to SMEs' digital transformation efforts, with external support for digital being the first step and operational technology readiness being the most challenging determinant of success [18]. Cooperation is reflected in various stages of SME digital transformation projects, such as business needs adjustment, project portfolio creation, technology solution selection, and later stages [19]. Studies have also found that three major resources—IT, human resources, and business strategy—have a positive impact on the digital transformation of SMEs; however, these factors are barriers to the digital transformation of these enterprises. Furthermore, digital transformation has a positive impact on the business outcomes of SMEs [20]. From a holistic perspective, six key factors for the digital transformation of SMEs are identified from the three dimensions of technology, organization, and environment: government support, partnership, top management, digital strategy, IT infrastructure, and IT management capabilities [6]. Employee skills are the moderating factor. Digital transformation is a long-term and arduous task, facing challenges in technology, business capacity building, talent training, and so on, but it is not unattainable. Only by focusing on key elements and by adding external assistance according to their own strength can SMEs iteratively innovate (Table 1).

**Table 1.** Summary of the literature reviewed.

### **3. Materials and Methods**

### *3.1. Resource-Based View*

The American economist Penrose was one of the earliest scholars to advocate for the concept of enterprise resources. Penrose defines resources as "the physical objects purchased, leased, or manufactured by an enterprise for its own use and the labor force employed on certain terms." She also emphasizes that the heterogeneity (rather than homogeneity) of productive or potentially productive services produced by firms from their own resources gives each firm its unique characteristics [21]. The publication of Wernerfelt's "Resource-based Theory of Enterprises" in 1984 signified the birth of resourcebased theory [22]. Barney's research suggests that there may be a kind of heterogeneity or difference between companies and that some companies maintain a competitive advantage [23]. Therefore, resource-based theory emphasizes strategic choices and believes that the strategic task of corporate management is to find, develop, and allocate this part of the distinctive key resources in order to maximize business returns. According to Peteraf's point of view, the resources controlled by an enterprise must satisfy four conditions (i.e., valuable, rare, inimitable, non-substitutable) to generate sustainable competitive advantage for the enterprise [24]. Adopting the resource-based view and the inheritance and development of this theory, Teece et al. defined dynamic capability as the ability of a company to integrate, construct, and reconfigure internal and external capabilities to cope with a rapidly changing environment [25]; from here, dynamic capability theory gradually formed and then developed rapidly.

At different stages of digital transformation, enterprises have different requirements for organizational structure, organizational culture, growth strategy, and digital and other related resources or capabilities, and their coordination and adaptation will help to promote enterprise digital transformation [7]. However, some studies have found that SMEs have difficulty starting their digital journey because of a lack of resources and expertise. As an enabling mechanism, dynamic capabilities can facilitate digital transformation [26]. Additionally, perception ability, learning ability, integration ability, digital leaders, and key resources have an important impact on the digital transformation of enterprises, among which perception ability and learning ability are also important "triggers" for enterprise digital transformation [27]. While mediating the relationship between digital transformation and enterprise performance, dynamic capabilities also mediate the joint effect of digital transformation and individual forgetting on innovation performance, and the joint effect of digital transformation and entrepreneurial orientation on innovation performance. The three interactive effects of entrepreneurial orientation also play a mediating role in the relationship between performance [28].

By embracing resource-based theory (including dynamic capability theory), we reviewed the relevant literature to better understand our assumptions about digital transformation and performance and the three key resources of SMEs—digital technology, employee digital skills, and digital transformation strategy.

### *3.2. Proposed Conceptual Model and Hypothesis Formulation*

Resource-based theory posits that an enterprise is a collection of various resources. Owing to various reasons, the resources owned by enterprises are different and heterogeneous, and this heterogeneity determines the differences in the competitiveness of enterprises. However, resources can only be used as a basis for competitive advantage if they conform to the VRIN framework. Specifically, VRIN refers to valuable resources (which are the basis for companies to conceive and execute corporate strategies, as well as improve efficiency and effectiveness); rare (that is, scarce) resources (because even if the resource is valuable, once owned by most companies, it cannot bring competitive advantage or sustainable competitive advantage); imperfectly imitable resources (that is, resources that cannot be imitated, which generally need to have the following three characteristics simultaneously: unique historical conditions, vague causes, and social complexity); and non-substitutable resources (that is, irreplaceable resources, which do not have a substitute that is both replicable and

not scarce). This is because enterprises have different tangible and intangible resources, which can be transformed into unique capabilities, and resources are immobile and difficult to replicate among enterprises; these unique resources and capabilities are the source of lasting competitive advantages for enterprises [22]. Compared with the external conditions of the enterprise, the internal conditions of the enterprise play a decisive role in obtaining competitive advantage in the market. Therefore, our research focused on the organization itself and identified three key resources (elements) that SMEs in digital transformation need: digital technology, digital skills, and digital transformation strategy. We use structural equation modeling to verify the impact of digital technology (x1), digital skills (x2), and digital transformation strategy (x3) on digital transformation (Y1) and performance (Y2). See Figure 1. not have a substitute that is both replicable and not scarce). This is because enterprises have different tangible and intangible resources, which can be transformed into unique capabilities, and resources are immobile and difficult to replicate among enterprises; these unique resources and capabilities are the source of lasting competitive advantages for enterprises [22]. Compared with the external conditions of the enterprise, the internal conditions of the enterprise play a decisive role in obtaining competitive advantage in the market. Therefore, our research focused on the organization itself and identified three key resources (elements) that SMEs in digital transformation need: digital technology, digital skills, and digital transformation strategy. We use structural equation modeling to verify the impact of digital technology (x1), digital skills (x2), and digital transformation strategy (x3) on digital transformation (Y1) and performance (Y2). See Figure 1.

*Sustainability* **2022**, *14*, x FOR PEER REVIEW 6 of 18

employee digital skills, and digital transformation strategy.

*3.2. Proposed Conceptual Model and Hypothesis Formulation*

innovation performance, and the joint effect of digital transformation and entrepreneurial orientation on innovation performance. The three interactive effects of entrepreneurial orientation also play a mediating role in the relationship between performance [28].

By embracing resource-based theory (including dynamic capability theory), we reviewed the relevant literature to better understand our assumptions about digital transformation and performance and the three key resources of SMEs—digital technology,

Resource-based theory posits that an enterprise is a collection of various resources. Owing to various reasons, the resources owned by enterprises are different and heterogeneous, and this heterogeneity determines the differences in the competitiveness of enterprises. However, resources can only be used as a basis for competitive advantage if they conform to the VRIN framework. Specifically, VRIN refers to valuable resources (which are the basis for companies to conceive and execute corporate strategies, as well as improve efficiency and effectiveness); rare (that is, scarce) resources (because even if the resource is valuable, once owned by most companies, it cannot bring competitive advantage or sustainable competitive advantage); imperfectly imitable resources (that is, resources that cannot be imitated, which generally need to have the following three characteristics simultaneously: unique historical conditions, vague causes, and social complexity); and non-substitutable resources (that is, irreplaceable resources, which do

**Figure 1.** Conceptual model and research hypothesis. **Figure 1.** Conceptual model and research hypothesis.

The model parameters are as follows:

$$y\_i = a + \mathbf{B}y\_i + \Gamma \mathbf{x}\_i + \mathcal{J}\_i \text{ var}(\mathcal{L}\_i) = \mathbf{Y}\_i$$

Given p-endogenous and q-exogenous variables:

*yi* is a p × 1 vector of observed endogenous variables *xi* is a q × 1 vector of observed exogenous variables *a* is a p × 1 vector of regression intercepts B is a p × p matrix of regression slopes Γ is a p × q matrix of regression slopes *ζ* is a p × 1 vector of disturbances (i.e., residuals) Ψ is a p × p covariance matrix of disturbances

### 3.2.1. Digital Technology

The basic idea behind the implementation of digital transformation by SMEs is to change work and business processes based on digital-technology-driven improvements; in this way, business operations can be made more efficient. Artificial intelligence has been proposed for decades, but it has only experienced explosive growth in the past two years. The reason lies in the increasing maturity of technologies such as cloud computing, the Internet of things (IoT), and big data. Cloud computing provides an open platform for artificial intelligence, the IoT ensures real-time data sharing, and big data provides unlimited resources for deep learning. In addition, the development of blockchain technology in 2018 can make up for the shortcomings of artificial intelligence in data security and data factors, and provide a reliable guarantee for the application of artificial intelligence in different scenarios. Some studies have found that digital transformation can be achieved through

artificial intelligence [29]. The IoT plays an important role in digital transformation [30,31]. Blockchain technology affects digital transformation [32,33]. Notably, 5G networks also play a role in digital transformation [34]. The use of social media in management affects the overall performance of enterprises [35]. In summary, driven by the digital technology represented by cloud computing, big data, artificial intelligence, and blockchain, the value chain is breaking and reshaping, new ecosystems are emerging, and industry boundaries are becoming increasingly blurred. An increasing number of traditional enterprises are trying to calmly restructure their business models to cope with industry changes and expand their businesses across traditional industry boundaries.

**Hypothesis 1 (H1).** *Digital technology is positively correlated with the digital transformation of SMEs*.

### 3.2.2. Digital Skills

In the digital transformation process, an increasing number of companies are beginning to realize the importance of talent team building, because the implementation of digital strategies requires the support of digital talents with business capabilities, overall views, as well as digital concepts and skills. Kane believes that people are the real key to digital transformation [36]. Therefore, the self-management team is key to starting the digital transformation of enterprise management [37]. The rapid development of employees' individual cognitive and process capabilities promotes the digital transformation process of enterprises [38]. Bessonova et al. discussed the digital literacy of employees as readiness for digital transformation [39]. Studies have found that employees' digital mindset can affect their participation in or exit from a company's digital transformation program [40]. Personal digital ability is related to SME growth and innovation performance [41]. However, some companies have not yet started digital transformation, which is also due to the lack of human capital and the digital skills of employees [42]. Therefore, organizations must develop virtual human resource development and use learning resources to prepare for the future [43]. The empowerment of the organization is effective only when the right people are selected, and everything we do in the future will be multiplied with half the effort. Therefore, regarding digital transformation, the biggest challenge of the organization is not the specific business, but the people.

**Hypothesis 2 (H2).** *Employee digital skills are positively correlated with SME digital transformation.*

### 3.2.3. Digital Transformation Strategy

A digital transformation strategy is a prerequisite for successful digital transformation. By developing an effective, clear, and sound digital transformation strategy, one can ensure that one's digital transformation is as seamless as possible. A digital transformation strategy is like a personalized map that can bring great value in business transformation. The formulation and implementation of a digital transformation strategy has become a key concern for organizations prior to digital transformation across many traditional industries [44]. Four common types of digital transformation strategies are formed via two dimensions: the use of digital technologies and the preparation of business models for digital operations [45]. Studies have found that SMEs are strengthening their digital transformation strategies through innovative technologies and new values that restructure business models and processes [46]. Presently, many enterprises have completed the strategy formulation stage of digital transformation and are in the strategy implementation stage [47]. A new strategic implementation framework can be adopted in digital transformation, which is divided into three phases: planning, implementation, and review [48]. In summary, digital transformation is the best strategy for an enterprise, and it must be reflected in the whole process execution of business, operation, and performance appraisal. It is no longer sufficient to

stay at the technical level; it is necessary to digitalize all aspects of decision making, work, and cooperation, and provide the best experience for customers.

**Hypothesis 3 (H3).** *Digital transformation strategies are positively correlated with the digital transformation of SMEs.*

### 3.2.4. Digital Transformation and Performance

Existing research finds that digital transformation has an impact on corporate financial performance [49]. Enterprise digital transformation has a positive effect on enterprise performance [50]. The positive impact of digital transformation on enterprise performance is more evident in large enterprises, state-owned enterprises, mature enterprises, and non-manufacturing (service) enterprises. The positive impact of digital transformation on enterprise performance and supply chain integration is not significant in small- and medium-sized enterprises; supply chain integration cannot play an intermediary role in the relationship between the digital transformation of manufacturing enterprises and enterprise performance [51]. Three major resources (IT, human resources, and business strategy) have a positive impact on the digital transformation of SMEs, and digital transformation has a positive impact on the business results of SMEs [20]. Digital transformation has a positive effect on the dynamic capabilities of enterprises; the higher the intensity of individual forgetting and the stronger the entrepreneurial orientation, the stronger the positive impact of digital transformation on the dynamic capabilities and innovation performance of enterprises [28]. Some of the benefits of digital transformation for enterprises are the transformation and optimization of traditional stock businesses through digital technology; improving the level of large-scale production and trading of traditional products; and realizing value benefits, such as efficiency improvement, cost reduction, and quality improvement.

**Hypothesis 4 (H4).** *Digital transformation is positively correlated with financial performance.*

### 3.2.5. Complementarity of Resources

Digital technology, employee digital skills, and digital transformation strategies are the three core elements for SMEs to carry out digital transformation from point to face, local to global, and in stages. All three are indispensable in the ongoing digital transformation process. Previous research has found that, in addition to technology adoption, important factors for successful digital transformation are the organization's ability to change and its operational excellence in integrating external digital services with internal IT support [14]. Another study reports that digital transformation at the enterprise level requires attention to the alignment of strategy, vision, and digital transformation investment; the suitability of innovation culture; intellectual property and know-how; the strength of digital capabilities; and the use of digital technology [12]. Digital transformation strategies have a positive impact on short- and long-term financial performance [52]. There is a significant correlation between big data, IoT, blockchain, and performance [53]. Other studies suggest that the variables that have the greatest impact on SME performance are management, technology, and marketing and innovation capabilities [54]. In short, the digital transformation of an enterprise is a dynamic process. Continuous iteration, the development of digital products and services based on data, and the realization of intelligent operations through digital technology are essential. When digital technology penetrates into every corner of an enterprise, continuous and rapid innovation capabilities will become the core driving force for enterprises to maintain competitiveness, thereby helping enterprises to make steady progress on the road of digital transformation. Enterprises that achieve intelligent operations can make real-time and correct decisions; fully integrate talent, data, and intelligent technology; drive process transformation and incorporate agility and rapid response capabilities; continuously improve user experience; and achieve breakthrough business results. Sustainable digital transformation can only be achieved through sustainable technological innovation and intelligent operations.

