Dynamic behavior in a Cournot duopoly with social responsibility

In an oligopoly with isoelastic demand, the paper analyzes the quantity competition between N_PM profit-maximizing firms and N_RS socially responsible firms whose objective function is a linear combination of profit and consumer surplus. From the static analysis it follows that greater social responsibility has a competitive effect, since reduces the equilibrium price and increases the market share of socially responsible firms. In addition, it increases both the consumer surplus and total surplus. For the duopoly case, the dynamic study leads to the conclusion that, if at least one of the firms follows the gradient rule as an adjustment mechanism, an increase in the speed of adjustment is a source of instability. An increase in the value of the elasticity of demand as well as a reduction in the marginal cost has a stabilizing effect on the Cournot equilibrium. A higher level of social responsibility exerts a stabilizing role on the dynamics as long as demand is sufficiently elastic.