1. Monopoly Production Decisions Consider a firm that produces a widget that is protected by a patent and for which there are no other close substitutes. Because of the patent protection, no other firm can duplicate the widget, giving this firm monopoly power. The inverse demand curve for this widget is given by P = 200 Q + 2A, where P is price, Q is quantity, and A is a measure ofthe widget's quality. From this equation, we can see that higher quality allows the firm to sell the same quantity of widgets at a higher price. The firm gets to choose the level of quality for their product, such that the cost of developing a design with quality A is C(A) = A2. However, higher-quality designs also require more expensive parts and complex production. As a result, once the design has been developed, a widget can be produced for a constant marginal cost per unit of 10 + A. Finally, the producer incurs other fixed costs F for research and development (R&D). a) Write down the equation that defines the producer's profits (5 points). b) Given this profit function, what levels of quantity and quality should the producer choose? (6 points) c) What price can the producer charge for this combination of quantity and quality? (2 points) d) What are the producer's profits ifthe fixed costs are F = 10000? (2 points) e) A consumer group accuses the firm of selling the widget at an inflated price. The producer responds by claiming that it must charge this price to cover its R&D costs. Is the producer's argument valid? Why or why not? In what sense is the producer's price \"inflated?\" (5 points)