**Hypothesis 5 (H5).** *The relationship between (a) digital technology, (b) employee digital skills, and (c) digital transformation strategy and financial performance is mediated through digital transformation.*

### **4. Results**

### *4.1. Measurement and Data Collection*

We tested five hypotheses among SMEs (1–299 employees) from various provinces within China, and the questionnaire was designed after on-site interviews with SMEs. After the review of relevant experts and the pre-test, we comprehensively considered the analysis results of 30 questionnaires and China's national conditions; adjusted the evaluation of questions, wording, and consistency; and improved the reliability and effectiveness of the questionnaire. The survey targets are executives of SMEs, who are familiar with the specific operation of the company and can ensure that the data truly reflect the actual application of digital technology in SMEs. The quantitative data were collected through an online survey platform that collected 335 complete and correctly filled questionnaires by the end of 2021. See Appendix A.

Independent variable: The design of the independent variables was conducted in advance through corporate interviews. Employee digital skills (DS) uses a seven-point Likert scale ranging from 1 ("strongly disagree") to 7 ("strongly agree"). Digital transformation strategy is evaluated using a seven-point Likert scale ranging from 1 ("strongly disagree") to 7 ("strongly agree"). Digital technology (DT) uses a seven-point Likert scale ranging from 1 ("very low") to 7 ("very high").

Dependent variable: Except for listed companies, Chinese SMEs are not obliged to publish financial data. The Entrepreneur Orientation Scale adopted by Lumpkin and Dess [55] was used. Financial performance variables (FP) were measured using a sevenpoint Likert scale ranging from 1 ("strongly disagree") to 7 ("strongly agree"). The scale measures how SME executives feel about the financial performance of their companies after digital transformation.

Mediating variable: The mediating variable, digital transformation (DX), is an assessment of an enterprise's digital transformation maturity, using the seven-point Likert scale adopted by Bley et al. [56], ranging from 1 ("very low") to 7 ("very high").

Control variable: Financial performance may be affected by other factors, and control variables can prevent test failures for the dependent variables [57,58]. The control variables are the number of employees, gender of executives, and readiness for digital transformation. The readiness for digital transformation is measured by Xiaodong Ma [59].

### *4.2. Measurement Model*

The SEMs approach used in this study is a method for establishing, estimating, and testing a causal relationship model. The model contains both observable explicit variables and latent variables that cannot be directly observed. Table 2 shows the descriptive statistics of the data sample: medium-sized enterprises account for 77% of the total. The information and communication technology industry, media, and finance accounted for 34%. Levels 2 and 3 of digital transformation are the most common, accounting for 33%.

SPSS 21 software is used to test reliability and validity, and the results are shown in Table 3, evaluated using mean, SD, Cronbach's alpha, CR, and AVE. All α and CR values exceeded the threshold of 0.70, and all AVE values were above the recommended threshold of 0.50; thus, all indicators showed good reliability. We used factor loadings and square root of AVE to measure convergent and discriminant validity, respectively. The results showed that all factor loadings were greater than 0.7 at the significance level of *p* < 0.01, indicating good convergent validity. The correlation coefficient of each factor with other factors confirmed the discriminant validity.

**Table 2.** Sample demographic information.

### **Table 3.** Descriptive statistics and correlations.

Note(s): \*\* *p* < 0.01, n = 335. Digital transformation (DX); employee digital skills (DS); digital transformation strategy (DTS); digital technology (DT); financial performance (FP).

### *4.3. Regression Analysis*

After factor analysis and reliability tests, we perform multiple regression analysis to test hypotheses H1–H4, and Table 4 shows the results of the multiple regression analysis.

**Table 4.** Results regression analysis.

Note(s): \*\* *p* < 0.01, Digital transformation (DX); employee digital skills (DS); digital transformation strategy (DTS); digital technology (DT); financial performance (FP).

### *4.4. Structural Model*

To ensure the consistency of the estimates, we use the "path analysis" in the web version of SPSSAU to estimate the coefficients and significance of each path. Figure 2 shows the path coefficients in the test results obtained using the structural equation model. It can be seen from Figure 2 that when digital transformation has an impact on financial performance, this path does not appear significant (z = 0.158, *p* = 0.875 > 0.05), thus indicating that digital transformation has no impact on financial performance. When digital skills have an impact on financial performance, this path does not appear significant (z = 1.872, *p* = 0.061 > 0.05), thus indicating that employees' digital skills have no impact on financial performance. When the digital transformation strategy has an impact on financial performance, the standardized path coefficient value is 0.615 > 0, and this path shows a significant level of 0.01 (z = 15.292, *p* = 0.000 < 0.01), thus indicating that the digital transformation strategy will have an impact on financial performance (significant positive impact relationship). When digital technology has an impact on financial performance, the standardized path coefficient value is 0.138 > 0, and this path shows a significant level of 0.05 (z = 2.523, *p* = 0.012 < 0.05), thus indicating that digital technology will have a significant impact on financial performance (positive influence relationship). When employees' digital skills have an impact on digital transformation, the standardized path coefficient value is 0.380 > 0, and this path shows a significant level of 0.01 (z = 7.466, *p* = 0.000 < 0.01), thus indicating that employees' digital skills will have an impact on digital transformation (significant positive impact relationship). When the digital transformation strategy has an impact on the digital transformation, this path does not appear significant (z = −0.786, *p* = 0.432 > 0.05), thus indicating that the digital transformation strategy has no influence on the digital transformation. When digital technology has an impact on digital transformation, the standardized path coefficient value is 0.401 > 0, and this path shows a significant level of 0.01 (z = 7.749, *p* = 0.000 < 0.01), which indicates that digital technology will have a significant impact on digital transformation (positive influence relationship). *Sustainability* **2022**, *14*, x FOR PEER REVIEW 12 of 18 the standardized path coefficient value is 0.380 > 0, and this path shows a significant level of 0.01 (z = 7.466, *p* = 0.000 < 0.01), thus indicating that employees' digital skills will have an impact on digital transformation (significant positive impact relationship). When the digital transformation strategy has an impact on the digital transformation, this path does not appear significant (z = −0.786, *p* = 0.432 > 0.05), thus indicating that the digital transformation strategy has no influence on the digital transformation. When digital technology has an impact on digital transformation, the standardized path coefficient value is 0.401 > 0, and this path shows a significant level of 0.01 (z = 7.749, *p* = 0.000 < 0.01), which indicates that digital technology will have a significant impact on digital transformation (positive influence relationship).

**Figure 2.** Results of structure model analysis. Note(s): \*\* *p* < 0.01. **Figure 2.** Results of structure model analysis. Note(s): \*\* *p* < 0.01.

DT, DS, DTS, and DX. Table 5 shows the results of the mediation analysis.

*4.5. Mediating Effect*

We use structural equation modeling to verify the impact of digital technology (x1),

We use the process plug-in in SPSS and the bootstrap method to test the mediation effect. That is, we measure the direct and indirect effects between the mediator variable DX and the dependent variable FP, and the effects of the three independent variables,

We use structural equation modeling to verify the impact of digital technology (x1), digital skills (x2), and digital transformation strategy (x3) on digital transformation (y1) and performance (y2). The results are shown in the following equation: y<sup>1</sup> = 0.401\*x<sup>1</sup> + 0.38\*x<sup>2</sup> − 0.032\*x3, y<sup>2</sup> = 0.008\*y<sup>1</sup> + 0.138\*x<sup>1</sup> + 0.100\*x<sup>2</sup> + 0.615\*x3.

### *4.5. Mediating Effect*

We use the process plug-in in SPSS and the bootstrap method to test the mediation effect. That is, we measure the direct and indirect effects between the mediator variable DX and the dependent variable FP, and the effects of the three independent variables, DT, DS, DTS, and DX. Table 5 shows the results of the mediation analysis.

**Table 5.** Results of mediation analysis.

\*\* *p* < 0.01.

In terms of the mediation path DT > DX > FP, findings showed that no clear mediating role between digital technology and financial performance. Its structural equation model results are as follows: y<sup>2</sup> = 3.361 + 0.373\*x1, y<sup>1</sup> = 1.290 + 0.680\*x1, y<sup>2</sup> = 3.319 + 0.350\*x<sup>1</sup> + 0.033\*y1.

For the mediation path DS > DX > FP, findings showed that no clear mediating role between digital skills and financial performance. Its structural equation model results are as follows: y<sup>2</sup> = 3.719 + 0.304\*x2, y<sup>1</sup> = 1.606 + 0.626\*x2, y<sup>2</sup> = 3.592 + 0.255\*x<sup>2</sup> + 0.079\*y1.

Regarding the mediation path DTS > DX > FP, findings showed that digital transformation partially mediates the relationship between digital transformation strategy and financial performance. Its structural equation model results are as follows: y<sup>2</sup> = 1.053 + 0.759\*x3, y<sup>1</sup> = 3.327 + 0.230\*x3, y<sup>2</sup> = 0.611 + 0.728\*x<sup>3</sup> + 0.133\*y1.

### **5. Discussion**

This paper contributes to a better understanding of the factors influencing the digital transformation of SMEs and their relationship to performance. The empirical examination examines the relationship between three key resources of SMEs (digital technology, employee digital skills, and digital transformation strategy) and digital transformation, and the impact of these three resources and digital transformation on financial performance. These results suggest some important findings.

First, digital technology has a positive impact on the digital transformation of SMEs (Hypothesis 1/H1).This shows that digital technologies (resources including artificial intelligence, blockchain, cloud technology, big data, 5G, IoT, social media, and cyber-security technologies) contribute to the digital transformation of SMEs. This shows that digital technology is the foundation of digital transformation, and SMEs should consider the different stages they are in and choose the digital technology that suits them, in order to contribute to digital transformation, rather than blindly choosing digital technologies without analysis, or simply using digital technologies to gain various benefits from digital transformation [6].

This result is consistent with RBV's complementary view that digital technology needs to be deeply integrated with the business and management of the enterprise, combined with the enterprise's strategy and the digital skills of its people, in order to form a strong dynamic capability to realize the value of digital technology [8].This can also explain why many SMEs have invested in digital technology, but digital transformation has not achieved much. Therefore, SMEs must understand and correctly use different digital technologies to give full play to their value in enabling digital transformation.

Second, employee digital skills have a positive impact on SMEs' digital transformation (Hypothesis 2/H2). This shows that digital transformation depends on employees with digital skills. Digital technology does not function independently, nor does it always work well. To successfully master these digital methods and technologies, SMEs will rely on a large number of employees who are familiar with and adept at digital tools [6]. For SMEs to successfully implement digital transformation, people are as important as technology, and everything from corporate vision and strategy to execution involves people. Employee digital skills are key to digital transformation.

Third, the digital transformation strategy has a relevant but not significant impact on the digital transformation of SMEs (Hypothesis 3/H3). To carry out digital transformation, we must first carry out top-level design. Previous studies have found that in order to successfully achieve digital transformation, companies must first develop a comprehensive digital transformation strategy [60]. It should be taken as an important part of the development strategy to root the data-driven concepts, methods, and mechanisms in the overall development strategy, and systematically design digital transformation around the vision, goals, business ecological blueprint, and other major strategic directions proposed by the company's overall development strategy. The digital transformation strategy of small- and medium-sized enterprises must be guided by value innovation and completely return to the essence of the business, so that it is possible to carry out digital transformation effectively, quickly, and comprehensively.

The results of intermediary analysis (h5a to h5c) show a more complex situation. The relationship between (a) digital technology, (b) employee digital skills, (c) digital transformation strategy, and financial performance is mediated through digital transformation. Regarding transformation, on the direct and indirect paths (H5c), digital transformation strategies had a positive mediating effect on financial performance, but digital technology (H5a) and employee digital skills (H5b) had no significant mediating effects on financial performance. We did multiple rounds of testing for the mediation effect, but the results were not perfect. We consider the following possibilities. One is that the digital transformation of SMEs has just started, and digital transformation is a long-term and complex system engineering [2], so the effect is not obvious, and the financial performance is not ideal. Second, at the moment of the epidemic, the cash flow of SMEs is very tight, and the price of digital technology is currently relatively expensive, so it is difficult for SMEs to bear the cost of digital transformation. Third, large enterprises, Internet companies, and information technology companies are the first to start digital transformation, which can attract talents with digital skills that are currently scarce at high salaries. SMEs are relatively less attractive, which leads to high recruitment costs and affects the process of digital transformation. Finally, it is relatively easy to formulate a digital transformation strategy. Referring to the digital transformation strategy of a benchmark enterprise and combining it with the actual situation of the enterprise can formulate a digital transformation strategy suitable for the enterprise.

### **6. Conclusions**

This research helps us to understand the resources that SMEs need to deploy to succeed in their digital transformation. Digital technologies, employees digital skills, and digital transformation strategies can help to drive digital transformation, which in turn can improve the financial performance of SMEs. The digital transformation strategy is identified as the key factor affecting financial performance. In previous research, Rogers pointed out

that "digital transformation is not fundamentally a technology, but a strategy" [61]. Smalland medium-sized enterprises generally have problems such as a lack of digital transformation thinking, a weak digital foundation, and large obstacles to digital transformation [11]. Digital technology is a major obstacle to the digital transformation of SMEs. The digital skills of employees is another major obstacle to the digital transformation of SMEs [62]. The limited capital of SMEs, coupled with various obstacles, complicates the path of digital transformation. Various types of SMEs are significantly different, which increases the difficulty of digital transformation. The sooner SMEs respond to these challenges, the sooner they can capitalize on the impact to better cope with competition.

This study has several limitations. First, the data were collected in mainland China, and regional restrictions may limit the generalization of the findings. Replicating this study in other parts of the world may improve the reliability and validity of the measurement models. Second, in China, except for listed companies, ordinary SMEs are not obliged to publish financial data. Therefore, the financial performance indicators in this study are based on self-assessed data. Studies have shown that self-assessment data correlate with objective performance measures [63].

We identify some research questions that can advance the digital transformation agenda of SMEs. First, how does digital technology affect the financial performance of SMEs? How different is the degree of impact of each of the different digital technologies? Second, how do employee digital skills affect the financial performance of SMEs? How are the digital skills assessment models? Third, what are the specific indicators of the five stages of digital transformation? How does each affect the financial performance of SMEs? Fourth, are the digital transformation paths of SMEs in different industries different? Fifth, how do different application scenarios of digital transformation of SMEs affect financial performance? Finally, what dynamic capabilities will be formed by digital technologies, employees' digital skills, and digital transformation strategies to influence the financial performance of SMEs?

