# Coping Decisions of Production Enterprises under Low-Carbon Economy

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Production Decisions of Enterprises under Carbon Constraints

#### 2.2. Emission Reduction Decisions of Enterprises under Carbon Constraints

#### 2.3. Consumers’ Low-Carbon Preference

## 3. Problem Description and Basic Assumptions

## 4. Build and Solve Revenue Model

#### 4.1. No Carbon Constraints

**Theorem**

**1.**

**Proof of Theorem**

**1.**

#### 4.2. NN Strategy

**Theorem**

**2.**

**Proof of Theorem**

**2.**

#### 4.3. YN Strategy

#### 4.3.1. YN1 Strategy

**Theorem**

**3.**

**Proof of Theorem**

**3.**

**Corollary**

**1.**

**Proof of Corollary**

**1.**

#### 4.3.2. YN2 Strategy

**Theorem**

**4.**

**Proof of Theorem**

**4.**

#### 4.4. NY Strategy

#### 4.4.1. NY1 Strategy

**Theorem**

**5.**

**Proof of Theorem**

**5.**

**Corollary**

**2.**

**Proof of Corollary**

**2.**

#### 4.4.2. NY2 Strategy

**Theorem**

**6.**

**Proof of Theorem**

**6.**

#### 4.5. YY Strategy

#### 4.5.1. YY1 Strategy

**Theorem**

**7.**

**Proof of Theorem**

**7.**

**Corollary**

**3.**

#### 4.5.2. YY2 Strategy

**Theorem**

**8.**

**Proof of Theorem**

**8.**

## 5. Numerical Analysis

#### 5.1. The Optimal Decision of Production Enterprises

#### 5.1.1. The Maximum Profits for Production Enterprises under Carbon Constraints

#### 5.1.2. The Optimal Output of Producers under Carbon Constraints

#### 5.1.3. The Optimal Total Carbon Emissions of Production Enterprises under Carbon Constraints

#### 5.1.4. The Optimal Emission Reduction Rate of Production Enterprises under Carbon Constraints

#### 5.2. Other Factors Influencing Production Decisions

#### 5.2.1. The Impact of Carbon Reduction Scale Cost Coefficient

#### 5.2.2. The Impact of Consumers’ Low-Carbon Preference

## 6. Conclusions and Discussion

#### 6.1. Findings and Managerial Implications

#### 6.2. Limitations and Future Directions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**(

**a**) The impact of $h$ on ${\pi}_{m}^{YN*}$ ($k=0.3$); (

**b**) the impact of $h$ on ${\pi}_{m}^{YY1*}$ ($k=0.3$).

**Figure 7.**(

**a**) The impact of $k$ on ${\pi}_{m}^{YN*}$ ($h=1500$); (

**b**) the impact of $k$ on ${\pi}_{m}^{YY*}$ ($h=1500$).

Initial Carbon Allowances | Strategies Adopted by Enterprises | Carbon Allowances after Adopting Strategy |
---|---|---|

Adequate (no carbon constraints) | Neither reduce emissions nor buy carbon allowances | Adequate (NCC) |

Inadequate (presence of carbon constraints) | Neither reduce emissions nor buy carbon allowances | Inadequate (NN) |

Reduce emissions without purchasing carbon allowances | Adequate (YN1) | |

Inadequate (YN2) | ||

Buying carbon allowances without reducing emissions | Adequate (NY1) | |

Inadequate (NY2) | ||

Both reduce emissions and purchase carbon allowances | Adequate (YY1) | |

Inadequate (YY2) |

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

$e$ | The initial carbon emissions per unit product when carbon emission reduction technologies are not used |

$p$ | Unit product price |

$\lambda $ | The emission reduction rate per unit of product when carbon emission reduction technologies are adopted, $\lambda =\Delta e/e$ and $0\le \lambda \le 1$ |

${c}_{m}$ | Production cost per unit of product |

${\omega}_{s}$ | Price per unit of carbon emission right |

${c}_{s}$ | Cost per unit of carbon emission right |

$q$ | Product output |

$E$ | Carbon allowances allocated for free by the government |

${E}_{0}$ | Maximum purchase of carbon allowances |

${E}^{x}$ | Total carbon emissions of production companies under $x$ strategy, $x=\mathrm{NN},\mathrm{YN}1,\mathrm{YN}2,\mathrm{NY}1,\mathrm{NY}2,\mathrm{YY}1,\mathrm{YY}2$. |

${\pi}_{m}$ | Profits of manufacturing enterprise |

${\pi}_{s}$ | Profits of carbon trading center |

$\mathit{a}$ | $\mathit{b}$ | $\mathit{k}$ | ${\mathit{c}}_{\mathit{m}}$ | ${\mathit{c}}_{\mathit{s}}$ | $\mathit{h}$ | $\mathit{e}$ | ${\mathit{E}}_{0}$ |
---|---|---|---|---|---|---|---|

100 | 0.5 | 0.3 | 5 | 4 | 1500 | 5 | 50 |

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**MDPI and ACS Style**

Yuan, Y.; Zhang, Y.; Wang, L.; Wang, L.
Coping Decisions of Production Enterprises under Low-Carbon Economy. *Sustainability* **2022**, *14*, 9593.
https://doi.org/10.3390/su14159593

**AMA Style**

Yuan Y, Zhang Y, Wang L, Wang L.
Coping Decisions of Production Enterprises under Low-Carbon Economy. *Sustainability*. 2022; 14(15):9593.
https://doi.org/10.3390/su14159593

**Chicago/Turabian Style**

Yuan, Yanhong, Yaru Zhang, Lei Wang, and Li Wang.
2022. "Coping Decisions of Production Enterprises under Low-Carbon Economy" *Sustainability* 14, no. 15: 9593.
https://doi.org/10.3390/su14159593