Environment, Development and Sustainability
Emission regulation of conventional energy-intensive industries
You-hua Chen
Chan Wang
Pu-yan Nie
First Online: 07 May 2019
Global climate change is closely related to conventional energy consumption. Taking the regulations for emissions into account, this article uses a game theory approach to identify industries depending on conventional energies to reduce emissions. This paper proposes to design a suitable supervisory system for emission regulation based on limited supervisor and asymmetric production efficiency. Two different supervision mechanism, random and selected supervisions, are employed. Some interesting conclusions are achieved. Firstly, the greater the level of competition, the smaller the number of firms with emission-reduction technology (ERT) are. Interestingly, the number of firms without ERT increases faster than does the number of firms with ERT. Secondly, under the asymmetric case, the threshold value for firms with low production costs that always employ emission-reduction technology is presented. Finally, this paper proves that firms with higher production costs have greater incentives to avoid emission restriction. Based on the above conclusions, the corresponding policy implications or regulation institutions to reduce climate changes are outlined. Random inspect is optimal if firms' efficiency information, measured by production cost, is incomplete, while selected supervise is better if efficiency information is complete.
Regulation Equilibrium Emission restriction Industries depending on energies
List of symbols
Number of firms
Outputs of firm i
Energy inputs of firm i
Emission of firm i
Marginal emission
Marginal costs
Number of supervisors
Probability of this firm being visited
πi
Profits of firm i with emission-reduction technology
Ex(πi)
Expected profits of firm i without emission-reduction technology
Number of firms use emission-reduction technology
\(\hat{h}\)
Number of firms without emission-reduction technology
Total outputs
This work is partially supported by National Natural Science Foundation of PRC (71771057, 71401057), the Humanities and Social Sciences Fund of the Ministry of Education (18YJC790156), the Guangdong Social Science Foundation (GD2018CYJ01), the Soft Science Project of Guangdong Province (2014A070704008), and Innovative Group Foundation (Humanities and Social Sciences) for Higher Education of Guangdong Province (2015WCXTD009). Sincerely thank to the anonymous reviewers.
Appendix: Threshold values
$$\hat{k} = \frac{{(A - \bar{c})\sqrt {\frac{N - m}{N}} - [A - (N + 1)c + N\bar{c}]}}{{(c - \bar{c})(1 - \sqrt {\frac{N - m}{N}} )}},$$
$$\hat{h} = \frac{{(N + 1)c - (L + 1)\bar{c} - (N - L)\bar{c}}}{{(c - \bar{c})(1 - \sqrt {\frac{N - m}{N}} )}} - \frac{{[A + Lc_{L} - (L + 1)\bar{c}]}}{{(c - \bar{c})}},$$
$$\hat{J} = \frac{{\sqrt {\frac{N - m}{N}} (A - \bar{c}) - [A - (N + 1)c_{L} + N\bar{c}]}}{{(c_{L} - c)(1 - \sqrt {\frac{N - m}{N}} )}},$$
$$\hat{h}^{0} = \frac{{(N + 1)c - (L + 1)\bar{c} - (N - L)\bar{c}}}{{(c - \bar{c})(1 - \sqrt {1 - \frac{m}{N - L}} )}} - \frac{{[A + Lc_{L} - (L + 1)\bar{c}]}}{{(c - \bar{c})}}.$$
Proof of Proposition 1
