# American Institute of Mathematical Sciences

January  2017, 13(1): 251-265. doi: 10.3934/jimo.2016015

## Influences of carbon emission abatement on firms' production policy based on newsboy model

 School of Humanities and Economic Management, China University of Geosciences (Beijing), 29#, Xueyuan Rd., Beijing, China, 100083

* Corresponding author: Dayi He

Received  December 2014 Revised  September 2015 Published  March 2016

Fund Project: The research is funded by the Fundamental Research Funds for the Central Universities (2-9-2015-033).

Carbon emission allowance(CEA) has been becoming an important factor for firms to make production policies. Cap-and-trade system is fulfilling in many countries and regions as a market scheme promoted by many politicians and economists for its efficiency in resources assignment and promotion to abatement of carbon emission. More and more firms take CEA into their production plan which makes them confronted with influences from two markets, product market and CEA trade market in the meanwhile. Based on the Newsboy model for simplicity, and with assumption that demand of product is a stochastic variable, this paper establishes optimization models to get the optimal production policy under administrative scheme (command-and-control) and market scheme (cap-and-trade) respectively. By comparing the firms' production policy and expected net income(ENI) with or without the existence of CEA trade market, it is found that CEA trade market can reduce the optimal amount of production and carbon emission on the one hand, and it does not decrease firms' ENI on the another hand because the CEA trade market provides more options for firms to make production policy. Hence, in the proposed complete and perfect market, we concluded cautiously that market-based carbon emission abatement scheme is effective to reduce carbon emission and to accomplish regulatory carbon emission abatement goal.

Citation: Dayi He, Xiaoling Chen, Qi Huang. Influences of carbon emission abatement on firms' production policy based on newsboy model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 251-265. doi: 10.3934/jimo.2016015
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Optimal decision making without CEA trading
Influence of CEA trading on firm's decision on production plan
Influence of CEA's price when production limited by CEA constraint
Influence of CEA's price when the firm is not limited by CEA constraint
Influence of product price when production limited by CEA constraint
Influence of CEA's price when production limited by CEA
 Pc Q1* E[Π(Q1*)] Limited by CEA Q2* E[Π(Q2*)] Producing 0 150 5999.99 Y - - - 30 150 5999.99 Y 246.07 8711.93 Y 50 150 5999.99 Y 227.82 6961.68 Y 70 150 5999.99 Y 0 6570 N 90 150 5999.99 Y 0 6570 N
 Pc Q1* E[Π(Q1*)] Limited by CEA Q2* E[Π(Q2*)] Producing 0 150 5999.99 Y - - - 30 150 5999.99 Y 246.07 8711.93 Y 50 150 5999.99 Y 227.82 6961.68 Y 70 150 5999.99 Y 0 6570 N 90 150 5999.99 Y 0 6570 N
Influence of CEA's price when the firm is not limited by CEA constraint
 Pc Q1* E[Π(Q1*)] Limited by CEA Q2* E[Π(Q2*)] Producing 0 272.18 11961.68 N - - - 30 272.18 11961.68 N 246.07 13211.93 Y 50 272.18 11961.68 N 227.82 14461.68 Y 70 272.18 11961.68 N 0 17250 N 90 272.18 11961.68 N 0 23250 N
 Pc Q1* E[Π(Q1*)] Limited by CEA Q2* E[Π(Q2*)] Producing 0 272.18 11961.68 N - - - 30 272.18 11961.68 N 246.07 13211.93 Y 50 272.18 11961.68 N 227.82 14461.68 Y 70 272.18 11961.68 N 0 17250 N 90 272.18 11961.68 N 0 23250 N
Influence of product price when production limited by CEA constraint
 Pm Q1* E[Π(Q1*)] Limited by CEA Q2* E[Π(Q2*)] Producing 35 150 2249.99 Y 227.29 2886.92 Y 45 150 2249.99 Y 237.44 5178.58 Y 55 150 2249.99 Y 243.67 7525.61 Y 65 150 2249.99 Y 248.16 9904.55 Y 75 150 2249.99 Y 251.65 12304.57 Y
 Pm Q1* E[Π(Q1*)] Limited by CEA Q2* E[Π(Q2*)] Producing 35 150 2249.99 Y 227.29 2886.92 Y 45 150 2249.99 Y 237.44 5178.58 Y 55 150 2249.99 Y 243.67 7525.61 Y 65 150 2249.99 Y 248.16 9904.55 Y 75 150 2249.99 Y 251.65 12304.57 Y
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