# Equilibrium Optimization with Multi-Energy-Efficiency-Grade Products: Government and Market Perspective

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Energy-Saving Subsidy Policy

#### 2.2. Marketing Efforts

#### 2.3. Supply Chain Network Equilibrium

## 3. Materials and Methods

#### 3.1. Problem Definition

#### 3.2. The Optimality Conditions of Manufacturers

#### 3.3. The Optimality Conditions of Retailers

**Theorem 1.**

**Proof**.

#### 3.4. The Optimality Conditions of Markets

#### 3.5. The Optimality Conditions of Supply Chain Network

**Definition 1.**

**Theorem 2.**

**Proof.**

## 4. Qualitative Property and Solution Method

#### 4.1. Qualitative Property

**Theorem 3**.

**Proof**.

#### 4.2. Solution Method

## 5. Numerical Example

^{−6}. It was mainly used to solve the following problems in Figure 3 and give corresponding management insights for the members of SCN.

#### 5.1. Data

_{u}= 0.1, and unit-inventory cost c

_{o}= 0.1.

#### 5.2. Results of Benchmark

## 6. Discussion and Comparative Analysis

#### 6.1. Scenarios When the Demand Scale for HEEP and LEEP Is Equal

**Case 1.**Government subsidizes HEEP sold by all retailers in market 1.

**Case 2.**Government only subsidizes HEEP sold by retailer 1 in market 1.

#### 6.2. Scenarios When the Demand Scales of HEEP and LEEP Is Different

**Case 3.**Government subsidizes HEEP sold by all retailers in market 1.

**Case 4.**Government only subsidizes HEEP sold by retailer 1 in market 1.

#### 6.3. Comparative Analysis

#### 6.4. Extensions

#### 6.5. Management Insights

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Abbreviation | Full Name |

${R}_{1}$ | $\begin{array}{l}\left({p}_{si}^{*n}\left(1+{G}_{s}^{n}\right)+{c}_{u}\right)\left({F}_{si}^{n}(x;{p}_{si}^{*n},{u}_{i}^{*n})-1\right)+\frac{\partial H{C}_{si}^{n}({q}_{si}^{*n})}{\partial {q}_{si}^{*n}}+{c}_{o}{F}_{si}^{n}(x;{p}_{si}^{*n},{u}_{i}^{*n})\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-{\theta}_{1i}^{n}+{\theta}_{2i}^{n}+\frac{\partial M{F}_{i}^{n}\left({u}_{i}^{*n},{q}_{si}^{*n}\right)}{\partial {q}_{si}^{n}}\end{array}$ |

${R}_{2}$ | ${p}_{mi}^{*n}+\frac{\partial H{C}_{mi}^{n}({q}_{mi}^{*n})}{\partial {q}_{mi}^{*n}}+{\theta}_{1i}^{n}-{\theta}_{2i}^{n}$ |

${R}_{3}$ | $\sum _{m=1}^{M}{q}_{mi}^{*n}}-{\displaystyle \sum _{s=1}^{S}{q}_{si}^{*n}$ |

${R}_{4}$ | $\sum _{s=1}^{S}{q}_{si}^{*n}}-{\displaystyle \sum _{m=1}^{M}{q}_{mi}^{*n}$ |

${R}_{5}$ | $\begin{array}{l}\frac{\partial M{F}_{i}^{n}\left({u}_{i}^{*n},{q}_{si}^{*n}\right)}{\partial {u}_{i}^{n}}+\left(1-{c}_{u}\right)\frac{\partial {\displaystyle {\int}_{0}^{{q}_{si}^{n}}{F}_{si}^{n}({q}_{si}^{*n};{p}_{si}^{*n},{u}_{i}^{*n})dx}}{\partial {u}_{i}^{n}}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-{p}_{si}^{*n}\left(1+{G}_{si}^{n}\right)\left({q}_{si}^{*n}-1\right)\frac{\partial {F}_{si}^{n}({q}_{si}^{*n};{p}_{si}^{*n},{u}_{i}^{*n})}{\partial {u}_{i}^{n}}\end{array}$ |

