Apple's iPod has been the portable MP3-player of choice among many gadget enthusiasts. Suppose that Apple is a dominant firm in the ipod market and has a constant marginal cost of 4 (assume no fixed cost) and that market demand is given by Q = 200 - 2P. Suppose there is a competitive fringe of 12 price-taking firms, each of which has a total cost function TC(q) =3q2 + 20q.
a) Find the supply function of the fringe (Hint: A competitive firm supplies along its marginal cost curve above its shutdown point), and the equation of Apple's residual demand curve.
b) What is Apple's optimal output? How many units will fringe providers sell? What is the market price? What is Apple's market share?