When do imperfectly competitive firms maximize profits? The lessons from a simple general equilibrium model with shareholders' voting

We consider a general equilibrium model with vertical preferences, where workers and consumers are differentiated, respectively, by their sensitivity to effort and their intensity of preference for quality. We consider a monopoly of which the shares are owned by a fraction of the general population. The price is determined through a vote among all the shareholders. We identify necessary and sufficient conditions for (i) an absolute (relative) majority to vote for the profit maximizing price; (ii) an absolute (relative) majority to vote for a different price. We argue that the more concentrated the ownership the more likely it is that the firm charges the profit-maximizing price.