${W}_{1}$ | $\frac{\partial H{C}_{mi}^{n}({q}_{mi}^{*n})}{\partial {q}_{mi}^{*n}}+\frac{\partial V{C}_{m}^{n}({q}_{m}^{*n})}{\partial {q}_{mi}^{*n}}+{\displaystyle \sum _{i=1}^{I}\frac{\partial T{C}_{mi}^{n}({q}_{mi}^{*n})}{\partial {q}_{mi}^{*n}}+{\theta}_{1i}^{n}-{\theta}_{2i}^{n}}$ |

${W}_{2}$ | $\begin{array}{l}\left({p}_{si}^{*n}\left(1+{G}_{si}^{n}\right)+{c}_{u}\right)\left({F}_{si}^{n}(x;{p}_{si}^{*n},{u}_{i}^{*n})-1\right)+\frac{\partial H{C}_{si}^{n}({q}_{si}^{*n})}{\partial {q}_{si}^{*n}}+\frac{\partial M{F}_{i}^{n}\left({u}_{i}^{*n},{q}_{si}^{*n}\right)}{\partial {q}_{si}^{n}}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-{c}_{o}{F}_{si}^{n}(x;{p}_{si}^{*n},{u}_{i}^{*n})-{\theta}_{1i}^{n}+{\theta}_{2i}^{n}\end{array}$ |

${W}_{3}$ | ${q}_{is}^{*n}-{D}_{si}^{n}({p}_{si}^{*n},{u}_{i}^{*n})$ |

${W}_{4}$ | $\begin{array}{l}\frac{\partial M{F}_{i}^{n}\left({u}_{i}^{*n},{q}_{si}^{*n}\right)}{\partial {u}_{i}^{n}}+\left(1-{c}_{u}\right)\frac{\partial {\displaystyle {\int}_{0}^{{q}_{si}^{n}}{F}_{si}^{n}({q}_{si}^{*n};{p}_{si}^{*n},{u}_{i}^{*n})dx}}{\partial {u}_{i}^{n}}\\ \hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}-{p}_{si}^{*n}\left(1+{G}_{si}^{n}\right)\left({q}_{si}^{*n}-1\right)\frac{\partial {F}_{si}^{n}({q}_{si}^{*n};{p}_{si}^{*n},{u}_{i}^{*n})}{\partial {u}_{i}^{n}}\end{array}$ |

## Appendix A

**Proof of Theorem 1.**

**Proof of Theorem 2**.

**Proof of Theorem 3**.

## Appendix B

**Table A1.**The equilibrium result of government subsidies to all retailers in market 1 when demand scale for HEEP and LEEP is equal.

Decision Variables | Energy-Saving Subsidy Rate ${\mathit{G}}_{\mathit{s}\mathit{i}}^{\mathit{n}}$ | ||||||
---|---|---|---|---|---|---|---|

0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |

${q}_{m}^{1*}$ | 0.3124 | 0.3168 | 0.3208 | 0.3246 | 0.3277 | 0.3307 | 0.3336 |

${q}_{m}^{2*}$ | 0.4247 | 0.4213 | 0.4185 | 0.4164 | 0.4140 | 0.4119 | 0.4105 |

${q}_{1i}^{1*}$ | 0.1562 | 0.1700 | 0.1837 | 0.1978 | 0.2122 | 0.2269 | 0.2416 |

${q}_{2i}^{1*}$ | 0.1562 | 0.1468 | 0.1370 | 0.1267 | 0.1155 | 0.1038 | 0.0920 |

${p}_{1i}^{1*}$ | 5.0508 | 4.9069 | 4.7741 | 4.6540 | 4.5413 | 4.4398 | 4.3477 |

${p}_{2i}^{1*}$ | 5.0508 | 5.0625 | 5.0684 | 5.0701 | 5.0620 | 5.0510 | 5.0379 |

${u}_{i}^{1*}$ | 0.4077 | 0.4040 | 0.4002 | 0.3958 | 0.3916 | 0.3867 | 0.3811 |

${u}_{i}^{2*}$ | 0.2885 | 0.2944 | 0.2998 | 0.3045 | 0.3093 | 0.3132 | 0.3165 |

${\pi}_{m}$ | 0.6810 | 0.6873 | 0.6927 | 0.6984 | 0.7026 | 0.7075 | 0.7124 |

${\pi}_{i}$ | 0.2760 | 0.2768 | 0.2792 | 0.2835 | 0.2887 | 0.2966 | 0.3067 |

SW | 2.3931 | 2.3950 | 2.3940 | 2.3907 | 2.3832 | 2.3732 | 2.3603 |

**Table A2.**The equilibrium result of government only subsidies to retailer 1 in market 1 when demand scale for HEEP and LEEP is equal.

