Situation: A monopolist faces an inverse demand curve given by:P=22100zQ z is an index of quality. The monopolist incurs a cost per unit of c=2+z2.

Answer the questions: Imagine that the firm must choose three quality levels, z=1, z=2, or z=3. Which quality choice will maximize the firm's profit? What is the profit maximizing output associated with this profit-maximizing quality level? What is the optimal price are associated with this profit-maximizing quality level? What is the quality choice that will maximize the social welfare? If the monopolist were constrained to produce this socially optimal quality, what price would the monopolist charge?