By the above analysis, there exists \(\hat{k} = \frac{{(A - \bar{c})\sqrt {\frac{N - m}{N}} - [A - (N + 1)c + N\bar{c}]}}{{(c - \bar{c})(1 - \sqrt {\frac{N - m}{N}} )}} = \frac{N + 1}{{1 - \sqrt {\frac{N - m}{N}} }} - \frac{{(A - \bar{c})}}{{(c - \bar{c})}}\), such that it has \(\frac{{[A - (N - \hat{k} + 1)c + (N - \hat{k})\bar{c}]^{2} }}{{(N + 1)^{2} }} = \frac{N - m}{N}\frac{{[A + \hat{k}c - (\hat{k} + 1)\bar{c}]^{2} }}{{(N + 1)^{2} }}\) or \(\frac{{A - (N - \hat{k} + 1)c + (N - \hat{k})\bar{c}}}{N + 1} = \sqrt {\frac{N - m}{N}} \frac{{A + \hat{k}c - (\hat{k} + 1)\bar{c}}}{N + 1}\). For \(k < \hat{k}\), it has the following relationship:
$$\begin{aligned} \frac{{A - (N - k + 1)c + (N - k)\bar{c}}}{N + 1} = \frac{{A - (N - \hat{k} + 1)c + (N - \hat{k})\bar{c}}}{N + 1} - \frac{{(\hat{k} - k)(c - \bar{c})}}{N + 1} \hfill \\ \quad < \sqrt {\frac{N - m}{N}} [\frac{{A + \hat{k}c - (\hat{k} + 1)\bar{c}}}{N + 1} - \frac{{(\hat{k} - k)(c - \bar{c})}}{N + 1}] = \sqrt {\frac{N - m}{N}} \frac{{A + kc - (k + 1)\bar{c}}}{N + 1}. \hfill \\ \end{aligned}$$
Thus, the expected profits of firms without emission-reduction technology are higher than are the expected profits for firms with emission-reduction technology for \(k < \hat{k}\). By the similar way, the opposite conclusions hold under \(k > \hat{k}\).Conclusions are achieved, and the proof is complete. □
Here, it addresses the effects of firm number in this industry on the equilibrium. For convenience, \(\hat{k} = \frac{N + 1}{{1 - \sqrt {\frac{N - m}{N}} }} - \frac{{(A - \bar{c})}}{{(c - \bar{c})}}\) manifests the following relationship: \(\frac{{\hat{k}}}{N} = \frac{{1 + \frac{1}{N}}}{{1 - \sqrt {\frac{N - m}{N}} }} - \frac{{(A - \bar{c})}}{{N(c - \bar{c})}} = \frac{{(N + 1)(1 + \sqrt {1 - \frac{m}{N}} )}}{m} - \frac{{(A - \bar{c})}}{{N(c - \bar{c})}}\). Apparently, \(\frac{{\hat{k}}}{N}\) increases with the number of firms in this industry. That is, \(\frac{{N - \hat{k}}}{{\hat{k}}}\) decreases with the number of firms in this industry. The ratios between firms with emission-reduction technology and firms without emission-reduction technology become smaller as the increase in total firms in this industry. On the other hand, \(N - \hat{k} = \frac{{Nm - N(N + 1)(1 + \sqrt {1 - \frac{m}{N}} )}}{m} + \frac{{(A - \bar{c})}}{{(c - \bar{c})}}\). Obviously, \(N - \hat{k}\) (or \(k^{*,1}\)) decreases with the number of firms in this industry.Conclusions are achieved, and the proof is complete. □
The conclusions in proposition 5 can be obtained based on Eqs. (19) and (20). On the one hand, \(c_{L} < c\) implies \(\frac{{A - (N - L + 1)c_{L} + (N - L - h)\bar{c} + hc}}{N + 1} > \frac{{A + Lc_{L} + (N - L - h)\bar{c} - (N + 1 - h)c}}{N + 1}\). On the other hand, for all h, it has \(A - (N + 1)c_{L} > \sqrt {\frac{N - m}{N}} [A - (N + 1)\bar{c}]\). And then the inequality \(\frac{{A - (N - L + 1)c_{L} + (N - L - h)\bar{c} + hc}}{N + 1} > \sqrt {\frac{N - m}{N}} \frac{{A + Lc_{L} - (L + h + 1)\bar{c} + hc}}{N + 1}\) is always hold.
Conclusions are achieved, and the proof is complete. □
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View author's OrcID profile
1.College of Economics and ManagementSouth China Agricultural UniversityGuangzhouPeople's Republic of China
2.Institute of Guangdong Economy and Social Development, School of Finance, Collaborative Innovation Center of Scientific Finance and IndustryGuangdong University of Finance and Economics (GDUFE)GuangzhouPeople's Republic of China
Chen, Y., Wang, C. & Nie, P. Environ Dev Sustain (2019). https://doi.org/10.1007/s10668-019-00364-x
Received 28 September 2018
First Online 07 May 2019
DOI https://doi.org/10.1007/s10668-019-00364-x
Publisher Name Springer Netherlands