Decision Variables | Energy-Saving Subsidy Rate ${\mathit{G}}_{\mathit{s}\mathit{i}}^{\mathit{n}}$ | ||||||
---|---|---|---|---|---|---|---|

0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |

${q}_{m}^{1*}$ | 0.3124 | 0.3147 | 0.3171 | 0.3197 | 0.3222 | 0.3247 | 0.3273 |

${q}_{m}^{2*}$ | 0.4247 | 0.4230 | 0.4214 | 0.4211 | 0.4206 | 0.4202 | 0.4193 |

${q}_{11}^{1*}$ | 0.1562 | 0.1796 | 0.2018 | 0.2229 | 0.2430 | 0.2623 | 0.2808 |

${q}_{21}^{1*}$ | 0.1562 | 0.1493 | 0.1428 | 0.1368 | 0.1311 | 0.1255 | 0.1201 |

${q}_{12}^{1*}$ | 0.1562 | 0.1359 | 0.1171 | 0.0995 | 0.0833 | 0.0683 | 0.0545 |

${q}_{22}^{1*}$ | 0.1562 | 0.1647 | 0.1726 | 0.1801 | 0.1870 | 0.1933 | 0.1992 |

${p}_{11}^{1*}$ | 5.0508 | 4.9429 | 4.8415 | 4.7483 | 4.6592 | 4.5750 | 4.4975 |

${p}_{21}^{1*}$ | 5.0508 | 5.0808 | 5.1103 | 5.1421 | 5.1715 | 5.2002 | 5.2303 |

${p}_{12}^{1*}$ | 5.0508 | 4.9855 | 4.9241 | 4.8686 | 4.8150 | 4.7641 | 4.7178 |

${p}_{22}^{1*}$ | 5.0508 | 5.0651 | 5.0802 | 5.0988 | 5.1162 | 5.1338 | 5.1540 |

${u}_{1}^{1*}$ | 0.4077 | 0.3880 | 0.3693 | 0.3512 | 0.3342 | 0.3183 | 0.3032 |

${u}_{2}^{1*}$ | 0.4077 | 0.4241 | 0.4405 | 0.4568 | 0.4735 | 0.4901 | 0.5057 |

${\pi}_{m}$ | 0.6810 | 0.6848 | 0.6898 | 0.6952 | 0.7013 | 0.7078 | 0.7164 |

${\pi}_{1}$ | 0.2760 | 0.2890 | 0.3039 | 0.3214 | 0.3398 | 0.3595 | 0.3813 |

${\pi}_{2}$ | 0.2760 | 0.2655 | 0.2570 | 0.2513 | 0.2465 | 0.2432 | 0.2416 |

SW | 2.3931 | 2.3933 | 2.3906 | 2.3862 | 2.3791 | 2.3700 | 2.3599 |

**Table A3.**The equilibrium result of government subsidies to all retailers in market 1 when demand scales of HEEP and LEEP is different.

