The perfectly competitive DVD copying industry is composed of many firms who can copy five DVDs per day at an average cost of $10 per DVD. Each firm must also pay a royalty to film studios, and the per-film royalty rate (r) is an increasing functions of total industry output (Q) given by r = 0.002Q
(a) Graph the royalty "supply" curve with r as a function of Q.
(b) Suppose the daily demand for copied DVDs is given by Demand: Q = 1,050 – 50P Assuming the industry is in long-run equilibrium, what are the equilibrium price and quantity of copied DVDs? How many DVD firms are there? What is the per-film royalty rate? (Hint: Use P = AC. Now AC = 10 + 0.002Q.)
(c) Suppose the demand for copied DVDs increases to Demand: Q = 1,600 – 50P Now, what are the long-run equilibrium price and quantity for copied DVDs? How many DVD firms are there? What is the per-film royalty rate?
(d) Graph these long-run equilibrium in the DVD market and calculate the increase in producer surplus between the situations described in part (b) and part (c).
(e) Use the royalty supply curve graphed in part (a) to show that the increase in producer surplus is precisely equal to the increase in royalties paid as Q expands incrementally from its level in part (b) to its level in part (c)
(f) Suppose that the government institutes a $5.50 per-film tax on the DVD-copying industry. Assuming that the demand for copied films is that given in part (c), how does this tax affect the market equilibrium?
(g) How is the burden of this tax allocated between consumers and producer? What is the loss of consumer and producer surplus?
(h) Show that the loss of producer surplus as a result of this tax is borne completely by the film studios. Explain your results intuitively.