# Low-Carbon Strategies Considering Corporate Environmental Responsibility: Based on Carbon Trading and Carbon Reduction Technology Investment

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## Abstract

**:**

## 1. Introduction

- (1)
- What is the optimal strategy for the producing enterprise when the initial carbon quotas change?
- (2)
- What are the impacts of initial carbon quotas on the strategy choice, optimal carbon reduction rate, and production quantity of the producing enterprise?
- (3)
- What is the impact of undertaking CER on the optimal decision-making of the producing enterprise?

## 2. Literature Review

#### 2.1. Optimal Decisions of Enterprises under the Cap-and-Trade System

#### 2.2. Carbon Reduction Strategy under the Cap-and-Trade System

#### 2.3. Corporate Environmental Responsibility (CER)

## 3. Problem Description and Basic Assumptions

#### 3.1. Problem Description

#### 3.2. Basic Assumptions

- (1)
- The producing enterprise considers both economic and environmental benefits in the production process, to achieve the maximum comprehensive benefit. The enterprise’s comprehensive benefit function is ${u}_{M}=\left(1-\beta \right){\pi}_{M}+\beta \lambda eq$.
- (2)
- The cost of carbon emission reduction is a one-time input, in line with the law of the diminishing marginal effect: with the gradual increase in carbon emission reduction investment, carbon emission reduction per unit investment decreases. The investment cost of carbon reduction technology is $C\left(\lambda \right)=\frac{1}{2}k{\lambda}^{2}$ [32].
- (3)
- Considering that it is very difficult to achieve almost zero carbon emissions in real life, and it also requires huge carbon reduction costs, we assume that when the producing enterprise adopts carbon reduction technology, $\underset{\lambda \to 1}{\mathrm{lim}}{u}_{M}\left(\lambda \right)\to -\infty $.
- (4)
- The manufacturer produces the products according to the order quantity, which means that the manufacturer can exactly produce the products to meet the market demand, and there is no inventory.
- (5)
- Under the cap-and-trade policy, the government’s quota allocation method is free allocation, which means that the total amount of carbon emissions is determined based on the carbon reduction target, and then the carbon quota is allocated to enterprises for free.

## 4. Optimal Strategy of the Producing Enterprise under Different Scenarios

#### 4.1. The Initial Carbon Quotas Are Sufficient

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**2.**

#### 4.2. The Initial Carbon Quotas Are Insufficient

**Theorem**

**3.**

**Proof**

**of**

**Theorem**

**3.**

**Theorem**

**4.**

**Proof**

**of**

**Theorem**

**4.**

**Theorem**

**5.**

**Proof**

**of**

**Theorem**

**5.**

## 5. Analysis of Carbon Reduction Strategy of Producing Enterprise

#### 5.1. The Influence of CER Coefficient

#### 5.2. The Influence of the Initial Carbon Quotas

#### 5.3. Changes in Production Quantity

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Effects of CER coefficient on comprehensive benefits under different strategies. (

**a**) E = 10; (

**b**) E = 60.

**Figure 4.**Effects of CER coefficient on optimal carbon reduction rates under different strategies. (

**a**) E = 10; (

**b**) E = 60.

**Figure 5.**Effects of the initial carbon quotas on comprehensive benefits under different strategies, (

**a**) β = 0.1; (

**b**) β = 0.9.

**Figure 6.**Effects of the initial carbon quotas on optimal carbon reduction rates under different strategies. (

**a**) Trade and Invest; (

**b**) Invest.

**Figure 7.**Changes in production quantity under different strategies with respect to CER coefficient and initial carbon quotas. (

**a**) Trade and Invest; (

**b**) Invest; (

**c**) Trade.

Symbol | Description |
---|---|

$a$ | $\mathrm{Market}\mathrm{size},a0$ |

$p$ | $\mathrm{Product}\mathrm{price},p0$ |

$c$ | $\mathrm{The}\mathrm{marginal}\mathrm{cost}\mathrm{of}\mathrm{production},c0$ |

$q$ | $\mathrm{Production}\mathrm{quantity},q=a-bp$ |

$e$ | $\mathrm{Marginal}\mathrm{carbon}\mathrm{emissions}\mathrm{of}\mathrm{products},e0$ |

$\lambda $ | $\mathrm{Carbon}\mathrm{emission}\mathrm{reduction}\mathrm{rate}\mathrm{per}\mathrm{unit}\mathrm{product},0\le \lambda 1$ |

$E$ | The free initial carbon quotas |

${p}_{e}$ | $\mathrm{Price}\mathrm{per}\mathrm{unit}\mathrm{of}\mathrm{carbon}\mathrm{emission}\mathrm{permit},{p}_{e}0$ |

$k$ | $\mathrm{Carbon}\mathrm{reduction}\mathrm{cos}\mathrm{t}\mathrm{coefficient},k0$ |

$\beta $ | $\mathrm{CER}\mathrm{coefficient},0\le \beta \le 1$ |

${u}_{M}$ | The comprehensive benefit of the producing enterprise |

${\pi}_{M}$ | Economic benefits of the producing enterprise |

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**MDPI and ACS Style**

Yuan, Y.; Zhang, B.; Wang, L.; Wang, L.
Low-Carbon Strategies Considering Corporate Environmental Responsibility: Based on Carbon Trading and Carbon Reduction Technology Investment. *Sustainability* **2022**, *14*, 6683.
https://doi.org/10.3390/su14116683

**AMA Style**

Yuan Y, Zhang B, Wang L, Wang L.
Low-Carbon Strategies Considering Corporate Environmental Responsibility: Based on Carbon Trading and Carbon Reduction Technology Investment. *Sustainability*. 2022; 14(11):6683.
https://doi.org/10.3390/su14116683

**Chicago/Turabian Style**

Yuan, Yanhong, Bowen Zhang, Lei Wang, and Li Wang.
2022. "Low-Carbon Strategies Considering Corporate Environmental Responsibility: Based on Carbon Trading and Carbon Reduction Technology Investment" *Sustainability* 14, no. 11: 6683.
https://doi.org/10.3390/su14116683