Decision Variables | Energy-Saving Subsidy Rate ${\mathit{G}}_{\mathit{s}\mathit{i}}^{\mathit{n}}$ | ||||||
---|---|---|---|---|---|---|---|

0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |

${q}_{m}^{1*}$ | 0.3359 | 0.3402 | 0.3442 | 0.3480 | 0.3513 | 0.3545 | 0.3573 |

${q}_{m}^{2*}$ | 0.4006 | 0.3971 | 0.3947 | 0.3922 | 0.3901 | 0.3882 | 0.3865 |

${q}_{1i}^{1*}$ | 0.1679 | 0.1819 | 0.1959 | 0.2102 | 0.2249 | 0.2399 | 0.2549 |

${q}_{2i}^{1*}$ | 0.1679 | 0.1583 | 0.1483 | 0.1378 | 0.1265 | 0.1146 | 0.1024 |

${p}_{1i}^{1*}$ | 5.3060 | 5.1500 | 5.0079 | 4.8799 | 4.7604 | 4.6520 | 4.5527 |

${p}_{2i}^{1*}$ | 5.3060 | 5.3154 | 5.3210 | 5.3234 | 5.3166 | 5.3060 | 5.2918 |

${u}_{i}^{1*}$ | 0.3759 | 0.3732 | 0.3701 | 0.3662 | 0.3625 | 0.3580 | 0.3533 |

${\pi}_{m}$ | 0.7030 | 0.7099 | 0.7159 | 0.7232 | 0.7288 | 0.7345 | 0.7400 |

${\pi}_{i}$ | 0.2724 | 0.2734 | 0.2766 | 0.2821 | 0.2884 | 0.2971 | 0.3079 |

SW | 2.4397 | 2.4412 | 2.4403 | 2.4374 | 2.4302 | 2.4200 | 2.4062 |

**Table A4.**The equilibrium result of government only subsidies to retailer 1 in market 1 when demand scales of HEEP and LEEP is different.

Decision Variables | Energy-Saving Subsidy Rate ${\mathit{G}}_{\mathit{s}\mathit{i}}^{\mathit{n}}$ | ||||||
---|---|---|---|---|---|---|---|

0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |

${q}_{m}^{1*}$ | 0.3359 | 0.3382 | 0.3405 | 0.3432 | 0.3457 | 0.3485 | 0.3512 |

${q}_{m}^{2*}$ | 0.4006 | 0.3987 | 0.3975 | 0.3969 | 0.3960 | 0.3955 | 0.3953 |

${q}_{11}^{1*}$ | 0.1679 | 0.1923 | 0.2155 | 0.2376 | 0.2587 | 0.2790 | 0.2984 |

${q}_{21}^{1*}$ | 0.1679 | 0.1605 | 0.1534 | 0.1470 | 0.1407 | 0.1348 | 0.1290 |

${q}_{12}^{1*}$ | 0.1679 | 0.1466 | 0.1268 | 0.1085 | 0.0914 | 0.0756 | 0.0611 |

${q}_{22}^{1*}$ | 0.1679 | 0.1769 | 0.1853 | 0.1933 | 0.2007 | 0.2076 | 0.2140 |

${p}_{11}^{1*}$ | 5.3060 | 5.1908 | 5.0825 | 4.9845 | 4.8902 | 4.8038 | 4.7214 |

${p}_{21}^{1*}$ | 5.3060 | 5.3359 | 5.3651 | 5.3984 | 5.4288 | 5.4613 | 5.4921 |

${p}_{12}^{1*}$ | 5.3060 | 5.2355 | 5.1691 | 5.1106 | 5.0536 | 5.0022 | 4.9528 |

${p}_{22}^{1*}$ | 5.3060 | 5.3192 | 5.3330 | 5.3520 | 5.3694 | 5.3900 | 5.4099 |

${u}_{1}^{1*}$ | 0.3760 | 0.3572 | 0.3395 | 0.3221 | 0.3060 | 0.2906 | 0.2763 |

${u}_{2}^{1*}$ | 0.3760 | 0.3924 | 0.4089 | 0.4252 | 0.4419 | 0.4580 | 0.4740 |

${\pi}_{m}$ | 0.7030 | 0.7074 | 0.7121 | 0.7188 | 0.7259 | 0.7344 | 0.7429 |

${\pi}_{1}$ | 0.2724 | 0.2870 | 0.3036 | 0.3233 | 0.3439 | 0.3668 | 0.3907 |

${\pi}_{2}$ | 0.2724 | 0.2606 | 0.2512 | 0.2449 | 0.2397 | 0.2365 | 0.2343 |

SW | 2.4397 | 2.4396 | 2.4363 | 2.4315 | 2.4236 | 2.4144 | 2.4030 |

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**Figure 5.**When the subsidy rate is 0, the SCNE results in different scenarios. (

