# Pricing Decisions in Construction and Demolition Waste Recycling Supply Chains under Carbon Tax Scenarios

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## Abstract

**:**

## 1. Introduction

- (1)
- How does consumers’ risk-averse behavior affect the pricing and profitability of traditional products and recycled building materials compared to a consumer risk-neutral scenario?
- (2)
- How can carbon tax policies mitigate the negative effects of consumer risk-averse behavior on CDW resourcing operations?

## 2. Description of the Problem and Related Assumptions

#### 2.1. Description of the Problem

#### 2.2. Assumptions

**Assumption**

**1:**

**Assumption**

**2:**

**Assumption**

**3:**

**Assumption**

**4:**

**Assumption**

**5:**

## 3. Modeling and Solving

#### 3.1. Consumer Risk Neutrality (NR)

#### 3.2. Consumer Risk Aversion (TR)

## 4. Model Analysis

**Proposition**

**1.**

- (1)
- If $0<t<\sqrt{\frac{4}{3}bh}$, then ${p}_{m}^{NR}>{p}_{m}^{TR}$.
- (2)
- If $t\in (0,\sqrt{bh})$, ${p}_{r}^{NR}>{p}_{r}^{TR}$; if $t\in (\sqrt{bh},\sqrt{\frac{4bh}{3}})$, ${p}_{r}^{NR}<{p}_{r}^{TR}$.

**Proposition**

**2.**

- (1)
- When $0<h<\frac{{v}^{2}{\left(2-\theta \right)}^{2}}{12{\left({c}_{m}-{c}_{r}\right)}^{2}b}$, if $0<t<\sqrt{bh}$, under the conditional of $0<k<A$, then ${\pi}_{m}^{NR}>{\pi}_{m}^{TR}$, under the condition of $k>A$, for ${\pi}_{m}^{NR}<{\pi}_{m}^{TR}$; if $\sqrt{bh}<t<\sqrt{\frac{4}{3}bh}$, ${\pi}_{m}^{NR}<{\pi}_{m}^{TR}$.
- (2)
- When $\frac{{v}^{2}{\left(2-\theta \right)}^{2}}{12{\left({c}_{m}-{c}_{r}\right)}^{2}b}<h<\frac{{v}^{2}}{{\left({c}_{m}-{c}_{r}\right)}^{2}b}$, if $t\in (0,\sqrt{bh})\cup (B,\sqrt{\frac{4}{3}bh})$, under the condition of $0<k<A$, then ${\pi}_{m}^{NR}>{\pi}_{m}^{TR}$, under the condition of $k>A$, for ${\pi}_{m}^{NR}<{\pi}_{m}^{TR}$; if $\sqrt{bh}<t<B$, then ${\pi}_{m}^{NR}<{\pi}_{m}^{TR}$.
- (3)
- When $h>\frac{{v}^{2}}{{\left({c}_{m}-{c}_{r}\right)}^{2}b}$, if $t\in (0,B)\cup (\sqrt{bh},\sqrt{\frac{4}{3}bh})$, under the condition of $0<k<A$, ${\pi}_{m}^{NR}>{\pi}_{m}^{TR}$, under the condition of $k>A$, for ${\pi}_{m}^{NR}<{\pi}_{m}^{TR}$; if $B<t<\sqrt{bh}$, then ${\pi}_{m}^{NR}<{\pi}_{m}^{TR}$.

**Proposition**

**3.**

- (1)
- When $0<h<\frac{{v}^{2}{\left(-2+\theta \right)}^{2}}{12b{\left({C}_{m}-{C}_{r}\right)}^{2}}$, if $0<t<E$, under the condition of $0<k<D$, ${\pi}_{r}^{NR}>{\pi}_{r}^{TR}$, under the condition of $k>D$, for ${\pi}_{r}^{NR}<{\pi}_{r}^{TR}$; if $E<t<\sqrt{\frac{4}{3}bh}$, ${\pi}_{r}^{NR}<{\pi}_{r}^{TR}$.
- (2)
- When $h>\frac{{v}^{2}{\left(-2+\theta \right)}^{2}}{12b{\left({C}_{m}-{C}_{r}\right)}^{2}}$, if $0<t<\sqrt{\frac{4}{3}bh}$, under the condition of $0<k<D$, then ${\pi}_{r}^{NR}>{\pi}_{r}^{TR}$; under the condition of $k>D$, ${\pi}_{r}^{NR}<{\pi}_{r}^{TR}.$