**Author Contributions:** Conceptualization, X.T. and Z.W.; methodology, X.T. and F.Y.; software, X.T.; validation, X.T. and F.Y.; formal analysis, X.T.; investigation, X.T.; resources, X.T.; data curation, X.T. and Z.W.; writing—original draft preparation, X.T.; writing—review and editing, X.T. and Z.W.; visualization, X.T.; supervision, Z.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The dataset generated and analyzed in this study is not publicly available. Dataset is available from the corresponding author on reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A**

**Table A1.** Research questionnaire.

### **Table A1.** *Cont.*

### **References**

## *Article* **Decisions on Pricing, Sustainability Effort, and Carbon Cap under Wholesale Price and Cost-Sharing Contracts**

**Doo-Ho Lee and Jong-Chul Yoon \***

Department of Artificial Intelligence and Software, Kangwon National University, 346 Joongang-ro, Samcheok-si 29513, Gangwon-do, Korea<EMAIL_ADDRESS>
**\*** Correspondence<EMAIL_ADDRESS>
**Abstract:** Rapid economic growth and industrialization have brought material abundance and convenience, but also social and environmental problems such as global warming, climate change, and ozone depletion. For this reason, the public and governments have continued to make efforts to reduce carbon oxide emissions worldwide over the past few decades. To achieve this mission, capand-trade regulations have been introduced as one of the most effective market-based mechanisms to control carbon emissions. Accordingly, sustainability efforts, including the development of green products and innovating manufacturing technologies, are being made by companies in supply chains to reduce their carbon emissions. In the context of sustainability innovations and carbon emission constraints, this article investigates pricing decisions, the degree of sustainability efforts, and carbon caps under two different supply chain contracts—in this case, wholesale price contract and costsharing contract. This article establishes a Stackelberg game model under each of the supply chain contract types and presents the equilibrium decisions made by players of the game. Major findings of this article reveal that (i) the performance of the supply chain is considerably affected by the presence of a carbon cap; (ii) the higher the carbon cap set by a government is, the more sustainability innovation efforts the supply chain makes; and (iii) the supply chain can improve its profitability and its sustainability under a cost-sharing contract.

**Keywords:** pricing; sustainability effort; carbon cap; wholesale price contract; cost-sharing contract

### **1. Introduction**

Economic growth, driven by rapid industrialization, has significantly improved the well-being of human societies. The global rush for economic development has led to unprecedented material affluence and convenience, but these are not without cost. In particular, environmental degradation has been a major concern in both developed and developing countries. With the growing consensus that economic development cannot be sustained without environmental protection, sustainability has become a mainstream imperative with regard to the running of a global economy. When attempting to enhance sustainability, numerous challenges exist, but global warming—a direct result of the rapid rise in carbon dioxide and other greenhouse gases—has become a primary concern for a global society, given its widespread impact on our planet. It is widely recognized that climate change threatens our ecosystem, affecting all aspects of life on the Earth. Apart from the long-term adverse impact on biodiversity, many people around the world have already fallen victim to the effects of global warming. An example of this is desertification expedited by rising global temperatures, which has displaced half a billion people while also destabilizing the food supply, particularly in Africa, where the majority of people live in poverty. The rising sea level also threatens the lives of people living on islands [1]. According to earlier research in this area, by 2100, 48 islands may disappear, and up to 187 million people may lose their homes to the rising ocean [2,3]. Given the increasing number of droughts, floods, and extreme weather events triggered by climate change,

**Citation:** Lee, D.-H.; Yoon, J.-C. Decisions on Pricing, Sustainability Effort, and Carbon Cap under Wholesale Price and Cost-Sharing Contracts. *Sustainability* **2022**, *14*, 4863. https://doi.org/10.3390/ su14084863

Academic Editors: Shaojian Qu, Qingguo Bai, Ying Ji and Congjun Rao

Received: 14 March 2022 Accepted: 15 April 2022 Published: 18 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the United Nations forecasts that the number of climate migrants may reach one billion worldwide by 2050 [4].

In recognition of the fact that climate change is one of the most serious threats faced by humanity, the world has made efforts to mitigate the harmful effects of global warming. In 1997, developed countries agreed on a legally binding treaty to reduce greenhouse gas emissions, known as the Kyoto Protocol, along with the introduction of mechanisms to curb the release of greenhouse gases. The three market-based mechanisms adopted under the Kyoto Protocol—the clean development mechanism, joint implementation, and emission trading—are considered effective ways to control greenhouse gas emissions [5]. The Paris Agreement, adopted in 2015, further strengthened global efforts to address climate change; it sets a specific target for limiting global warming—1.5~2 ◦C above preindustrial levels and requires nearly all countries to reduce their national emissions. Climate change is also included as an important agenda item in the Sustainable Development Goals, which were agreed upon by all United Nations member states in 2015.

Private companies have also joined such sustainability efforts either voluntarily or involuntarily by implementing environmentally friendly practices. The growing awareness of 'responsible consumption' has called for companies increasingly to care about eco-friendly business practices, from manufacturing and packaging to marketing. Over the past decade, the private sector has actively recognized the issue of climate change as part of its 'Corporate Social Responsibility' (CSR). In Velazquez-Cazares et al. [6], CSR is defined as "the responsibility of the enterprises for their impact on the society", highlighting their role in the sustainability, competitiveness, and innovation of the business practices. Globalization, technology, inequalities, crisis, and climate change have pressured companies toward CSR. At the World Economic Forum in 2015, for instance, the CEOs of 79 companies and 20 economic sectors announced their commitment to sharing the responsibility to reduce carbon emissions. On the other hand, other companies are forced to comply with regulations to cut carbon emissions by means of, for instance, cap-and-trade systems. Under a cap-and-trade system, the government puts a cap on the carbon emissions allowed by each company but allows them to trade emissions allowances. This market-based approach is accepted as an effective measure by which to control carbon emissions as it gives companies more flexibility to control their emissions as they operate their business. Studies undertaken to date have shown that the emission cap has a direct impact on a carbon trading price [7–9]. For example, in 2006, companies were allocated 10% more than the emission cap they actually needed to cover their 2005 emissions. This caused carbon trading prices to plummet by 60% in a week in carbon trading markets [10,11]. Therefore, there may be an inverse relationship between the cap and the emission trading price.

A wholesale price contract is a contractual agreement that is widely adopted in many supply chains. With a wholesale price contract, a manufacturer charges a retailer for each product without collaboration (cooperation). However, various strategies to induce collaboration among supply chain participants have been proposed to achieve sustainable supply chain operation. Among them, cost sharing is considered one of the most desirable cooperative contracts, in which supply chain participants can enhance not only their profitability but also their sustainability by sharing their costs incurred during production, marketing, or R&D [12–16]. Thus, this paper focuses on supply chains with wholesale price contracts and cost-sharing contracts that are governed by a cap-and-trade system. As mentioned, because the emission trading price is directly influenced by the emission cap, the supply chain participants' decisions will be affected by the cap. In addition, the collaboration among supply chain participants also has a large effect on their production decisions. To the best of the authors' knowledge, there has been no study on setting the carbon cap under a wholesale price contract and a cost-sharing contract in consideration of the inverse relationship between the carbon cap and the emission trading price. Thus, the main research questions addressed in this article are as follows:

• Under wholesale price and cost-sharing contracts, how does the carbon cap affect manufacturers' sustainability efforts and production decisions?

The rest of this article is organized as follows. In Section 2, a review of the relevant literature is presented. Section 3 reviews the notations and the assumptions in this article. In Section 4, the main results and various numerical examples are presented. The last section provides a summary and some directions for future research.

### **2. Literature Review**

This section reviews the relevant literature considering three different streams of research on sustainable operations: sustainability innovation, collaboration decisions, and operational management under cap-and-trade regulations.

### *2.1. Sustainability Innovation in Supply Chains*

The topic of sustainable operations is a growing concern for supply chain management [17,18]. Hassini et al. [19] defined sustainable supply chain management as the "management of supply chain operations, resources, information, and funds in order to maximize the supply chain profitability while at the same time minimizing the environmental impacts and maximizing social well-being". For the purpose of this article, this subsection focuses on sustainability innovations in supply chains.

Product design is a crucial tool for those involved in sustainable development. Krikke et al. [20] suggested a model that integrates product design with a closed-loop supply chain design. By combining costs and environmental impacts into an objective function, they evaluated three potential designs of a refrigerator in different supply chain configurations. Subramanian et al. [21] examined optimal product-design decisions and demonstrated how financial aid could be used as a lever to encourage firms to design environmentally friendly products by considering two key decisions related to product design: performance and remanufacturability. Chen [22] developed a quality-based model that considers the green features of products as a quality attribute and analyzed strategic decision issues related to the development of sustainable products. Shen et al. [23] discussed optimal product line design for green and nongreen products in terms of quality differentiation. They argued that only when the quality difference between green and nongreen products is large enough does designing and selling green products benefit consumers and generate high social welfare. Zhu and He [24] studied green product design in competitive supply chains and derived equilibrium decisions on the greenness degrees of products. Thies et al. [25] conducted a valuable survey of sustainable product designs with extensive bibliographical references

Firms are increasingly paying more attention to sustainable technology innovations in recent years because of stricter regulations and greater consumer concern over corporate social responsibility and environmental protection. The introduction of new product designs and technology/process innovations requires firms to evaluate the complex cost and environmental tradeoffs. Stuart et al. [26] developed a technology selection model for a firm that considers yield, reliability, and environmental impact tradeoffs. They modeled several constraints for environmental effects, including material/energy consumption and technology/process waste generation. Debo et al. [27] solved the issue of joint pricing and production technology selections by manufacturers in the market where new and remanufactured products coexist. They showed that investing in remanufacturing technology is more profitable when there are more environmentally conscious customers in the market. Drake et al. [9] studied the impact of the carbon tax and cap-and-trade regulations on firms' technology selections and capacity investment decisions. They revealed that a firm's profits are greater and carbon emissions are lower under governmental cap-andtrade regulations, while production quantities are greater under a carbon tax regulation. Raz et al. [28] considered a newsvendor problem for decisions affecting production quantity and environmentally focused process design efforts. They determined a firm's sustainable technology innovation efforts at each stage of the product lifecycle.

### *2.2. Collaboration Decisions in Supply Chain*

This work is also related to the literature on supply chain collaboration between manufacturers and their upstream suppliers or downstream retailers. Klassen and Vachon [29] discovered that supply chain collaboration plays a key role in determining both the form and level of environmental technology investments. Zhu et al. [30] and Green et al. [31] also support the view that collaboration between supply chain members on sustainability innovation efforts enhances both environmental and financial performance outcomes and that collaborative innovation is critical for the success of a circular economy initiative.

As pointed out by Ge et al. [32], most studies in this line of research deal with horizontal R&D cooperation in supply chains [33–35]. Few papers investigate collaboration among firms with vertical relationships. Talluri et al. [36] considered a manufacturer allocating funds to its suppliers to improve performance and found conditions in which the manufacturer benefits from collaborating with its suppliers. They presented a Markowitz portfolio investment model that can be used to help a manufacturer optimally allocate its available dollars while maintaining expected benefits. Under production cost uncertainty, Kim and Netessine [37] investigated how information asymmetry and procurement contracting strategies affect supply chain members' incentives to collaborate. According to their results, a manufacturer prefers an expected margin commitment contract if collaboration results in a large reduction in the unit production cost and demand fluctuations are low. Ghosh and Shah [14] explored collaboration issues in a green supply chain and studied the influence of cost-sharing contracts on the key decisions by supply chain members undertaking green initiatives. Two models of cost-sharing contracts were considered—one where a retailer drives a cost-sharing contract and the other where supply chain members negotiate it.

More recently, Ji et al. [38] investigated the collaboration between manufacturers and retailers in online and offline shops and analyzed how a governmental cap-and-trade policy affects supply chain profits and social welfare by adding supply chain members' efforts to reduce their carbon emissions. Yenipazarli [39] studied the impact of collaboration via supply chain contracts on suppliers' investments in carbon emission reductions during their manufacturing processes. Further, Dai et al. [15] devised game models to investigate two collaboration mechanisms between supply chain members in relation to green R&D investments: cartelization and cost-sharing contracts. Hong and Lee [16] analyzed two popular contract types, revenue- and cost-sharing contracts, considering the development time uncertainties caused by the R&D capabilities of suppliers. They argued that a contract mechanism to determine the fraction of the revenue or cost that a manufacturer shares with its supplier affects supply chain profits and the expected time required for new product development. Ji et al. [11] derived manufacturer equilibrium production decisions under wholesale pricing and revenue sharing contracts and determined optimal governmental carbon caps. They showed that the equilibrium production quantities increase with a carbon cap, whereas manufacturer profit can decrease with stronger carbon cap regulations. They also found that the overall supply chain profit under a revenue-sharing contract is greater than that under a wholesale price contract. Cachon [40] provided an extensive review of the supply chain literature, focusing on the management of incentive conflicts with contracts, where various contracts in supply chains are identified, and their benefits and drawbacks are illustrated.

### *2.3. Operations Management under Cap-and-Trade Regulation*

Given the increasing severity of global warming, many studies of supply chains with cap-and-trade regulations have been actively conducted over the past few decades. The literature on supply chain management under cap-and-trade regulations includes

numerous topics, including pricing, production, inventory, carbon emissions reduction, and carbon cap determination.