**A**) there is no difference in the demand scale of the same retailer in the same market. (

**B**) different retailers in the same market have different demand scales. (

**C**) different markets have different demand scales for the same retailer.

**Figure 7.**The SCNE results of retailer i’s profit and marketing efforts for HEEP in different scenarios.

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

Set | M | A set of all manufacturers in SCN, where $m\in M$ |

I | A set of all retailers in SCN, where $i\in I$ | |

S | A set of all markets in SCN, where $s\in S$ | |

N | A set of all products’ energy-efficiency-grade, where $n\in N$ | |

Decision variables | ${q}_{m}^{n}$ | The quantity of n energy-efficiency-grade products (n-EEGP) produced by manufacturer m |

${q}_{mi}^{n}$ | The transaction quantity of n-EEGP between manufacturer m and retailer i | |

${q}_{is}^{n}$ | The distribution quantity of n-EEGP between retailer i and market s | |

${p}_{si}^{n}$ | The transaction price that consumers in market s pay for n-EEGP of retailer i. | |

${u}_{i}^{n}$ | Retailer i’s marketing investment in n-EEGP | |

Parameter | ${G}_{si}^{n}$ | Energy-saving subsidy rate when the customer of market s purchase unit n-EEGP in retailer i |

${v}_{si}^{n}$ | Demand scales of market s for retailer i’s n-EEGP | |

c_{o} | Unit-shortage cost of retailer i | |

c_{u} | Unit-inventory cost of retailer i | |

Function | $V{C}_{m}^{n}({q}_{m}^{n})$ | The product cost function of n-EEGP of manufacturer m |

$T{C}_{mi}^{n}({q}_{mi}^{n})$ | Transaction cost function of n-EEGP between manufacturer m and retailer i | |

$H{C}_{mi}^{n}({q}_{mi}^{n})$ | The handle cost function of retailer i handles n-EEGP from manufacturer m | |

$H{C}_{si}^{n}({q}_{si}^{n})$ | The handle cost function of retailer i handles n-EEGP to market s | |

$M{F}_{i}^{n}({u}_{i}^{n},{q}_{si}^{n})$ | Retailer i’s marketing efforts for n-EEGP | |

${D}_{si}^{n}({p}_{si}^{n},{u}_{i}^{n})$ | Market s’s demand for n-EEGP at retailer i |

Cost Functions | Notation |
---|---|

$V{C}_{m}^{H}=2.5{q}_{m}^{H}{}^{2}+{q}_{m}^{H}{q}_{3-m}^{H}+{q}_{m}^{H}$ | The production cost function of HEEP of manufacturer m. |

$V{C}_{m}^{L}=0.5{q}_{m}^{L}{}^{2}+{q}_{m}^{L}{q}_{3-m}^{L}+{q}_{m}^{L}$ | The production cost function of LEEP of manufacturer m. |

$T{C}_{m}^{n}({q}_{mi}^{n})=0.5{\displaystyle \sum _{i=1}^{I}{q}_{mi}^{n}{}^{2}}+0.5{\displaystyle \sum _{i=1}^{I}{q}_{mi}^{n}}$ | Transaction cost function between manufacturer m and retailer i. |

$H{C}_{i}^{n}({q}_{mi}^{n})=0.5{\displaystyle \sum _{m=1}^{M}{q}_{mi}^{n}{}^{2}}$ | Handle cost function between retailer m and manufacturers i. |

$H{C}_{i}^{n}({q}_{si}^{n})=0.5{\displaystyle \sum _{s=1}^{S}{q}_{si}^{n}{}^{2}}$ | Handle cost function between retailers and manufacturers. |

$M{F}_{i}^{n}({u}_{i}^{n},{q}_{si}^{n})=\frac{1}{2}{u}_{i}^{n}{}^{2}{q}_{si}^{n}$ | The marketing efforts cost of retailer i for ${q}_{si}^{n}$ units of n-EEGP. |

Decision Variables | Energy-Saving Subside Rate ${\mathit{G}}_{\mathit{s}\mathit{i}}^{\mathit{n}}$ | ||||||
---|---|---|---|---|---|---|---|

