Abstract:

Under the goals of carbon peaking and carbon neutrality， carbon emission reduction is an inevitable choice for firms， which affects firms’ mergers and acquisitions （M&A） decisions in the industry. In addition， facing numerous economic risks， M&A is one of the feasible ways for firms in the manufacturing industry to seek development. According to CV source of Statistics' data on China's M&A market for 2021， the manufacturing sector was predominant in both quantity and disclosed transaction volume. With 774 transactions， it constituted 19.6% of all deals. Furthermore， it also accounted for the largest disclosed transaction volume at 45.094 billion dollars， contributing 20.8% to the total. Carbon emission reduction yields two distinct effects：While it mitigates the negative impact of societal and environmental concerns on product pricing， it concurrently increases firms' operating costs due to the expenses of implementation. As a result， firms strive to identify an optimal carbon emission reduction strategy to enhance their profitability. Based on this， an oligopoly industry M&A model is constructed. The real-options approach is utilized to study the impact mechanism of carbon emission reduction on the industry's product market equilibrium and firms' M&A decisions， and provides possible theoretical guidance for government policy formulation and firms' M&A decisions.Following Aguerrevere（2003）， Bigerna（2019）， Chevalier-Roignant and Kort（2020）， it is assumed that the inverse demand function of industry products at time t is given by：P_t=a{Y}_t-\phi {\displaystyle \sum _{i=\mathrm{1}}^N}{q}_i\left(\mathrm{1}-{\varphi }_i\right)-b{Q}_t,whereY_{\mathrm{t}} denotes all firms at the　\mathrm{d}{Y}_t=\mu Y_t\mathrm{d}t+\sigma Y_t\mathrm{d}{Z}_t,Y\left(\mathrm{0}\right)=y_{\mathrm{0}},moment observed industry demand shocks. The industry demand shocks Y_{\mathrm{t}} is given by：where　denotes the demand exposure to industry-wide shocks， and b denotes the sensitivity of demand price， and a，bare positive constant. Where {\varphi }_{\mathrm{i}}\in \left(\mathrm{0,1}\right) is constant represents the proportion of carbon emissions handled by firm i， \phi represents social environment concern， q_i is the output of firm i， and Q_t is the industry-wide output， and Q_t is given by：where　represents the expected growth rate， \sigmarepresents the volatility， \mu、\sigmaare positive constant， and Z_t is a standard Brownian motion.where　denotes the conditional expectation operator， given that the current industry shock takes the value Y\left(\mathrm{0}\right)=y_{\mathrm{0}}. Consider that there are two types of firms in this industry before M&A that is， large and small firm， and the capital stocks are k_l and k_s， respectively， where k_l=k，andk_s=k. Without loss of generality， the model considers a merger between a large firm and a small firm in the industry. The merged firm is called a super large firm， and its capital stock is \mathrm{3}k/\mathrm{2}.the profit of firmi consists of three parts　product revenue P_t{q}_i， production cost C， and carbon emission reduction cost \eta {\left({\varphi }_i{q}_i\right)}^{\mathrm{2}}/\mathrm{2}. Following Hackbarth and Miao Jianjun（2012）， the cost function brought by the output is quadratic canonical form， and is given byC=q_i^{\mathrm{2}}/\left(\mathrm{2}{k}_i\right)， and it is assumed that shareholders are risk neutral and the discount factor is risk-free rate r. To ensure that the present value of profits is finite， the model assumes .

Key words: social and environmental concerns, carbon emissions reduction, mergers and acquisitions, real options