Consistent Conjectural Variations Equilibrium in the Semi-Mixed Oligopoly

We study a variant of the mixed oligopoly model with conjectural variations equilibrium, in which one of the producers maximizes not his net profit but the convex combination of the latter with the domestic social surplus. The coefficient of this convex combination is named socialization level. The producers’ conjectures concern the price variations depending upon their production output variations. In this work, we extend the models studied before, considering the case of the producers’ cost functions being convex but not necessarily quadratic. The notion of exterior and interior equilibrium is introduced (similarly to previous works), developing a consistency criterion for the conjectures. Existence and uniqueness theorems are formulated and proven. Results concerning the comparison between conjectural variations, perfect competition, and Cournot equilibriums are provided. Based on these results, we formulate an optimality criterion for the election of the socialization level. The existence of the optimal socialization level is proven under the condition that the public company cannot be too weak as compared to the private firms.

Mixed Duopoly Stochastic Sales Model with Advertising and Experience Gains for the Public and Foreign Competitors

In this research, we propose a stochastic model with the finite horizon of time for sales competition between the state-owned company and private (foreign) competitor. We assume that the foreign company objective function is to maximize revenues and the state-owned agent is concerned about welfare maximization. There are many stochastic models for sales, but what is new in our case is that we assume mixed oligopoly and have different types of firms: private and state owned. They have somewhat different objective functions. As a control variable, we take the advertisement expenses of the private firm. Sale bursts rate depends and the advertisement expenditure and experience stock gained. For the public firm, we assume that advertising efforts are fixed. It means that the optimal control is to maximize private firm revenues taking into account possible uncertainties of stochastic profit flow using Bellman’s optimality condition. We can find out that the Advertisement-Experience (AE) efforts of the private firm are increasing if sales are increasing. Next, the AE might decrease if the experience level of the private firm increases and we have a sales burst. To optimize the governmental policies, we check for optimal AE effort of the public firm so the social welfare achieves the maximum value.