0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |

${q}_{m}^{1*}$ | 0.3124 | 0.3124 | 0.3124 | 0.3124 | 0.3124 | 0.3124 | 0.3124 |

${q}_{m}^{2*}$ | 0.4246 | 0.4183 | 0.4128 | 0.4070 | 0.4022 | 0.3973 | 0.3927 |

${p}_{si}^{1*}$ | 5.0508 | 4.9219 | 4.8018 | 4.6914 | 4.5887 | 4.4923 | 4.4038 |

${u}_{i}^{1*}$ | 0.4077 | 0.4006 | 0.3938 | 0.3871 | 0.3804 | 0.3744 | 0.3681 |

${u}_{i}^{2*}$ | 0.2885 | 0.3007 | 0.3123 | 0.3233 | 0.3336 | 0.3436 | 0.3528 |

${\pi}_{m}$ | 0.6813 | 0.6945 | 0.7074 | 0.7215 | 0.7356 | 0.7500 | 0.7654 |

${\pi}_{i}$ | 0.2760 | 0.2776 | 0.2801 | 0.2842 | 0.2893 | 0.2950 | 0.3023 |

SW | 2.3931 | 2.3985 | 2.4010 | 2.4016 | 2.4002 | 2.3965 | 2.3917 |

**Table 4.**The effect of ${G}_{si}^{n}$ on SCNE when the demand scales for HEEP and LEEP are different.

Decision Variables | Energy-Saving Subside Rate ${\mathit{G}}_{\mathit{s}\mathit{i}}^{\mathit{n}}$ | ||||||
---|---|---|---|---|---|---|---|

0.00 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | |

${q}_{m}^{1*}$ | 0.3358 | 0.3449 | 0.3538 | 0.3623 | 0.3707 | 0.3791 | 0.3872 |

${q}_{m}^{2*}$ | 0.4002 | 0.3944 | 0.3885 | 0.3830 | 0.3778 | 0.3734 | 0.3688 |

${p}_{si}^{1*}$ | 5.3060 | 5.1650 | 5.0360 | 4.9150 | 4.8040 | 4.7008 | 4.6048 |

${u}_{i}^{1*}$ | 0.3759 | 0.3702 | 0.3645 | 0.3592 | 0.3537 | 0.3486 | 0.3435 |

${u}_{i}^{2*}$ | 0.3043 | 0.3173 | 0.3294 | 0.3414 | 0.3523 | 0.3629 | 0.3727 |

${\pi}_{m}$ | 0.7034 | 0.7182 | 0.7342 | 0.7496 | 0.7660 | 0.7825 | 0.7999 |

${\pi}_{i}$ | 0.2724 | 0.2753 | 0.2797 | 0.2847 | 0.2911 | 0.2982 | 0.3064 |

SW | 2.4397 | 2.4454 | 2.4489 | 2.4495 | 2.4486 | 2.4455 | 2.4408 |

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**MDPI and ACS Style**

Zhu, Q.; Zhou, X.; Liu, A.; Gao, C.; Xu, L.; Zhao, F.; Zhang, D.; Lev, B. Equilibrium Optimization with Multi-Energy-Efficiency-Grade Products: Government and Market Perspective. *Energies* **2022**, *15*, 7376.
https://doi.org/10.3390/en15197376

**AMA Style**

Zhu Q, Zhou X, Liu A, Gao C, Xu L, Zhao F, Zhang D, Lev B. Equilibrium Optimization with Multi-Energy-Efficiency-Grade Products: Government and Market Perspective. *Energies*. 2022; 15(19):7376.
https://doi.org/10.3390/en15197376

**Chicago/Turabian Style**

Zhu, Qiuyun, Xiaoyang Zhou, Aijun Liu, Chong Gao, Lei Xu, Fan Zhao, Ding Zhang, and Benjamin Lev. 2022. "Equilibrium Optimization with Multi-Energy-Efficiency-Grade Products: Government and Market Perspective" *Energies* 15, no. 19: 7376.
https://doi.org/10.3390/en15197376