Monopolistic Trades, Accuracy of Beliefs and the Persistence of Long-Run Profit

In a model that encompasses a general equilibrium framework, we consider a monopolist (a producer) with subjective beliefs that endogenously hedges against fluctuations in input prices in a complete market. We introduce a notion of entropy of beliefs, and we characterize long-run optimal rational investments with this entropy. For irrational beliefs, we show that long-run profits are a decreasing function of this entropy. However, long-run profits always remain positive as long as the entropy remains finite despite the Market Selection Hypothesis that would predict long-run 0-profit. Allowing for Cournot competition in this economy, we show that if at least one entrant makes accurate predictions, the monopolist must also make accurate predictions or else its long-run profit will converge to zero for almost every path. In this latter case, the whole market power switches to the firm making the most accurate predictions