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.

中文翻译：

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半混合寡头垄断中的一致猜想变化均衡

我们研究了具有推测变化均衡的混合寡头模型的一个变体，其中一个生产者不是最大化他的净利润，而是最大化后者与国内社会剩余的凸组合。这种凸组合的系数称为社会化水平。生产者的推测涉及价格变化取决于他们的生产产量变化。在这项工作中，我们扩展了之前研究的模型，考虑到生产者的成本函数是凸的但不一定是二次的。引入了外部和内部平衡的概念（类似于以前的工作），为猜想制定了一致性标准。存在性和唯一性定理被制定和证明。关于推测变异、完全竞争、和古诺均衡被提供。基于这些结果，我们制定了社会化水平选择的最优标准。最优社会化水平的存在是在上市公司相对于私营公司不能太弱的条件下被证明的。