Structure of demand and consistent conjectural variations equilibrium (CCVE) in a mixed oligopoly model

We study conjectured variations equilibrium (CVE) in a model of mixed oligopoly with not necessarily continuous demand functions. The agents' conjectures concern the price variations depending upon their production output increase or decrease. We establish the existence and uniqueness results for the CVE (called exterior equilibrium) for any set of feasible conjectures. To introduce the notion of interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as CVE with consistent conjectures, or CCVE). In addition, we also examine the behavior of the consistent conjectures as functions of a parameter representing the demand's derivative with respect to the market price. The latter results allow one to predict the behavior of groups of consumers with different consumption abilities. The proposed techniques permit one to develop a qualitative description of the dependence of the market price on the active demand component, too. It should be noticed that due to the non-smoothness of the demand function, there is possibly a path dependency and indeterminacy of equilibria in certain cases. This is, on the one hand, a theoretically inconvenient result (multiple equilibria), but on the other hand, it may happen to be extremely useful for applications. Indeed, the latter multiplicity of equilibria might serve as a rationale for the regulatory intervention to induce a change of equilibrium whenever the total welfare could be improved (cf., for example, the Keynesian stimulus).