monopoly retailer prefers to provide plastic drinking straws under the subsidy strategy if and only if the subsidy fee is low and the number of environment-conscious consumers is low.

4.2. Equilibrium Results in Competitive Markets

Proposition 6.

Retailer 2 prefers to provide biodegradable drinking straws under fine policy when the fine fee is high (i.e.,$\mu f>\mu f_2=\frac{{(\alpha c_1-\alpha c_2+\alpha t+\alpha \Delta v+2t)}^2}{18\alpha t}-\left(\left(2v+2q-2c_1-t\right)/4\right)$. The threshold value increases with the number of environment-oblivious consumers (i.e.,$\frac{\partial \mu f_2}{\partial \alpha }>0$) if and only if the number of environment-oblivious consumers is high. Additionally, it exists$\mu f_2<\mu f_1$if and only if$v>\frac{17t}{18}-\frac{1+q-c_1-c_2}{2}-\frac{4t^2+{\alpha }^2{(q-t-c_1+c_2-1)}^2}{9\alpha \left(q-t-c_1+c_2-1\right)}$.

This result of proposition 6 is identical to the condition shown in proposition 4(a). Figure 4 shows the intuitive result that retailer 2 offers biodegradable drinking straws when the fine fee is high. When the fine fee is low, retailer 2 offers plastic drinking straws. Note that the threshold value of the fine fee is related to the number of environment-conscious consumers. Specifically, the threshold value is high if the number of environment-oblivious consumers is high, and vice versa. This implies that environment-conscious consumers have replaced the implementation of fine policy to some extent. Moreover, the fine fee is the product of the cost of the fine multiplied by the probability of detection. Therefore, the fine fee is related to the type of retailer. If the retailer is risk averse, they will provide biodegradable drinking straws. If the retailer is risk seeking, they will offer plastic drinking straws. If the retailer is risk neutral, the retailer’s choice depends on the government fine policy. Comparing the threshold value in monopoly and competitive markets, we find that the fine threshold fee under competitive markets is higher when product quality is low. In other words, the fine threshold fee under competitive markets is lower when product quality is high. The result also implies that the government encourages competition when the quality of a product is high. Actually, in many government policies, it is highlighted that the market should play the leading role in the smooth implementation of policies. For instance, New Energy Automobile Industry Development Plan (2021–2035), issued by General Office of the State Council on Oct 20, 2020, states that “it is paramount to facilitate the key role of the market in resource allocation and support the sustainable and prosperous development of renewable energy automotive industry” [30]. Additionally, the fine fee would be higher in the competitive market for low-quality products; the reason for the counterintuitive result is that the retailer would provide plastic drinking straws with better experience and lower cost to improve its competitive power. This means the government should encourage retailers to improve the quality of low-quality products.

Proposition 7.

Retailer 2 prefers to provide biodegradable drinking straws under the subsidy policy when the subsidy fee is high (i.e.,$\frac{2\alpha (c_1-c_2-q+t+1)+13t-3\sqrt{4\alpha t\left(v-c_2+1\right)+2\alpha t^2+17t^2}}{2\alpha }=s_2<s$). Particularly, the threshold value increases with the number of environment-oblivious consumers (i.e.,$\frac{\partial s_2}{\partial \alpha }>0$) if and only if the number of environment-oblivious consumers is high. Additionally, it exists$s_2>s_1$if and only if$v<\frac{2{\alpha }^{2}t+18\alpha c_2+17\alpha t-18\alpha +8t}{18\alpha }$.

Proposition 7 shows an intuitive result that retailer 2 provides biodegradable drinking straws when the subsidy fee is high. In other words, retailer 2 provides plastic drinking straws when the subsidy fee is low (Figure 5). Similar to the result in proposition 6, the threshold value of the subsidy fee is related to the number of the environment-conscious consumers. Specifically, the threshold value is high if the number of environment-oblivious consumers is high, and vice versa. This implies that environment-conscious consumers have replaced the implementation of a subsidy policy to some extent. From propositions 6 and 7, we conclude that environment-conscious consumers have replaced the implementation of government policies. That is, the government should implement some strategies to improve the number of environment-conscious consumers, thereby lowering policy costs. Similar to proposition 6, the results of proposition 7 also mean that the government encourages competition when the quality of the product is high and encourages retailers to improve the quality of low-quality products. Specifically, the subsidy threshold fee under competitive markets is lower when product quality is high. The subsidy fee would be higher in the competitive market for low-quality products.

Proposition 8.

Compared with the fine policy, the subsidy policy would allow the retailer who provides biodegradable drinking straws to obtain more profit.

Proposition 8 shows that subsidy strategy is always more beneficial to retailers that obey The Ban. The reason for this is that the fine strategy is a measure for retailers using plastic drinking straws and it is not effective for those using biodegradable drinking straws. The subsidy strategy can make retailers using biodegradable drinking straws reduce straw costs, increasing profits. It is worth noting that, when two retailers provide biodegradable drinking straws, the product prices and product demands of the two retailers are equal, irrespective of whether the government adopts a fine strategy or a subsidy strategy. This is because the model assumes that the market is completely covered, meaning that the retailers are symmetrical when they provide the same type of straws. Additionally, the two retailers extract undifferentiated consumer surplus. Therefore, it has nothing to do with whether the government adopts a subsidy policy or not.

