Stochastic Limit Pricing

If a monopolist is selling a commodity to consumers who could, if they chose, produce a close substitute, but only after incurring heavy capital investment (we have oil in mind), then the monopolist's optimal limit pricing strategy may involve randomizing prices even though stable prices would be feasible. This runs counter to intuition, much of which rests on Samuelson's conclusion that where price stability is feasible it is desirable -- a conclusion which is only proved at a competitive equilibrium. The cause of the randomness lies in the nonconvexity of the problem, which appears to be of quite general concern. Indeed, the problem as modeled is formally identical to the choice of optimal commodity taxes which shows that random taxes may be desirable.