Xu et al. [41] studied joint production and the pricing problems of a manufacturer who produces multiple products under cap-and-trade and carbon tax regulations. They presented comparative results on the impacts of the two types of regulation on total carbon emissions, the profits of the firm, and social welfare. Xu et al. [42] extended the work of Xu et al. [41] to study production and pricing issues in a make-to-order (MTO) supply chain with cap-and-trade regulations. Xu et al. [42] analyzed the impact of emission trading prices on the optimal production decisions and the profits of the supply chain members. Bai et al. [43] also considered an MTO supply chain and showed that the profit of a decentralized supply chain can be improved and that carbon emissions can be significantly reduced through supply chain coordination efforts. Yang et al. [44] modeled chain-to-chain competition under cap-and-trade regulations. In their model, each supply chain can either be vertically or horizontally integrated. Yang et al. [44] suggested that a retailer-driven revenue-sharing contract may encourage manufacturers to give up horizontal cooperation, which not only helps all supply chain members achieve a win–win situation but also benefits the environment via a greater reduction in the rate of emissions. Wang et al. [45] examined manufacturing/remanufacturing planning decisions by manufacturers under cap-and-trade regulations. They showed that capital constraints force manufacturers to remanufacture used products at a high level of quality and can considerably reduce carbon emissions. Xu et al. [46] analyzed the equilibrium decisions and coordination mechanisms of a two-echelon supply chain under cap-and-trade regulations and revealed that a twopart tariff contract outperforms a revenue-sharing contract in terms of the profit of a supply chain and the reduction in carbon emissions. Shu et al. [47] dealt with a closed-loop supply chain considering social responsibility and explored the effects of carbon caps and CSR on retailers' recycling decision behavior. They showed that manufacturers' CSR has a positive impact on recycling rates and that CSR dramatically leads to a decrease in carbon emissions. From an inventory management perspective, Hua et al. [7] discussed how firms could control carbon emissions as part of their inventory management effort under cap-and-trade regulations. They demonstrated that the carbon cap and emission trading price have a considerable impact on order decisions, carbon emissions, and total costs. Ji et al. [48] analyzed decisions on carbon emissions reductions and inventory replenishment efforts given low-carbon preferences held by consumers. They suggested that a joint carbon tax and cap-and-trade policy work best for emissions reduction and that a government must tighten the carbon cap to realize a clean industry. Shen et al. [49] studied an inventory model for perishable items under a carbon tax policy with collaborative preservation technology investments. They identified optimal decisions on production, delivery, ordering, and investments to maximize the total supply chain profits considering a carbon tax policy. Bai et al. [50] discussed the influence of reducing carbon emissions on the coordination of the supply chain with a vendor-managed inventory system. They showed that a revenuesharing contract could be introduced to improve profits and reduce carbon emissions in a decentralized supply chain.

Determination of the carbon cap is a crucial decision by a government as part of its work to maximize social welfare. Du et al. [51] considered a supply chain in which an emission-dependent manufacturer and an emission permit supplier interact with each other under cap-and-trade regulations. They determined the optimal allocation of the carbon cap of a manufacturer through consideration of what was termed a fairness distribution in social welfare. Xu et al. [41] found that as the unit environmental damage of a product increases, the government's optimal carbon cap decreases or remains constant. He et al. [52] studied the optimal production of a self-pricing manufacturer and the optimal carbon cap of a government. They found that the optimal carbon cap and the total carbon emissions initially increase and then decrease as the emissions intensity increases. Ji et al. [11] also argued that if the environmental impact of carbon emissions is low or high, the government should keep the optimal carbon cap unchanged; otherwise, the government may decrease the cap.

### **3. Research Methodology**

As discussed, there are many in-depth studies of sustainable innovations and collaborative decisions in supply chains with carbon emission regulations. The literature review in Section 2 shows that governmental cap-and-trade regulations represent a key factor in the profitability and sustainability of supply chains. However, most studies overlook the relationship between cap-and-trade regulations and manufacturers' sustainability innovation efforts. Because a significant relationship is found between a carbon cap and decision making in supply chains, it is natural that governmental cap-and-trade regulations affect the sustainability innovation efforts of a supply chain. This article aims to identify the relationship between such a cap and sustainability efforts in a supply chain. Moreover, most studies assumed that carbon trading prices are permanently constant for analytical simplicity, but this article assumes an inverse relationship between a carbon cap and the emission trading price. According to Section 1, the assumption of such an inverse relationship is reasonable and helps supply chain participants gain meaningful managerial insights.

This article provides Stackelberg game models under both wholesale price and costsharing contracts and presents the equilibrium decisions made by players of each game. In each game, supply chain participants want to maximize or achieve their goals, and their decisions influence each other. The sequence of each Stackelberg game is detailed in Section 4.

### *3.1. Notations*

This article uses the notations in Table 1.

### **Table 1.** Notations.

### *3.2. Assumptions*

This article considers a simple supply chain composed of a downstream retailer and an upstream manufacturer that develops a sustainable product. The supply chain distributes only one type of sustainable product. The retailer purchases the manufacturer's products at the wholesale price *w*. The retailer provides the product to the consumers in the market at a retail price *p*. In the supply chain considered here, the manufacturer makes a sustainability effort *e*, which can boost product demand *d*. This assumption is intuitive because consumers may have higher utility by consuming the sustainable product, meaning that their willingness-to-pay increases, leading to greater demand. Hence, the demand function for the product is formulated as shown below

$$d = 1 - p + e \tag{1}$$

As indicated in Equation (1), the potential market base is assumed to be scaled to 1. Note that without a loss of generality, we assume that *e* has a positive coefficient of one (i.e., effort sensitivity of demand *γ* = 1). This assumption is justified because the results for an arbitrary *γ* can be obtained by scaling the equilibrium effort *e* = *γe* 0 .

To capture the decreasing marginal effect of the sustainability efforts, assume that the investment in developing the sustainable product is an increasing and convex function of the efforts. Hence, the effort cost can be expressed as *θe* <sup>2</sup>/2, where *θ* is the cost coefficient of the effort and assume that *θ* = 1 for analytical convenience. In addition, assume that the sustainability effort affects the unit production cost *c* = *c*<sup>0</sup> + *βe* with the base cost *c*<sup>0</sup> normalized to 0. *β* represents the scenario where the sustainability effort results in an increase in the unit production cost. For example, in the coffee industry, environment-friendly manufacturing processes increase the unit production cost by about 30%. [53]. Additionally, assume that *β* ∈ [0, 1) so that the manufacturer exerts positive sustainability efforts.

Based on an MTO supply chain, this article deals with two types of contracts between the manufacturer and the retailer, specifically a wholesale price contract and a cost-sharing contract. In such a supply chain, the manufacturer and the retailer do not have to focus on the inventory cost or the salvage cost for unsold products. The purpose of this paper is to specify not only the decisions of the supply chain members but also the optimal carbon cap of the government under a cap-and-trade regulation taking into consideration the two types of contracts. Consider the wholesale price contract (cost-sharing contract) as a noncooperative contract (cooperative contract). Under both contracts, the government is assumed to play the role of a Stackelberg game leader. A detailed description of the Stackelberg game under each contract is presented in Section 4. According to the cap-and-trade regulation, the manufacturer is initially given a free quantity of carbon emission credits (also known as carbon emission permits) from a central government. The manufacturer is obligated to hold the credits in an amount larger than or equal to its carbon emissions. The manufacturer can purchase or sell these credits through an outside emissions trading system (ETS). The manufacturer produces the product depending on both the retailer's order and the allocated cap. In this situation, the government wants to determine the optimal carbon cap which maximizes social welfare.

Let *λ* be the carbon emissions incurred when producing one unit of product. Therefore, the total carbon emissions associated with production is *M* = *λd*. A similar expression of *M* can be found in Ji et al. [11] and Gong and Zhou [54]. If the total carbon emission exceeds the given cap (i.e., *M* > *P*), the manufacturer must purchase the emission credits via the ETS to avoid a large penalty. Otherwise, the manufacturer can sell the excess credits via the ETS to obtain economic incentives. Similar to Hua et al. [7], Benjaafar et al. [8], and Ji et al. [11], assume that the carbon trading price is a linear function of the carbon cap, i.e., *b*<sup>0</sup> = *a* − *bP* ≥ 0 (or equivalently *P* ≤ *a*/*b*), where *a* is the maximal price of the emission credits and *b* is the price sensitivity of the cap. The retailer also faces a challenge to lessen the amount of carbon emissions it creates during marketing and selling activities, but the retailer's carbon emissions are neglected because the amount is relatively small.

### **4. Analysis and Interpretation of Results**

With the notations and assumptions in Section 3, the main results and numerical examples of this article are presented in Propositions and Corollaries. Note that all numerical experiments are carried out based on artificially simulated parameter settings. All proofs in Section 4 are given in Appendix A.

### *4.1. Equilibrium Analysis with the Given Carbon Cap*

This subsection presents the equilibrium decisions of the manufacturer and the retailer with the given carbon cap *P*. Hereafter we utilize the superscript *l* ∈ {*W*, *C*}, where *W* and *C* represent the wholesale price contract and the cost-sharing contract, respectively.

### 4.1.1. Wholesale Price Contract

First, consider the wholesale price contract between the manufacturer and the retailer. The profit functions of the manufacturer and the retailer are expressed, respectively, as follows

$$
\pi\_m = (w - \beta \varepsilon)d - \frac{\varepsilon^2}{2} - (a - bP)(M - P) \text{ and } \pi\_r = (p - w)d,\tag{2}
$$

where *π<sup>m</sup>* and *π<sup>r</sup>* denote the profits of the manufacturer and the retailer, respectively. The sequence of the two-stage Stackelberg game under the wholesale price contract is as follows. In the first stage of the game, the manufacturer announces the wholesale price *w* and the sustainability efforts *e*. After specifying the values of *w* and *e*, the retailer determines the retail price for the product *p*. Applying backward induction, the equilibrium values of the decision variable and the profit for each player can be obtained in Proposition 1.

**Proposition 1.** *Given the carbon cap P, the equilibrium values in the wholesale price contract game are determined as follows*

$$\begin{array}{l} w^W = \frac{2 - \beta + \lambda (a - bP)}{3 - \beta}, \; p^W = \frac{3 + \beta (1 - \beta + \lambda (a - bP))}{(1 + \beta)(3 - \beta)}, \; e^W = \frac{(1 - \beta)(1 - \lambda (a - bP))}{(1 + \beta)(3 - \beta)}, \; d^W = \frac{1 - \lambda (a - bP)}{(1 + \beta)(3 - \beta)},\\ M^W = \frac{\lambda (1 - \lambda (a - bP))}{(1 + \beta)(3 - \beta)}, \; \pi^W\_{\text{m}} = \frac{(1 - \lambda (a - bP))^2}{2(1 + \beta)(3 - \beta)} + P(a - bP), \; and \; \pi^W\_r = \left(\frac{1 - \lambda (a - bP)}{(1 + \beta)(3 - \beta)}\right)^2. \end{array} \tag{3}$$

When the government initially sets the carbon cap to zero, the inequality *aλ* < 1 should be assumed to avoid negative demand for the product. From Proposition 1, Corollaries 1–3 can be derived as shown below.

**Corollary 1.** *Under the wholesale price contract, the equilibrium decisions have the following relationships:*

$$
\frac{\partial w^W}{\partial P} < 0, \ \frac{\partial p^W}{\partial P} < 0, \ \frac{\partial e^W}{\partial P} > 0, \ \frac{\partial d^W}{\partial P} > 0, \ and \ \frac{\partial M^W}{\partial P} > 0. \tag{4}
$$

Corollary 1 presents the important fact that the equilibrium decision of each supply chain member depends on the carbon cap. The equilibrium wholesale price decreases with the carbon cap, which encourages the retailer to decrease its retail price. As a result, the demand for the product inevitably increases. This occurs because as the allocated carbon cap increases, the carbon trading price decreases, which leads to a higher marginal profit per unit of the product. Another important fact is that the manufacturer's sustainability effort increases as the carbon cap increases. The manufacturer can obtain higher profits as it produces more products. Therefore, the manufacturer may try to increase the demand for the product, which requires a greater sustainability effort. As the carbon cap increases, sustainability efforts increase, and the manufacturer can thus obtain higher profits. As the cap increases, the production quantity also increases, resulting in more carbon emissions.

**Corollary 2.** *Under the wholesale price contract, the equilibrium profits have the following relationships:*

$$\frac{\partial \pi\_r^W}{\partial P} > 0 \text{ and } \frac{\partial \pi\_m^W}{\partial P} = \begin{cases} > 0, \text{ if } 0 < b < \mathcal{K}\_1 \text{ and } 0 < P < \mathcal{K}\_2, \\\ > 0, \text{ if } b > \mathcal{K}\_1, \\\ < 0, \text{ if } 0 < b < \mathcal{K}\_1 \text{ and } P > \mathcal{K}\_2. \end{cases} \tag{5}$$

$$where \ K\_1 = \frac{2(1+\beta)(3-\beta)}{\lambda^2} \text{ and } K\_2 = \frac{a(1+\beta)(3-\beta) + b\lambda(1-a\lambda)}{b(2(1+\beta)(3-\beta) - b\lambda^2)}.$$

Corollary 2 expresses the relationship between the equilibrium profit and the carbon cap. As indicated in Equation (5), the retailer's equilibrium profit increases with respect to the cap. This conclusion is rather intuitive because the higher the carbon cap, the higher the retailer's marginal profit and the higher the demand for the product and the retailer's profit will increase as well. When the price sensitivity of the carbon cap *b* is lower than the threshold *K*1, the trend of the manufacturer's profit with respect to the carbon cap differs based on the range of the cap. That is, if the cap is under the threshold *K*2, the manufacturer's profit increases along with the cap. Otherwise, the manufacturer's profit decreases. This means that the manufacturer's profit reaches its maximum when the government sets the carbon cap to *K*2. In contrast, when *b* exceeds the threshold *K*1, the manufacturer's profit always increases with the cap. Figure 1 illustrates the relationship between the carbon cap and the manufacturer's profit with the following parameter settings: *λ* = 0.8, *β* = 0.05, *a* = 1, *K*<sup>1</sup> = 9.68 (a) *b* = 0.5 < *K*1, and (b) *b* = 10 > *K*1, which confirms that when 0 < *b* < *K*1, the maximal manufacturer's profit is obtained at *K*<sup>2</sup> = 1.0817, and also confirms that when *b* > *K*1, the manufacturer's profit increases with the cap. In previous studies, such as Xu et al. [41], Gong and Zhou [54], Zhang and Xu [55], Du et al. [56], Xu et al. [57], and Zhang et al. [58], it is argued that the carbon cap always has a positive impact on the manufacturer's profit. However, our result shows that the manufacturer's profit is either positively or negatively affected by the carbon cap; thus, determining the appropriate carbon cap is crucial for the manufacturer. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 10 of 23

**Figure 1.** Carbon cap vs. manufacturer's profit when (**a**) <sup>1</sup> 0 *b K* and (**b**) <sup>1</sup> *b K* . **Figure 1.** Carbon cap vs. manufacturer's profit when (**a**) 0 < *b* < *K*<sup>1</sup> and (**b**) *b* > *K*<sup>1</sup> .