From propositions 6–8, the results in competitive markets are identical to those in monopoly markets, which proves the robustness of our main insights derived from the monopoly model. In competitive markets, the straws choice for retailers does not change, but the threshold value is altered. Thus, all of our previous insights still hold.

5. Conclusions

This study established a tripartite game to explore the optimal strategy of China’s Plastic Drinking Straws Ban based on consumer heterogeneity and retailer competition. The main conclusions of this article are as follows:

(1).

Regardless of whether it is in monopoly or competitive markets, the government’s subsidy strategy for retailers will make retailers more profitable. As profit-seekers, retailers are more willing to accept the government’s subsidy strategy, cooperate with the policy implementation, and enable the government to achieve its policy goals. Therefore, in the process of replacing plastic products in the food and beverage industry in the future, such as the replacement of take-out lunch boxes, the government could consider subsidizing the research and development of plastic alternative products, which will help achieve the ultimate policy goal of the comprehensive replacement of plastic products.

(2).

In monopoly markets, the following four scenarios are true: (a) Penalties are high enough, (b) fines are low but there are enough environment-conscious consumers, (c) subsidies are high, (d) subsidies are low but there are enough environment-conscious consumers, meaning retailers are more inclined to provide biodegradable drinking straws. Although the policy is now in effect, there are still many retailers on the market that provide plastic drinking straws. Therefore, the government can increase subsidies and fines and/or educate consumers to increase their environmental awareness. In fact, according to the retailer survey, 83 retail stores in Zhejiang Province were inspected by the Municipal Supervision Bureau for straw issues. Among them, a dozen were penalized with verbal criticism or confiscation of plastic drinking straws. Unfortunately, during the retailer survey, 18 stores neglected the severity of the problem and continued using plastic drinking straws. Consequently, the Chinese government needs more severe punishment measures than verbal criticism and confiscation.

(3).

Consumer heterogeneity also impacts policy results. When there are enough environment-conscious consumers, it will compel retailers to only use biodegradable drinking straws, without intervention from the government, thus reducing policy costs. In other words, the number of environment-conscious consumers and government policy measures is complementary. Specifically, when the number of environment-conscious consumers is large, the government’s fines and subsidies are relatively small, and when the number of environment-conscious consumers is small, the government’s fines and subsidies are relatively large. Therefore, in order to reduce the cost of implementing policies, the government should aim for higher environmental awareness among consumers. The consumer survey shows that only 3.7% of consumers are willing to report the retailers offering plastic drinking straws. Such a low number also contributes to the poor implementation of environmental policies. Consumers play a highly important role in realizing The Ban. Therefore, the government should give correct guidance and encourage consumers to take practical actions, such as encouraging consumers to report retailers who still offer plastic straws, refusing to accept products with plastic straws, advocating for a reduction in disposable plastic consumption, etc., to promote the ban on plastic products.

(4).

In competitive markets, when the fines or subsidies are high, retailers providing plastic drinking straws will resort to biodegradable drinking straws, which is the same result as in monopoly markets (conclusion (2)); this shows the robustness of the model in this paper. This is also consistent with the results of Thornton et al. [31]. That is, the general level of punishment only serves as a reminder to an enterprise. The cost of breaking the law is lower than the cost of complying with the policy, which is also one of the reasons for the failure of pollution control in the Huai River [32] and many other environmental control issues. Therefore, the appropriate increase in policy subsidies, especially the increase in fines, will increase the cost of illegal enterprises, which is an important means to achieve China’s plastic ban in the future. In addition, this paper finds that, when the quality of the product is high, the fine and subsidy costs in competitive markets are lower than those in monopoly markets. This means that, for high-quality products, competitive markets have replaced government policies to a certain extent. Consequently, in order to cut expenditure on policy implementation, the government should advocate competition among retailers for high-quality products. In comparison, for low-quality products, competition will compel retailers to adopt low-cost and better user-experience plastic straws, so the government must increase policy costs in competitive markets in order to implement the policy properly. To avoid such a situation, the government should use administrative powers to reduce the market share of low-quality products. At the same time, retailers themselves should also be aware that proactively catering to the expectations of consumers and the government and providing high-quality biodegradable straws is beneficial to their own development. Therefore, retailers should increase their environmental responsibility and provide high-quality biodegradable straws, thus actively embracing The Ban.

In addition to the ban on plastic straws, the model could also be applied to other corporate activities related to sustainability, such as plastic bags, plastic bottles, etc., and its connection to government policies. This research has significance and a theoretical reference value for realizing the substitution of banned single-use plastic products. However, there are several issues in this study that need to be studied in the future. For example, this study did not include straw manufacturers and straw recycling in the model. Additionally, this research did not consider price sensitivities in the manner of Widodo and Januardi [33]. Therefore, these will be added in future research to create more in-depth studies.