**Proposition**

**4.**

- (1)
- If $0<t<\sqrt{\frac{4}{3}bh}$, ${p}_{m}$ is negatively correlated with $k$.
- (2)
- If $0<t<\sqrt{bh}$, ${p}_{r}$ is negatively correlated with $k$; if $\sqrt{bh}<t<\sqrt{\frac{4}{3}bh}$, ${p}_{r}$ is positively correlated with $k$.

**Proposition**

**5.**

- (1)
- When $0<h<\frac{{v}^{2}{\left(2-\theta \right)}^{2}}{12{\left({c}_{m}-{c}_{r}\right)}^{2}b}$, if $0<t<\sqrt{bh}$, ${\pi}_{m}$ has a U-shaped trend about $k$; if $\sqrt{bh}<t<\sqrt{\frac{4}{3}bh}$, ${\pi}_{m}$ is positively correlated with $k$.
- (2)
- When $\frac{{v}^{2}{\left(2-\theta \right)}^{2}}{12{\left({c}_{m}-{c}_{r}\right)}^{2}b}<h<\frac{{v}^{2}}{{\left({c}_{m}-{c}_{r}\right)}^{2}b}$, if $t\in (0,\sqrt{bh})\cup (B,\sqrt{\frac{4}{3}bh})$, ${\pi}_{m}$ has a U-shaped trend about $k$; if $\sqrt{bh}<t<B$, ${\pi}_{m}$ is positively correlated with $k$.
- (3)
- When $h>\frac{{v}^{2}}{{\left({c}_{m}-{c}_{r}\right)}^{2}b}$, if $t\in (0,B)\cup (\sqrt{bh},\sqrt{\frac{4}{3}bh})$, ${\pi}_{m}$ has a U-shaped trend about $k$; if $B<t<\sqrt{bh}$, ${\pi}_{m}$ is positively correlated with $k$.

**Proposition**

**6.**

- (1)
- When $0<h<\frac{{v}^{2}{\left(-2+\theta \right)}^{2}}{12b{\left({C}_{m}-{C}_{r}\right)}^{2}}$, if $0<t<E$, ${\pi}_{r}$ has a U-shaped trend about $k$; if $E<t<\sqrt{\frac{4}{3}bh}$, ${\pi}_{r}$ is positively correlated with $k$.
- (2)
- When $h>\frac{{v}^{2}{\left(-2+\theta \right)}^{2}}{12b{\left({C}_{m}-{C}_{r}\right)}^{2}}$, if $0<t<\sqrt{\frac{4}{3}bh}$, ${\pi}_{r}$ has a U-shaped trend about $k$.

## 5. Numerical Simulation

#### 5.1. Impacts on the Prices of Traditional Products and Recycled Building Materials

#### 5.2. Impacts on the Profitability of Building Materials Manufacturers

#### 5.3. Impacts on the Profitability of Construction Material Remanufacturers

## 6. Conclusions and Implications

#### 6.1. Conclusions

- (1)
- For conventional products, consumer risk-averse behavior leads to lower sales prices. For recycled building materials, the price is negatively correlated with consumers’ risk aversion in the case of a low-carbon tax. In the case of a high carbon tax, we obtain the opposite result.
- (2)
- On one hand, when the abatement cost coefficient is lower than the threshold value, under the condition of a low carbon tax, the profits of the building materials manufacturer and remanufacturer show a U-shaped trend regarding consumer risk aversion. Under the condition of a high carbon tax, consumer risk-averse behavior always favors the profits of the building material manufacturer and the building material remanufacturer. On the other hand, when the abatement cost coefficient is above the threshold, there is an interval in which consumer risk-averse behavior only always positively affects the profits of building materials manufacturers if the carbon tax satisfies the interval. In other cases, the profits of the building materials manufacturer and remanufacturer show a U-shaped trend with respect to consumer risk aversion.

