On the existence of equilibrium in the super manager model

The super manager model developed in Baranchuk et al. (2011) is revisited in this paper. We show that an important condition required for the firm’s optimization problem was overlooked. Once this condition is imposed, the market equilibrium derived in the original paper may fail to exist for certain parameter values. In particular, the existence of interior hierarchical equilibrium is conditional on managerial productivity exceeding organizational costs, and disappears when demand is sufficiently weak, in the sense that no admissible interior super-manager equilibrium existsWe derive the corrected equilibrium system and provide numerical illustrations showing that sufficiently weak demand can eliminate any admissible interior super-manager equilibrium. Our results not only clarify the conditions under which the equilibrium of the super manager model is well defined, but also provide economic interpretations when no admissible interior super-manager equilibrium exists.