**Corollary 3.** *Under the wholesale price contract, the manufacturer purchases <sup>W</sup> M P emission credits if either Condition 1 or 2 is met. Meanwhile, the manufacturer sells <sup>W</sup> P M emission credits if Condition 3 is met.* **Corollary 3.** *Under the wholesale price contract, the manufacturer purchases <sup>M</sup><sup>W</sup>* <sup>−</sup> *<sup>P</sup> emission credits if either Condition 1 or 2 is met. Meanwhile, the manufacturer sells <sup>P</sup>* <sup>−</sup> *<sup>M</sup><sup>W</sup> emission credits if Condition 3 is met.*

<sup>3</sup> *K* 12.39 , <sup>4</sup> *K* 0.1469

If *P K* 4

*<sup>W</sup> M P*

emission credits if

manufacturer purchases (sells)

*(iii) Condition 3:*  3 4 <sup>0</sup> *b K and P K , where*  3 2 (1 )(3 ) *<sup>K</sup> and*  4 2 (1 ) (1 )(3 ) *a K b .*  (*iii*) *Condition 3:* 0 < *b* < *K*<sup>3</sup> *and P* > *K*4*, where K*<sup>3</sup> = (1+*β*)(3−*β*) *<sup>λ</sup>*<sup>2</sup> *and K*<sup>4</sup> = *λ*(1−*aλ*) (1+*β*)(3−*β*)−*bλ*<sup>2</sup> .

Corollary 3 shows the manufacturer's equilibrium behavior for purchasing/selling emission credits. When the price sensitivity of the carbon cap *b* is under the threshold *K*3 , the manufacturer's purchasing/selling behavior differs according to the range of the carbon cap. If the cap is lower than the threshold *K*4 , the manufacturer must purchase additional emission credits to avoid the penalty and enhance the cap level. Otherwise, the manufacturer is willing to sell excess emission credits to achieve a financial incentive. In contrast, when *b* exceeds the threshold *K*3 , the manufacturer always purchases the Corollary 3 shows the manufacturer's equilibrium behavior for purchasing/selling emission credits. When the price sensitivity of the carbon cap *b* is under the threshold *K*3, the manufacturer's purchasing/selling behavior differs according to the range of the carbon cap. If the cap is lower than the threshold *K*4, the manufacturer must purchase additional emission credits to avoid the penalty and enhance the cap level. Otherwise, the manufacturer is willing to sell excess emission credits to achieve a financial incentive. In contrast, when *b* exceeds the threshold *K*3, the manufacturer always purchases the emission

> 0.5 ,

<sup>3</sup> *b K* 13

*<sup>W</sup> P M* ) emission credits if

. Figure 2a shows that the

*P K* <sup>4</sup> ( *P K* <sup>4</sup> ).

0.05, *a* 0.4 ,

*<sup>W</sup> M P*

emission credits. In summary, there is a threshold for purchasing and selling the emission credits because of the linearly inverse relationship between the carbon cap and the emission trading price. Figure 2 depicts the manufacturer's decision on purchasing/selling

, and (b)

. Meanwhile, as shown in Figure 2b, the manufacturer always purchases

, the manufacturer neither purchases nor sells the emission credits because

*<sup>W</sup> M P* (

, (a)

<sup>3</sup> *b K* .

credits. In summary, there is a threshold for purchasing and selling the emission credits because of the linearly inverse relationship between the carbon cap and the emission trading price. Figure 2 depicts the manufacturer's decision on purchasing/selling the emission credits with the following parameter settings: *λ* = 0.5, *β* = 0.05, *a* = 0.4, *K*<sup>3</sup> = 12.39, *K*<sup>4</sup> = 0.1469, (a) *b* = 1.5 < *K*3, and (b) *b* = 13 > *K*3. Figure 2a shows that the manufacturer purchases (sells) *<sup>M</sup><sup>W</sup>* <sup>−</sup> *<sup>P</sup>* (*<sup>P</sup>* <sup>−</sup> *<sup>M</sup>W*) emission credits if *<sup>P</sup>* <sup>&</sup>lt; *<sup>K</sup>*<sup>4</sup> (*<sup>P</sup>* <sup>&</sup>gt; *<sup>K</sup>*4). If *<sup>P</sup>* <sup>=</sup> *<sup>K</sup>*4, the manufacturer neither purchases nor sells the emission credits because *M<sup>W</sup>* = *P*. Meanwhile, as shown in Figure 2b, the manufacturer always purchases *<sup>M</sup><sup>W</sup>* <sup>−</sup> *<sup>P</sup>* emission credits if *b* > *K*3. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 11 of 23

**Figure 2.** Carbon cap vs. emission credit when (**a**) <sup>3</sup> 0 *b K* and (**b**) <sup>3</sup> *b K* . **Figure 2.** Carbon cap vs. emission credit when (**a**) 0 < *b*< *K*<sup>3</sup> and (**b**) *b* > *K*3.

#### 4.1.2. Cost-Sharing Contract 4.1.2. Cost-Sharing Contract

*C*

*p*

*d*

lower than 0.125 because

Next, consider the collaboration model. Under a cost-sharing contract between supply chain members, the retailer shares fraction of the manufacturer's cost related to the production and sustainability innovation efforts. The profit functions of the manufacturer and the retailer are then expressed, respectively, as shown below. Next, consider the collaboration model. Under a cost-sharing contract between supply chain members, the retailer shares *δ* fraction of the manufacturer's cost related to the production and sustainability innovation efforts. The profit functions of the manufacturer and the retailer are then expressed, respectively, as shown below.

$$\text{and the retained are then expressed, respectively, as shown below.}$$

$$\pi\_{\text{ll}} = (w - (1 - \delta)\beta\epsilon)d - \frac{(1 - \delta)\epsilon^2}{2} - (a - bP)(M - P) \text{ and } \pi\_{\text{r}} = (p - w - \delta\beta\epsilon)d - \frac{\delta\epsilon^2}{2}. \tag{6}$$

Under the cost-sharing contract, the sequence of the three-stage Stackelberg game is as follows. In the first stage, the retailer determines the collaboration level that maximizes its profit. In the second stage, the manufacturer announces the wholesale price *w* and the sustainability effort *e* . After specifying the values of *w* and *e* , the retailer determines the retail price for the product *p* in the last stage. Applying backward induction, the equilibrium values of the decision variable and the profit for each player are obtained in Proposition 2. Under the cost-sharing contract, the sequence of the three-stage Stackelberg game is as follows. In the first stage, the retailer determines the collaboration level *δ* that maximizes its profit. In the second stage, the manufacturer announces the wholesale price *w* and the sustainability effort *e*. After specifying the values of *w* and *e*, the retailer determines the retail price for the product *p* in the last stage. Applying backward induction, the equilibrium values of the decision variable and the profit for each player are obtained in Proposition 2.

**Proposition 2.** *Given the carbon cap P , the equilibrium values in the cost-sharing contract game are determined as follows:* 2 (1 ) 2 3 (1 )(2 )(7 2 ) ( )(3 )(2 5 ) *<sup>C</sup> a bP* **Proposition 2.** *Given the carbon cap P, the equilibrium values in the cost-sharing contract game are determined as follows:*

$$\begin{split} \text{Transined as follows:}\\ \delta^{\mathbb{C}} &= \frac{(1-\beta^{2})}{8}, \; w^{\mathbb{C}} = \frac{(1+\beta)(2-\beta)(7+2\beta-\beta^{2}) + \lambda(a-bP)(3-\beta)(2+5\beta+\beta^{3})}{4(5+6\beta-3\beta^{2})},\\ p^{\mathbb{C}} &= \frac{21+14\beta-11\beta^{2}-\lambda(a-bP)(1-10\beta+\beta^{2})}{4(5+6\beta-3\beta^{2})}, \; e^{\mathbb{C}} = \frac{2(1-\beta)(1-\lambda(a-bP))}{5+6\beta-3\beta^{2}}\\ d^{\mathbb{C}} &= \frac{(7+2\beta-\beta^{2})(1-\lambda(a-bP))}{4(5+6\beta-3\beta^{2})}, \; M^{\mathbb{C}} = \frac{\lambda(7+2\beta-\beta^{2})(1-\lambda(a-bP))}{4(5+6\beta-3\beta^{2})},\\ \pi\_{\mathbb{M}}^{\mathbb{C}} &= \frac{(7+2\beta-\beta^{2})(1-\lambda(a-bP))^{2}}{8(5+6\beta-3\beta^{2})} + P(a-bP), \; and \; \pi\_{r}^{\mathbb{C}} = \frac{(9-2\beta+\beta^{2})(1-\lambda(a-bP))^{2}}{16(5+6\beta-3\beta^{2})}. \end{split} \tag{7}$$

*a*1  2 2

to avoid the negative

(0, 1) . From Proposition

2 (7 2 ) 1 ( ) ( ) 8(5 6 3 ) *C m P a bP , and*  2 (9 2 ) 1 ( ) 16(5 6 3 ) *C r a bP .* Under the cost-sharing contract, we assume that *aλ* < 1 to avoid the negative demand for the product. Note that the equilibrium retailer's collaboration level must be lower than

demand for the product. Note that the equilibrium retailer's collaboration level must be

is a decreasing function when

Under the cost-sharing contract, we assume that

*C*

 2 2

0.125 because *δ <sup>C</sup>* is a decreasing function when *<sup>β</sup>* <sup>∈</sup> (0, 1). From Proposition 2, Corollaries 4–6 are derived as shown below.

**Corollary 4.** *Under the cost-sharing contract, the equilibrium decisions have the following relationships:*

$$
\frac{\partial w^{\mathbb{C}}}{\partial P} < 0, \,\frac{\partial c^{\mathbb{C}}}{\partial P} > 0, \,\frac{\partial d^{\mathbb{C}}}{\partial P} > 0, \,\frac{\partial M^{\mathbb{C}}}{\partial P} > 0, \,\text{and } \frac{\partial p^{\mathbb{C}}}{\partial P} = \left\{ \begin{array}{c} > 0, \,\, if \, 0 < \beta < 5 - 2\sqrt{6} \\ < 0, \,\, if \, 5 - 2\sqrt{6} < \beta < 1. \right\} \end{array} \tag{8}
$$

Under the cost-sharing contract, if 0 < *β* < 5 − 2 √ 6 (5 − 2 √ 6 < *β* < 1), the retail price increases (decreases) with respect to the carbon cap. Regarding the wholesale price, the sustainability effort, and the demand for the product, relationships similar to Corollary 1 are found. Accordingly, further statements are omitted.

**Corollary 5.** *Under the cost-sharing contract, the equilibrium profits have the following relationships:*

$$
\frac{\partial \pi\_r^{\mathbb{C}}}{\partial P} > 0 \text{ and } \frac{\partial \pi\_m^{\mathbb{C}}}{\partial P} = \left\{ \begin{array}{c} > 0, \ if f \, 0 < b < \mathbb{K}\_5 \,\text{and} \,\, 0 < P < \mathbb{K}\_6 \\\ > 0, \ if f > \mathbb{K}\_5. \\\ < 0, \ if f \, 0 < b < \mathbb{K}\_5 \,\text{and} \,\, P > \mathbb{K}\_6. \end{array} \right. \tag{9}
$$

.

*where K*<sup>5</sup> = 8(5+6*β*−3*β* 2 ) *<sup>λ</sup>*2(7+2*β*−*<sup>β</sup>* 2) *and K*<sup>6</sup> = 4*a*(5+6*β*−3*β* 2 )+*bλ*(1−*aλ*)(7+2*β*−*β* 2 ) *b*(8(5+6*β*−3*β* <sup>2</sup>)−*bλ*2(7+2*β*−*<sup>β</sup>* <sup>2</sup>))

Corollary 5 shows results similar to those of Corollary 2. Even under the cost-sharing contract, the retailer's profit increases as the carbon cap increases. When the price sensitivity of the carbon cap *b* is under the threshold *K*5, the trend of the manufacturer's profit differs according to the range of the cap. That is, if the cap is under (exceeds) threshold *K*6, the manufacturer's profit increases (decreases) along with the cap. Hence, the manufacturer obtains its maximal profit at *P* = *K*6. On the other hand, when *b* exceeds the threshold *K*5, the manufacturer's profit always increases. Comparing the critical cap shown in Corollaries 2 and 5, the following relation is found that

$$K\_6 - K\_2 = \frac{\lambda (2 - a\lambda)(1 - \beta^4)}{(2(3 - \beta)(1 + \beta) - b\lambda^2)(8(5 + 6\beta - 3\beta^2) - b\lambda^2(7 + 2\beta - \beta^2))} > 0,\tag{10}$$

which means that by adopting the cost-sharing contract, the manufacturer maintains its profit growth with a relatively higher carbon cap. This argument is depicted in Figure 3 with the following parameter settings: *λ* = 0.8, *β* = 0.05, *a* = 1, *b* = 0.5, *K*<sup>2</sup> = 1.0817, and *K*<sup>6</sup> = 1.085. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 13 of 23

**Figure 3.** Comparison of the critical carbon cap between two contracts with respect to the manufacturer's profit. **Figure 3.** Comparison of the critical carbon cap between two contracts with respect to the manufacturer's profit.

<sup>8</sup> 2 2 2 (1 )(7 2 ) 4(5 6 3 ) (7 2 )

4

*b*

(1 )(1 ) <sup>0</sup>

<sup>8</sup> *K* 0.1534

, the manufacturer must purchase additional emission credits

, the manufacturer can sell excess emission credits

, the manufacturer purchases emission

*a*

which means that the threshold of purchasing/selling the emission credits with the costsharing contract is higher than that under the wholesale price contract. Figure 4 shows the difference in the manufacturer's carbon trading decision between the wholesale price

, and

*K P K* 4 8

credits under the cost-sharing contract, whereas it sells them under the wholesale price

(3 )(1 ) 4(5 6 3 ) (7 2 ) *a*

*b b*

8 4 2 2 2 2

contract and the cost-sharing contract with the following parameter settings:

Corollary 6 shows the manufacturer's equilibrium decision with regard to purchasing/selling the emission credits under the cost-sharing contract. Corollary 6 is similar to Corollary 3; thus, redundant statements are omitted here. Comparing the critical

2

,

. Figure 4 confirms the

(11)

0.5 ,

*.*

*<sup>C</sup> M P emission*

*<sup>C</sup> P M emission*

7 8 0 *b K and P K ,*

*and*

*K*

cap shown in Corollaries 3 and 6, the following relation is found that

*P K* <sup>8</sup>

*credits if Condition 6 is met.*

*K K*

following: (i) when

under both contracts; (ii) when

under both contracts; and (iii) when

<sup>7</sup> *b K ,*

7 2 2 4(5 6 3 ) (7 2 )

2

0.05 , *a* 0.4 , *b* 1.5 , <sup>4</sup> *K* 0.1469

*P K* <sup>4</sup>

*(i) Condition 4:*

*(ii) Condition 5:*

*(iii) Condition 6:*

*K*

*where*

contract.

