Final answer:
In a perfectly competitive market, the price per widget would be set at the marginal cost of production which is $9, as long-run equilibrium forces the price to equal marginal cost.
Step-by-step explanation:
In a perfectly competitive market, price is determined by the intersection of the supply and demand curves. For the widget producer in question, if the marginal cost of producing a widget is constant at $9 per widget, and there are no fixed costs, then the price in a perfectly competitive market would be where the marginal cost equals the market demand. Since the marginal cost is $9, and assuming no price discrimination, the monopolist is forced to behave like a competitive firm by setting the price equal to marginal cost in long-run equilibrium. Therefore, the price per widget in a perfectly competitive market should be $9.