In this work, we examine a mixed oligopoly model within the framework of consistent conjectural variations, in which one of the producers is a labor-managed company competing with other private firms, and consumer demand is given by a discontinuous function. Private firms attempt to maximize their net profit while the labor-managed company attempts to maximize the convex combination of its net profit with an income-per-worker function, which describes the mixed nature of the model. Each producer conjectures the dependence of the market-clearing price on its own production volume and then selects its most suitable conjecture based on a verification procedure. We introduce the notions of exterior and interior equilibrium and prove the existence and uniqueness of the conjectural variation equilibrium, as well as the existence of the particular equilibrium states known as consistent. Finally, we analyze the behavior of the market's consistent equilibrium state in response to changes in consumer demand. © 2013 IEEE.