**Corollary 6.** *Under the cost-sharing contract, the manufacturer purchases*

*credits if either Condition 4 or 5 is met. Meanwhile, the manufacturer sells*

**Corollary 6.** *Under the cost-sharing contract, the manufacturer purchases <sup>M</sup><sup>C</sup>* <sup>−</sup> *<sup>P</sup> emission credits if either Condition 4 or 5 is met. Meanwhile, the manufacturer sells <sup>P</sup>* <sup>−</sup> *<sup>M</sup><sup>C</sup> emission credits if Condition 6 is met.*

$$where \ K\_7 = \frac{4(5 + 6\beta - 3\beta^2)}{\lambda^2(7 + 2\beta - \beta^2)} \text{ and } \ K\_8 = \frac{\lambda(1 - a\lambda)(7 + 2\beta - \beta^2)}{4(5 + 6\beta - 3\beta^2) - b\lambda^2(7 + 2\beta - \beta^2)}.$$

Corollary 6 shows the manufacturer's equilibrium decision with regard to purchasing/selling the emission credits under the cost-sharing contract. Corollary 6 is similar to Corollary 3; thus, redundant statements are omitted here. Comparing the critical cap shown in Corollaries 3 and 6, the following relation is found that

$$K\_8 - K\_4 = \frac{\lambda (1 - a\lambda)(1 - \beta^4)}{((3 - \beta)(1 + \beta) - b\lambda^2)(4(5 + 6\beta - 3\beta^2) - b\lambda^2(7 + 2\beta - \beta^2))} > 0,\tag{11}$$

which means that the threshold of purchasing/selling the emission credits with the costsharing contract is higher than that under the wholesale price contract. Figure 4 shows the difference in the manufacturer's carbon trading decision between the wholesale price contract and the cost-sharing contract with the following parameter settings: *λ* = 0.5, *β* = 0.05, *a* = 0.4, *b* = 1.5, *K*<sup>4</sup> = 0.1469, and *K*<sup>8</sup> = 0.1534. Figure 4 confirms the following: (i) when *P* < *K*4, the manufacturer must purchase additional emission credits under both contracts; (ii) when *P* > *K*8, the manufacturer can sell excess emission credits under both contracts; and (iii) when *K*<sup>4</sup> < *P* < *K*8, the manufacturer purchases emission credits under the cost-sharing contract, whereas it sells them under the wholesale price contract. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 14 of 23

**Figure 4.** Comparison of the critical carbon cap between two contracts with respect to the emission credits. **Figure 4.** Comparison of the critical carbon cap between two contracts with respect to the emission credits.

#### 4.1.3. Comparison 4.1.3. Comparison

*<sup>W</sup> m*

and

contract.

*<sup>C</sup> m*

(1 ) *W W C C C m e e m*

*4.2. Government's Optimal Decision on Carbon Cap*

Thus far, this article has regarded the carbon cap

optimal carbon cap, the government will achieve this objective.

initially set by the government. However, henceforth, we consider

One may be curious about the differences in the equilibrium values between two contracts. This subsection conducts a comparative analysis by comparing Propositions 1 and 2. The result is as follows. One may be curious about the differences in the equilibrium values between two contracts. This subsection conducts a comparative analysis by comparing Propositions 1 and 2. The result is as follows.

Corollary 7 shows that a cost-sharing contract outperforms a wholesale price contract in terms of the profitability and sustainability of a supply chain. It must be first noted that the sustainability effort under the cost-sharing contract is greater than that under the

denote the marginal cost under the wholesale price and cost-sharing

is obtained. That is, the higher marginal cost under the cost-

*P*

as an exogenous parameter

as an endogenous

*P*

the burden of product development and reduce production costs, ultimately leading to greater sustainability efforts. This makes it possible for the product to become more sustainable, which increases consumer utility as well as the demand for the product. Let

contracts, respectively. Following Equations (2) and (6), the relation

sharing contract forces the manufacturer to raise the wholesale price, which results in an increase in the retail price. Corollary 7 also confirms that the profit of each supply chain member as well as the supply chain profit will increase if the retailer adopts a cost-sharing contract. Under the cost-sharing contract, the demand and prices increase at the same time, resulting in a natural increase in the profit of each supply chain member and leading to an increase in the overall supply chain profits. Finally, more carbon emissions are inevitable owing to the increased production of the product under the cost-sharing

decision variable. In reality, the government may have a goal when implementing capand-trade regulations. Assume that the following possible objective is considered by the government: the government wants to maximize social welfare. By determining the

**Corollary 7.** *The following relation is found that* **Corollary 7.** *The following relation is found that*

$$\varepsilon^{\mathsf{W}} < \varepsilon^{\mathsf{C}}, \; d^{\mathsf{W}} < d^{\mathsf{C}}, \; w^{\mathsf{W}} < w^{\mathsf{C}}, \; p^{\mathsf{W}} < p^{\mathsf{C}}, \; M^{\mathsf{W}} < M^{\mathsf{C}}, \; \pi^{\mathsf{W}}\_{\mathsf{m}} < \pi^{\mathsf{C}}\_{\mathsf{m}}, \; \pi^{\mathsf{W}}\_{\mathsf{r}} < \pi^{\mathsf{C}}\_{\mathsf{r}}, \; \text{and } \pi^{\mathsf{W}}\_{\mathsf{sc}} < \pi^{\mathsf{C}}\_{\mathsf{sc}}.\tag{12}$$

Corollary 7 shows that a cost-sharing contract outperforms a wholesale price contract in terms of the profitability and sustainability of a supply chain. It must be first noted that the sustainability effort under the cost-sharing contract is greater than that under the wholesale price contract. Cost sharing with the retailer can help the manufacturer reduce the burden of product development and reduce production costs, ultimately leading to greater sustainability efforts. This makes it possible for the product to become more sustainable, which increases consumer utility as well as the demand for the product. Let *m<sup>W</sup>* and *m<sup>C</sup>* denote the marginal cost under the wholesale price and cost-sharing contracts, respectively. Following Equations (2) and (6), the relation *m<sup>W</sup>* = *βe <sup>W</sup>* <sup>&</sup>lt; (<sup>1</sup> <sup>−</sup> *<sup>δ</sup> <sup>C</sup>*)*βe <sup>C</sup>* = *m<sup>C</sup>* is obtained. That is, the higher marginal cost under the cost-sharing contract forces the manufacturer to raise the wholesale price, which results in an increase in the retail price. Corollary 7 also confirms that the profit of each supply chain member as well as the supply chain profit will increase if the retailer adopts a cost-sharing contract. Under the costsharing contract, the demand and prices increase at the same time, resulting in a natural increase in the profit of each supply chain member and leading to an increase in the overall supply chain profits. Finally, more carbon emissions are inevitable owing to the increased production of the product under the cost-sharing contract.

### *4.2. Government's Optimal Decision on Carbon Cap*

Thus far, this article has regarded the carbon cap *P* as an exogenous parameter initially set by the government. However, henceforth, we consider *P* as an endogenous decision variable. In reality, the government may have a goal when implementing cap-and-trade regulations. Assume that the following possible objective is considered by the government: the government wants to maximize social welfare. By determining the optimal carbon cap, the government will achieve this objective.

Once again, this section analyzes the government's optimal decisions regarding the carbon cap under both contracts. To do this, we initially formulate the revenue and cost terms separately. We then integrate them to derive the objective function of the government problem. Social welfare *SW* is a function of the cap and takes the form of

$$SW(P) = \int\_{p}^{p\_{\text{max}}} (1 - p + e) dp + \pi\_{\text{sc}} - \eta M\_{\prime} \tag{13}$$

where *<sup>p</sup>*max is the maximum price of the product. The first term R *<sup>p</sup>*max *p* (1 − *p* + *e*)*dp* represents the value of the consumer surplus, which, in economics, is defined as the gap between the maximum price consumers are willing to pay and the actual price they pay. From simple algebra, it is obtained that R *<sup>p</sup>*max *p* (1 − *p* + *e*)*dp* = *d* <sup>2</sup>/2. The second term is the supply chain profit, which is defined as the sum of the manufacturer's and retailer's profits. The government wants to minimize environmental degradation as the manufacturer produces the product. Let *η* be the unit environmental impact of the product. The coefficient *η* measures the degree of environmental damage due to the manufacturer's production process and the associated pollutants in monetary terms. Thus, the total environmental damage costs caused by production are expressed as *ηM*. It is important to note that the carbon trading cost (revenue) is not included in the social welfare function in Equation (13) because it is a transaction between the manufacturer and the government.

Assume that the government is an overall game leader under both a wholesale price contract and a cost-sharing contract. Let *P <sup>l</sup>* denote the equilibrium carbon cap. Under each contract, *P l* is obtained by solving the following maximization problem:

$$P^l = \underset{0 \le P \le a/b}{\text{argmax}} \, \, \mathcal{W}^l(P), \,\, for \,\, l \in \{W, \,\, \mathbb{C}\}. \tag{14}$$

The main results of this subsection are presented in Propositions 3 and 4.

0.3248 *<sup>C</sup> P*

and

*(i) If*

*(ii) If*

*(iii) If*

*(iv) If*

*where*

<sup>11</sup> *b K*

<sup>11</sup> *b K*

<sup>11</sup> *b K ,*

obtained as follows: **Corollary 8.** *Assuming*

*K*

*and K*<sup>12</sup>

*and K*<sup>12</sup> *,*

*<sup>C</sup> a P*

*b ,*

**Proposition 3.** *Under the wholesale price contract, the government's optimal decision on the carbon cap is given by:*

$$\text{(i)}\quad\text{If }b0.$$

$$\text{(ii)}\quad \text{If } b = \text{K}\_{\partial} \text{ and } \eta > \text{K}\_{10\prime}\stackrel{\text{}P^W}{\underset{\text{....}}{=}} 0.$$

Proposition 3 shows that the government's optimal decision about the carbon cap differs based on the price sensitivity of the cap *b* and the unit environmental impact cost *η*. If *b* < *K*9, the social welfare function is strictly concave with respect to the cap; therefore, solving the first-order condition determines the global maximizer of the government's problem in Equation (14). If *b* = *K*<sup>9</sup> and *η* > *K*<sup>10</sup> (*η* < *K*10), social welfare is a linearly decreasing (increasing) function of the carbon cap; thus, the optimal carbon cap equals zero (*a*/*b*). Lastly, social welfare is a convex and increasing function of the cap if *b* > *K*9. Accordingly, the optimal carbon cap equals *a*/*b*. Figure 5 depicts Proposition 3 with the following parameter settings: *λ* = 0.8, *β* = 0.1, *a* = 1, *K*<sup>9</sup> = 5.1374, and *K*<sup>10</sup> = 1.4553. In Figure 5a, the set *b* = 2 < *K*9, and the social welfare is maximized at *P <sup>C</sup>* = 0.3248. Figure 5b–d correspond to Proposition 3(ii), 3(iii) and 3(iv), respectively. *Sustainability* **2022**, *14*, x FOR PEER REVIEW 16 of 23 <sup>10</sup> *K* 1.4553 . In Figure 5a, the set 9 *b K* 2 , and the social welfare is maximized at . Figure 5b–d correspond to Proposition 3(ii), 3(iii) and 3(iv), respectively.

.

**Figure 5.** Carbon cap vs. social welfare when (**a**) <sup>9</sup> *b K* 2 , (**b**) <sup>9</sup> *b K* and 10 2 *K* , (**c**) <sup>9</sup> *b K* 10 1 *K* , (**d**) <sup>9</sup> *b K* 10 . **Figure 5.** Carbon cap vs. social welfare when (**a**) *b* = 2 < *K*<sup>9</sup> , (**b**) *b* = *K*<sup>9</sup> and *η* = 2 > *K*10, (**c**) *b* = *K*<sup>9</sup> and *η* = 1 < *K*10, (**d**) *b* = 10 > *K*9.

**Proposition 4.** *Under the cost-sharing contract, the government's optimal decision on the carbon cap is given by* 2 2 2 2 3 4 16(5 6 3 ) (279 324 134 28 7 ) *a b* **Proposition 4.** *Under the cost-sharing contract, the government's optimal decision on the carbon cap is given by*

2

*a*

*.*

4(5 6 3 )(2 ) (7 2 )

<sup>12</sup> 3 2

*l W C* { , } *.* (15)

*b*

can up 5 green by
$$\begin{array}{ll} a\left(16\left(5+6\beta-3\beta^{2}\right)^{2}-b\lambda^{2}\left(279+324\beta-134\beta^{2}-28\beta^{3}+7\beta^{4}\right)\right) \\\quad\text{(i)}\quad f\ b < K\_{11}, P^{\mathbb{C}} = \frac{+b\lambda\left(279+324\beta-134\beta^{2}-28\beta^{3}+7\beta^{4}-4\eta\lambda\left(5+6\beta-3\beta^{2}\right)\left(7+2\beta-\beta^{2}\right)\right)}{b\left(32\left(5+6\beta-3\beta^{2}\right)^{2}-b\lambda^{2}\left(279+324\beta-134\beta^{2}-28\beta^{3}+7\beta^{4}\right)\right)}, \end{array}$$

min{ , } 9 11 *b K K , it is found that*

*, for*

0

*l P*

Proposition 4 presents the government's optimal decision regarding the carbon cap under the cost-sharing contract. Because Proposition 4 is similar to Proposition 3, we skip any redundant explanations. Following Propositions 3 and 4, Corollaries 8 and 9 are

*and*

*K*

*,* 0 *<sup>C</sup> P ,*

<sup>11</sup> 2 2 3 4 32(5 6 3 ) (279 324 134 28 7 )

*<sup>C</sup> a P*

*b ,*

2 2

$$\begin{array}{ll} \text{(ii)} & \text{If } b = K\_{11} \text{ and } \eta > K\_{12}, P^C = 0, \\\text{(iii)} & \text{If } b = K\_{11} \text{ and } \eta < K\_{12}, P^C = \frac{\mathfrak{g}}{b}, \\\text{(iv)} & \text{If } b > K\_{11}, P^C = \frac{\mathfrak{g}}{b}, \\\text{where } K\_{11} = \frac{32(5 + 6\beta - 3\beta^2)^2}{\lambda^2 (279 + 324\beta - 134\beta^2 - 28\beta^3 + 7\beta^4)} \text{ and } K\_{12} = \frac{4(5 + 6\beta - 3\beta^2)(2 - a\lambda)}{b\lambda^3 (7 + 2\beta - \beta^2)}. \end{array}$$

Proposition 4 presents the government's optimal decision regarding the carbon cap under the cost-sharing contract. Because Proposition 4 is similar to Proposition 3, we skip any redundant explanations. Following Propositions 3 and 4, Corollaries 8 and 9 are obtained as follows:

**Corollary 8.** *Assuming b <* min{*K*9, *K*11}*, it is found that*

$$\frac{\partial P^l}{\partial \eta} < 0,\text{ for }l \in \{\mathcal{W}, \mathbb{C}\}.\tag{15}$$

Corollary 8 confirms that the carbon cap decreases as the unit environmental impact cost *η* increases. As indicated in Equation (13), *η* has a negative influence on social welfare. When *η* increases, the total environmental damage cost also increases; thus, the government wants to reduce the environmental damage by reducing the production quantity of the product. In our model, the only way for the government to reduce the manufacturer's production quantity is to lower the carbon cap. Note that from Corollaries 1 and 4, the demand for the product decreases as the carbon cap decreases.