#### 6.2. Implications

- (1)
- The remanufacturer of building materials should consider the carbon tax and consumer risk aversion to set the sales price of recycled building materials, while the manufacturer of building materials only needs to consider consumer risk aversion.
- (2)
- For the government, the risk aversion of consumers and the pressure of enterprises to reduce emissions should be taken into account when setting a carbon tax. When the pressure on enterprises is relatively low, consumers’ risk aversion can transform into a favorable factor to realize environmental and economic win–win situations by raising the carbon tax. When the pressure on enterprises is relatively high, setting a moderate carbon tax can help building materials manufacturers to cope with consumers’ risk-averse behaviors. However, whether this approach is beneficial for building material remanufacturers needs to be considered in conjunction with the degree of consumer risk aversion.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Impacts on sales prices of traditional products and recycled building materials. Of these, (

**a**) shows the impact on traditional products and (

**b**) shows the impact on recycled building materials.

**Figure 3.**Impacts on the profits of construction material manufacturers. (

**a**) h = 0.4; (

**b**) h = 1; (

**c**) h = 5.

References | Using a Stackelberg Game Model | Risk-Aversion Behavior of Consumers | Carbon Taxes | Consumption Value Theory |
---|---|---|---|---|

[19,20,21] | √ | × | √ | × |

[39,40,41] | × | √ | × | × |

[42,43,44,45,46,47,48] | × | × | × | √ |

Parameters | Meaning | Reference |
---|---|---|

${p}_{m}$ | Market price of traditional products | [20] |

${p}_{r}$ | Market prices for recycled building materials | [20] |

${e}_{m}$ | Degree of emission reduction efforts by building material manufacturers | [25] |

${e}_{r}$ | Building material remanufacturers’ emission reduction efforts | [25] |

${c}_{m}$ | Carbon emissions per unit of traditional products | [27] |

${c}_{r}$ | Carbon emissions per unit of recycled building materials | [27] |

$t$ | Taxes per unit of carbon emissions | [20] |

$h$ | Abatement cost factor | [25] |

$v$ | Consumers’ assessment of the value of a unit of traditional products | [19] |

${q}_{m}$ | Demand for traditional products | [19] |

${q}_{r}$ | Demand for recycled building materials | [19] |

$b$ | Rate of change in marginal utility | [55] |

$k$ | Consumer risk aversion factor | [56] |

$\theta $ | Consumer discount factor for the value of recycled building materials | [19] |

$\sigma $ | Standard deviation of the coefficient of value per unit of recycled building materials | [55] |

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## Share and Cite

**MDPI and ACS Style**

Zhang, H.; Chen, W.; Peng, J.; Wang, Y.; Zeng, L.; Gao, P.; Zhu, X.; Li, X.
Pricing Decisions in Construction and Demolition Waste Recycling Supply Chains under Carbon Tax Scenarios. *Systems* **2024**, *12*, 35.
https://doi.org/10.3390/systems12010035

**AMA Style**

Zhang H, Chen W, Peng J, Wang Y, Zeng L, Gao P, Zhu X, Li X.
Pricing Decisions in Construction and Demolition Waste Recycling Supply Chains under Carbon Tax Scenarios. *Systems*. 2024; 12(1):35.
https://doi.org/10.3390/systems12010035

**Chicago/Turabian Style**

Zhang, Hao, Weihong Chen, Jie Peng, Yuhan Wang, Lianghui Zeng, Peiao Gao, Xiaowen Zhu, and Xingwei Li.
2024. "Pricing Decisions in Construction and Demolition Waste Recycling Supply Chains under Carbon Tax Scenarios" *Systems* 12, no. 1: 35.
https://doi.org/10.3390/systems12010035