Regulating Environmental Externalities through Public Firms: A Differential Game

We investigate the possibility of using public firms to abate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the open-loop Nash equilibrium of the Cournot game among profit-seeking firms, showing that such equilibrium is strongly time consistent because firms neglect the externality; (ii) the feedback solution of social planning equilibrium where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) a mixed setup where at least one firm is public (i.e., controlled by the social planner), while the others remain profit-seeking agents. Our analysis shows the conditions whereby having one public firm as a regulatory instrument suffices to drive the industry to the same levels of output, externality and ultimately also social welfare as under social planning. Intuitively, this is due to constant returns, under which the regulator needs no more than a single firm to compensate for the output distortion due to strategic interaction among Cournot firms.