**Corollary 9.** *Assuming b* < min{*K*9, *K*11}*, it is found that*

$$P^W - P^\mathbb{C} = \left\{ \begin{array}{c} \le 0, \text{ if } \eta \le K\_{13} = \frac{(2 - a\lambda)(111 + 148\beta - 46\beta^2 - 28\beta^3 + 7\beta^4)}{8\lambda(1 + \beta)(3 - \beta)(5 + 6\beta - 3\beta^2) - b\lambda^3(3 + 10\beta - 5\beta^2)} \land \\ > 0, \text{ otherwise.} \end{array} \right\} \tag{16}$$

Corollary 9 shows a comparison of the carbon caps under each contract. If *η* is low, the government sets a higher carbon cap under the cost-sharing contract. By setting a higher carbon cap when *η* is relatively low, the government wants to maintain the cooperation between the manufacturer and the retailer for greater supply chain profit and greater consumer surplus. On the other hand, if *η* is high, the government sets a higher carbon cap under the wholesale price contract. By doing so, the government encourages the manufacturer to increase its sustainable innovation efforts, which boosts the demand for the product. The increased demand raises consumer surplus as well as the supply chain profit, which compensates for the total environmental impact cost. Figure 6 shows a comparison between the optimal carbon caps under each type of contract with the following parameter settings: *λ* = 0.8, *β* = 0.1, *a* = 1, *b* = 2, *η* = 0.5, *K*<sup>13</sup> = 1.3711, *P <sup>W</sup>* = 0.4069, and *P <sup>C</sup>* = 0.4137. As illustrated in Figure 6, the optimal carbon cap under the cost-sharing contract is greater than that under the wholesale price contract when *η* is under the threshold *K*13.

Corollary 8 confirms that the carbon cap decreases as the unit environmental impact

government wants to reduce the environmental damage by reducing the production quantity of the product. In our model, the only way for the government to reduce the manufacturer's production quantity is to lower the carbon cap. Note that from Corollaries

1 and 4, the demand for the product decreases as the carbon cap decreases.

*P P <sup>b</sup>*

0.8 ,

min{ , } 9 11 *b K K , it is found that*

*a*

Corollary 9 shows a comparison of the carbon caps under each contract. If

the government sets a higher carbon cap under the cost-sharing contract. By setting a

cooperation between the manufacturer and the retailer for greater supply chain profit and

carbon cap under the wholesale price contract. By doing so, the government encourages the manufacturer to increase its sustainable innovation efforts, which boosts the demand for the product. The increased demand raises consumer surplus as well as the supply chain profit, which compensates for the total environmental impact cost. Figure 6 shows a comparison between the optimal carbon caps under each type of contract with the

the cost-sharing contract is greater than that under the wholesale price contract when

0.1 , *a* 1 , *b* 2 ,

increases, the total environmental damage cost also increases; thus, the

<sup>13</sup> 2 3 2

8 (1 )(3 )(5 6 3 ) (3 10 5 )

is relatively low, the government wants to maintain the

. As illustrated in Figure 6, the optimal carbon cap under

(2 )(111 148 46 28 7 ) 0, ,

has a negative influence on social

2 3 4

is high, the government sets a higher

0.5 , <sup>13</sup> *K* 1.3711 ,

(16)

is low,

increases. As indicated in Equation (13),

0, .

*if K*

*otherwise*

greater consumer surplus. On the other hand, if

0.4137 *<sup>C</sup> P*

*K*<sup>13</sup> .

**Figure 6.** Comparison of the optimal carbon caps when *η* < *K*13.

### **5. Conclusions**

cost

welfare. When

**Corollary 9.** *Assuming*

higher carbon cap when

following parameter settings:

, and

is under the threshold

0.4069 *<sup>W</sup> P*

*W C*

This article discussed equilibrium decisions about pricing and sustainability efforts in a supply chain under wholesale price and cost-sharing contracts. The major findings of this article are summarized below:

This article provides several recommendations for firms that undertake sustainability efforts and face carbon emission constraints. However, there are also limitations that can be expanded upon and improved in future research: (1) Newsvendor model: the assumption of uncertain demand for the product is more complex but more realistic; (2) retailer's sustainability effort: an extended model can assume that the retailer can participate in sustainability activities, such as green retailing and green marketing; (3) other contracts: a comparative analysis of other supply chain cooperation contracts will provide more meaningful insights; and (4) multiple participants: in reality, multiple manufacturers and retailers either collaborate or compete in various supply chains. It would be worthwhile to analyze a supply chain with more complex but realistic conditions.

**Author Contributions:** Conceptualization, D.-H.L. and J.-C.Y.; Methodology, D.-H.L.; Software, D.-H.L.; validation, J.-C.Y.; Formal analysis, D.-H.L. and J.-C.Y.; Investigation, D.-H.L. and J.-C.Y.; Data curation, J.-C.Y.; writing—original draft preparation, D.-H.L. and J.-C.Y.; writing—review and editing, D.-H.L. and J.-C.Y.; visualization, D.-H.L. and J.-C.Y.; supervision, D.-H.L. and J.-C.Y.; funding acquisition, J.-C.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Basic Science Research through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2019R1I1A3A01061157).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **Appendix A**

**Proof of Proposition 1.** Because *∂* <sup>2</sup>*πr*/*∂p* <sup>2</sup> <sup>=</sup> <sup>−</sup><sup>2</sup> <sup>&</sup>lt; 0, *<sup>π</sup><sup>r</sup>* is strictly concave with respect to *p*. Thus, solving the first-order condition (FOC) of the retailer's problem yields *p* = (1 + *e* + *w*)/2. Integrating *p* into the manufacturer's problem, the following Hessian matrix is obtained:

$$\mathbf{H}^{W} = \begin{pmatrix} \frac{\partial^2 \pi\_{\rm H}}{\partial w^2} & \frac{\partial^2 \pi\_{\rm H}}{\partial y \partial \epsilon} \\ \frac{\partial^2 \pi\_{\rm H}}{\partial c \partial w} & \frac{\partial^2 \pi\_{\rm H}}{\partial c^2} \end{pmatrix} = \begin{pmatrix} -1 & \frac{1+\beta}{2} \\ \frac{1+\beta}{2} & -1-\beta \end{pmatrix}. \tag{A1}$$

We define ∆ *l k* as the leading principal minor of order *k* in **H***<sup>l</sup>* for *l* ∈ {*W*, *C*}. We then find that ∆ *W* <sup>1</sup> = −1 < 0 and ∆ *W* <sup>2</sup> = (1 + *β*)(3 − *β*)/4 > 0, which implies that the manufacturer's profit is strictly concave with respect to *w* and *e*. By solving the FOCs of the manufacturer's problem, the equilibrium decisions and profits under the wholesale price contract are determined, as presented in Equation (3).

**Proof of Corollary 1.** Under the wholesale price contract, the first-order derivatives of the equilibrium decisions with respect to the carbon cap *P* are given by

$$\begin{array}{lcl} \frac{\partial w^{W}}{\partial P} = -\frac{b\lambda}{3-\beta} < 0, \; \frac{\partial p^{W}}{\partial P} = -\frac{b\beta\lambda}{(1+\beta)(3-\beta)} < 0, \; \frac{\partial e^{W}}{\partial P} = \frac{b\lambda(1-\beta)}{(1+\beta)(3-\beta)} > 0, \\\frac{\partial d^{W}}{\partial P} = \frac{b\lambda}{(1+\beta)(3-\beta)} > 0, \; \text{and} \; \frac{\partial M^{W}}{\partial P} = \frac{b\lambda^{2}}{(1+\beta)(3-\beta)} > 0. \end{array} \tag{A2}$$

Equation (A2) confirms Corollary 1.

**Proof of Corollary 2.** Under the wholesale price contract, the first-order derivatives of the equilibrium profits with respect to the carbon cap *P* are given by

$$\frac{\partial \pi\_r^W}{\partial P} = \frac{2b\lambda \left(1 - \lambda (a - bP)\right)}{\left(1 + \beta\right)^2 \left(3 - \beta\right)^2} > 0 \text{ and } \frac{\partial \pi\_m^W}{\partial P} = \frac{b\lambda \left(1 - \lambda (a - bP)\right)}{\left(1 + \beta\right) \left(3 - \beta\right)} + a - 2bP. \tag{A3}$$

When *b* > *K*1, *∂π<sup>W</sup> <sup>m</sup>* /*∂P* > 0 regardless of *P*. When 0 < *b* < *K*1, *∂π<sup>W</sup> <sup>m</sup>* /*∂P* > 0 (< 0) if 0 < *P* < *K*<sup>2</sup> (*P* > *K*2).

**Proof of Corollary 3.** Under the wholesale price contract, the following equation holds:

$$M^W - P = \frac{\lambda (1 - a\lambda) - P \left( (1 + \beta)(\mathfrak{3} - \beta) - b\lambda^2 \right)}{(1 + \beta)(\mathfrak{3} - \beta)}.\tag{A4}$$

When either Condition 1 or 2 in Corollary 3 is satisfied, *M<sup>W</sup>* > *P*, which means that the carbon emissions caused by production exceed the carbon cap. Therefore, the manufacturer should purchase additional emission credits. On the other hand, when Condition 3 in Corollary 3 is satisfied, *M<sup>W</sup>* < *P*, which means that the carbon emission levels are under the cap. Accordingly, the manufacturer can sell excess emission credits.

**Proof of Proposition 2.** Because *∂* <sup>2</sup>*πr*/*∂p* <sup>2</sup> <sup>=</sup> <sup>−</sup><sup>2</sup> <sup>&</sup>lt; 0, *<sup>π</sup><sup>r</sup>* is strictly concave with respect to *p*. Thus, solving the FOC of the retailer's problem yields *p* = (1 + *w* + *e*(1 + *βδ*))/2. Integrating *p* into the manufacturer's problem, the following Hessian matrix is obtained:

$$\mathbf{H}^{\mathbb{C}} = \begin{pmatrix} \frac{\partial^2 \pi\_{\mathfrak{m}}}{\partial \mathfrak{w}^2} & \frac{\partial^2 \pi\_{\mathfrak{m}}}{\partial \mathfrak{w} \partial \mathfrak{e}}\\ \frac{\partial^2 \pi\_{\mathfrak{m}}}{\partial \mathfrak{e} \partial \mathfrak{w}} & \frac{\partial^2 \pi\_{\mathfrak{m}}}{\partial \mathfrak{e}^2} \end{pmatrix} = \begin{pmatrix} -1 & \frac{1 + \beta(1 - 2\delta)}{2} \\\ \frac{1 + \beta(1 - 2\delta)}{2} & -(1 - \delta)(1 + \beta(1 - \beta\delta)) \end{pmatrix}. \tag{A5}$$

We then find that ∆ *C* <sup>1</sup> = −1 < 0 and ∆ *C* <sup>2</sup> = (1 + *β*)(3 − *β*)/4 − *δ*. If the condition *δ* < (1 + *β*)(3 − *β*)/4 is met, ∆ *C* <sup>2</sup> > 0, implying that the manufacturer's profit is strictly concave with respect to *w* and *e*. By solving the FOCs of the manufacturer's problem, we have

$$w = \frac{(1+\beta)(2-\beta)(1-\delta) + \lambda(a-bP)(1+\beta-\delta(2-\beta+\beta^2))}{(1+\beta)(3-\beta)-4\delta} \text{ and } e = \frac{(1-\beta)(1-\lambda(a-bP))}{(1+\beta)(3-\beta)-4\delta}.\tag{A6}$$

To determine the retailer's optimal collaboration level, substitute *w* and *e* in Equation (A6) into the retailer's objective function and the second-order condition of the retailer's problem then yields

$$\frac{\partial^2 \pi\_r}{\partial \delta^2} = -\frac{2(1-\beta)^2(1-\lambda(a-bP))^2(3+10\beta-5\beta^2+16\delta)}{\left((1+\beta)(3-\beta)-4\delta\right)^4} < 0. \tag{A7}$$

Hence, by solving the FOC of the retailer's problem, we have *δ* = (1 − *β*) 2 /8. Finally, we calculate the equilibrium decisions and profits under the cost-sharing contract, as presented in Equation (7).

**Proof of Corollary 4.** Under the cost-sharing contract, the first-order derivatives of the equilibrium decisions with respect to the carbon cap *P* are given by

$$\begin{array}{ll} \frac{\partial w^{\mathbb{C}}}{\partial \overline{P}} = -\frac{b\lambda(3-\beta)(2+5\beta+\beta^{3})}{4(5+6\beta-3\beta^{2})} < 0, & \frac{\partial c^{\mathbb{C}}}{\partial \overline{P}} = \frac{2b\lambda(1-\beta)}{5+6\beta-3\beta^{2}} > 0, & \frac{\partial c^{\mathbb{C}}}{\partial \overline{P}} = \frac{b\lambda(7+2\beta-\beta^{2})}{4(5+6\beta-3\beta^{2})} > 0, \\\frac{\partial M^{\mathbb{C}}}{\partial \overline{P}} = \frac{b\lambda^{2}(7+2\beta-\beta^{2})}{4(5+6\beta-3\beta^{2})} > 0, & \text{and } \frac{\partial p^{\mathbb{C}}}{\partial \overline{P}} = \frac{b\lambda(1-10\beta+\beta^{2})}{4(5+6\beta-3\beta^{2})}. \end{array} \tag{A8}$$

$$\text{If } 0 < \beta < 5 - 2\sqrt{6} \text{, then } \partial p^{\mathbb{C}} / \partial P > 0 \text{; otherwise, } \partial p^{\mathbb{C}} / \partial P < 0.\text{ }\square$$

**Proof of Corollary 5.** Under the cost-sharing contract, the first-order derivatives of the equilibrium profits with respect to the carbon cap *P* are given by

$$\frac{\partial \pi\_r^{\mathbb{C}}}{\partial P} = \frac{b\lambda(9 - 2\beta + \beta^2)(1 - \lambda(a - bP))}{8(5 + 6\beta - 3\beta^2)} > 0 \text{ and } \frac{\partial \pi\_{\mathbb{H}}^{\mathbb{C}}}{\partial P} = \frac{b\lambda(7 + 2\beta - \beta^2)(1 - \lambda(a - bP))}{4(5 + 6\beta - 3\beta^2)} + a - 2bP. \tag{A9}$$

When *b* > *K*5, *∂π<sup>C</sup> <sup>m</sup>*/*∂P* > 0 regardless of *P*. When 0 < *b* < *K*5, *∂π<sup>C</sup> <sup>m</sup>*/*∂P* > 0 (< 0) if 0 < *P* < *K*<sup>6</sup> (*P* > *K*6). This completes the proof.

**Proof of Corollary 6.** Under the cost-sharing contract, the following equation holds:

$$M^{\mathbb{C}} - P = \frac{\lambda (1 - a\lambda)(7 + 2\beta - \beta^2) - P \left(4(5 + 6\beta - 3\beta^2) - b\lambda^2(7 + 2\beta - \beta^2)\right)}{4(5 + 6\beta - 3\beta^2)}.\tag{A10}$$

The rest of the proof of Corollary 6 is quite similar to that of Corollary 3. Consequently, the details are omitted.

**Proof of Corollary 7.** From Equations (3) and (7), the following relationships can be obtained:

*e <sup>W</sup>* <sup>−</sup> *<sup>e</sup> <sup>C</sup>* <sup>=</sup> <sup>−</sup> (1−*β*) 3 (1−*λ*(*a*−*bP*)) (1+*β*)(3−*β*)(5+6*β*−3*β* 2) < 0, *d <sup>W</sup>* <sup>−</sup> *<sup>d</sup> <sup>C</sup>* <sup>=</sup> <sup>−</sup> (1−*β*) 4 (1−*λ*(*a*−*bP*)) 4(1+*β*)(3−*β*)(5+6*β*−3*β* 2) < 0, *w <sup>W</sup>* <sup>−</sup> *<sup>w</sup> <sup>C</sup>* <sup>=</sup> <sup>−</sup> (1−*β*) 4 (2−*β*)(1−*λ*(*a*−*bP*)) 4(3−*β*)(5+6*β*−3*β* 2) < 0, *p <sup>W</sup>* <sup>−</sup> *<sup>p</sup> <sup>C</sup>* <sup>=</sup> <sup>−</sup> (1−*β*) 3 (3+*β*)(1−*λ*(*a*−*bP*)) 4(1+*β*)(3−*β*)(5+6*β*−3*β* 2) < 0, *<sup>M</sup><sup>W</sup>* <sup>−</sup> *<sup>M</sup><sup>C</sup>* <sup>=</sup> <sup>−</sup> *λ*(1−*β*) 4 (1−*λ*(*a*−*bP*)) 4(1+*β*)(3−*β*)(5+6*β*−3*β* 2) < 0, *π W <sup>m</sup>* − *π C <sup>m</sup>* = − (1−*β*) 4 (1−*λ*(*a*−*bP*)) 2 8(1+*β*)(3−*β*)(5+6*β*−3*β* 2) < 0, and *π W <sup>r</sup>* − *π C <sup>r</sup>* = − (1−*β*) 6 (1−*λ*(*a*−*bP*)) 2 16(1+*β*) 2 (3−*β*) 2 (5+6*β*−3*β* 2) < 0. (A11)

Because *π l sc* = *π l <sup>m</sup>* + *π l r* for *l* ∈ {*W*, *C*}, it is found that *π W sc* − *π C sc* < 0.

**Proof of Proposition 3.** Proposition 3 describes the optimal government decision on the carbon cap under the wholesale price contract. Integrating the equilibrium values in Equation (3) into the social welfare function, the SOC of the government's problem is given by

$$\frac{\partial^2 SW^W}{\partial P^2} = b \left( -2 + \frac{b\lambda^2 (6 + 2\beta - \beta^2)}{\left(1 + \beta\right)^2 \left(3 - \beta\right)^2} \right). \tag{A12}$$

If *b* < *K*9, the social welfare function *SW<sup>W</sup>* is strictly concave with respect to the carbon cap *P* and solving the FOC of the government's problem yields the optimal carbon cap *P <sup>W</sup>*. If *b* = *K*<sup>9</sup> and *η* > *K*<sup>10</sup> (*η* < *K*10), *SW<sup>W</sup>* is a linearly decreasing (increasing) function of *P* within the interval *P* ∈ [0, *a*/*b*]. Therefore, *P <sup>W</sup>* should be equal to the minimum (maximum) value of *P*. Lastly, if *b* > *K*9, *SW<sup>W</sup>* is a convex and increasing function of *P*. Thus, *P <sup>W</sup>* should be equal to the maximum value of *P*.

**Proof of Proposition 4.** The proof of Proposition 4 is quite similar to that of Proposition 3. As above, the details are omitted.

**Proof of Corollary 8.** Under each supply chain contract, the following are obtained:

$$\begin{array}{c} \frac{\partial P^{\mathsf{W}}}{\partial \eta} = -\frac{\lambda^{2}(1+\mathsf{\beta})(3-\mathsf{\beta})}{2(1+\mathsf{\beta})^{2}(3-\mathsf{\beta})^{2}-b\lambda^{2}(6+2\mathsf{\beta}-\mathsf{\beta}^{2})} \text{ and} \\ \frac{\partial P^{\mathbb{C}}}{\partial \eta} = -\frac{4\lambda^{2}(5+6\mathsf{\beta}-3\mathsf{\beta}^{2})(7+2\mathsf{\beta}-\mathsf{\beta}^{2})}{32(5+6\mathsf{\beta}-3\mathsf{\beta}^{2})^{2}-b\lambda^{2}(279+324\mathsf{\beta}-134\mathsf{\beta}^{2}-28\mathsf{\beta}^{3}+7\mathsf{\beta}^{4})}. \end{array} \tag{A13}$$

In Equation (A13), the condition *b* < min{*K*9, *K*11} guarantees that *∂P <sup>l</sup>*/*∂η* < 0 for *l* ∈ {*W*, *C*}.

**Proof of Corollary 9.** Assuming that *b* < min{*K*9, *K*11} and following Propositions 3 and 4, we have Equation (A14).

$$P^{\mathbb{P}} - P^{\mathbb{C}} = \frac{\lambda (1 - \beta)^4 \left( \begin{array}{c} \eta (8\lambda (1 + \beta)(3 - \beta)(5 + 6\theta - 3\theta^2) - b\lambda^3 (3 + 10\theta - 5\theta^2)) \\ - (111 + 148\theta - 46\theta^2 - 28\theta^3 + 7\theta^4)(2 - a\lambda) \end{array} \right)}{\left( 2(1 + \beta)^2 (3 - \beta)^2 - b\lambda^2 (6 + 2\theta - \beta^2) \right) \left( 32(5 + 6\theta - 3\theta^2)^2 - b\lambda^2 (279 + 324\theta - 134\theta^2 - 28\theta^3 + 7\theta^4) \right)}. \tag{A14}$$

$$\text{If } \eta \le K\_{13} \text{ in Equation (A14), } P^W \le P^C; \text{ otherwise, } P^W > P^C. \square$$

### **References**

## *Article* **Measurement of China's Building Energy Consumption from the Perspective of a Comprehensive Modified Life Cycle Assessment Statistics Method**

**Qiurui Liu <sup>1</sup> , Juntian Huang <sup>2</sup> , Ting Ni <sup>3</sup> and Lin Chen 1,\***

**Abstract:** This paper proposes a new life cycle assessment (LCA) statistics method to calculate the energy consumption of Chinese buildings from the perspective of LCA under the sustainable supply chain system. We divide the life cycle of buildings into the materialization stage, the construction stage, and the operation stage. Based on the new LCA statistics method, we obtain the following findings. First, the growth of total building energy consumption has slowed down since 2014, and its share of the Chinese total energy consumption levels off, remaining at about 40%. In 2018, the stages of materialization, construction, and operation account for about 34.02%, 4.65%, and 61.33% in total building energy consumption, respectively. Second, the materialization and operation stages are the main sources of energy consumption in the whole supply chain. Energy consumption in the materialization stage has been declining year by year since 2014, due to the impact of energy-saving policy. Moreover, we find that energy consumption in the operation and construction stages has been increasing year by year. Finally, in the life cycle of Chinese buildings, energy consumption in the operation stage plays a dominant role. This paper puts forward some managerial suggestions to relevant departments and provides some measures to optimize energy consumption in the Chinese building industry.

**Keywords:** sustainability; supply chain of construction industry; building energy consumption; life cycle assessment; building embodied sector

### **1. Introduction**

Nowadays, energy shortage and excessive emission of greenhouse gas have become hot topics in the world [1,2]. After more than 30 years of rapid economic development, China has become the world's largest carbon transfer site and has surpassed the United States as the world's largest carbon emitter since 2005 [3,4]. Economic development is inevitably accompanied by an increase in energy consumption [5]. In 2017, China's total energy consumption reached 4.49 billion tons of standard coal, 6.9 times higher than 1978, with an average annual growth rate of about 5.4% [6]. The Chinese Revolutionary Action Plan on Energy Production and Consumption has set a goal of limiting total energy consumption to 6 billion tons of coal equivalent, with non-fossil energy accounting for no less than 20% by 2030 [7]. As a result, China faces serious challenges in reducing energy consumption and coping with increasing environmental problems [8].

With the above attention to energy issues, the energy transformation of China has achieved great progress in recent years. The development of new energy and renewable energy is gradually improving [9–11]. However, energy problems such as excessive production, unreasonable energy consumption, energy shortage, and lack of effective regulation

**Citation:** Liu, Q.; Huang, J.; Ni, T.; Chen, L. Measurement of China's Building Energy Consumption from the Perspective of a Comprehensive Modified Life Cycle Assessment Statistics Method. *Sustainability* **2022**, *14*, 4587. https://doi.org/10.3390/ su14084587

Academic Editors: Shaojian Qu, Qingguo Bai, Ying Ji, Congjun Rao and Nicholas Chileshe

Received: 16 February 2022 Accepted: 7 April 2022 Published: 12 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

still exist [12,13]. In addition to energy transformation and the active promotion of new energy development, energy conservation and emission reduction are also very important to solve energy problems [14–16].

Specifically, the construction industry is one of the most energy and carbon-intensive industries, accounting for about 30% to 40% of the global total energy consumption and more than one-third of the global CO<sup>2</sup> emissions [16]. China has become the second-largest country in terms of building energy consumption. With the urbanization in China in recent years, total building energy consumption keeps increasing. As demonstrated in Guo et al. [17], building energy consumption in China has grown continually from 2001 to 2014. By the end of 2015, China's overall floorage had exceeded 60 billion square meters. According to the new Urbanization Plan (2014–2020), China's overall floorage will exceed 70 billion square meters by 2030, and the government sector will face a more severe situation regarding energy conservation and emission reduction [18,19].

To achieve the goal of energy conservation and emission reduction in the building sector, it is necessary to have an accurate baseline evaluation of building energy consumption, and a clear goal of building energy consumption control. Evaluation and accurate data of building energy consumption are also essential to provide a benchmark for policy-making of the construction sector, which can serve as an important reference for evaluating the measures of energy conservation and emission reduction.

In previous literature, several energy conversion methods have been designed with changes in statistical range to calculate building energy consumption [20,21]. This microscopic view provides detailed data for the energy consumption planning of a specific building. However, building energy consumption is inseparable from other industries as all industries cannot exist independently of buildings. The heterogeneity of the existing literature hinders the government's efforts in energy planning and policy assessment from a macrolevel. A more comprehensive perspective should be considered when measuring and evaluating building energy consumption [22]. Some researchers have calculated the energy consumption generated by the whole supply chain of the Chinese construction industry and then determined the energy consumption of the Chinese buildings [23,24]. Therefore, it is worth using the LCA theory from the national level of the supply chain of the construction industry to evaluate the energy consumption of the Chinese buildings.

LCA has been applied to the construction industry for about 10 years [25,26]. As it takes a comprehensive and systematic approach to environmental assessment; LCA methods have been incorporated into the construction industry to select eco-friendly products [27], evaluate performance [1], and optimize construction processes [28]. In the specific LCA steps, a building can be subdivided into the materialization stage, transportation stage, construction stage, operation stage, and demolition stage [28–30]. However, most studies focus on civil building and operation energy consumption, few of them cover the construction and demolition stages.

Moreover, there are some studies about the building energy consumption at the national level [6,23]. By tracing sources along the supply chains, Li et al. [6] find that the effects of China's building construction at the national and global scales are calculated as 55.21% and 5.67% of energy consumption, respectively. Some studies have found that energy consumption in the operation stage of buildings accounts for about 70% of the building's total energy consumption [23]; however, for the remaining 30%, which also has the potential to be optimized, there is a lack of attention. In other words, the calculation method of building energy consumption is fragmented [31]. Some researchers choose to accept or renounce all of the indexes and calculation methods from industrial enterprises when incorporating them into building energy consumption. Others mainly compute the energy consumption of building materials in the construction field but ignore the building energy consumption of industrial enterprises.

Based on the above discussions, this paper focuses on the following questions: First, how should the Chinese building energy consumption be calculated more comprehensively and accurately? Second, what are the differences among the materialization stage, construction stage, and operation stage of Chinese building energy consumption during recent years? Third, what policies should be kept or strengthened to control building energy consumption effectively?

To answer the aforementioned questions, we consider the building energy consumption within related industries, such as mineral mining, building materials manufacturing, and construction-related transportation, and incorporate them all into the calculation of the materialization, construction, and the operation stages of building energy consumption, based on LCA. A calculation model, which includes the materialization, construction, and the operation stages, is proposed to calculate the total energy consumption in various industries, from the perspective of the whole life cycle.