Upper Peninsula Underground Recordings (UPUR) has a monopoly on the recordings of the famous rock group Moosecake. Moosecake’s music is only provided on digital tape, and blank digital tapes cost them c per tape. There are no other manufacturing or distribution costs. Let p(x) be the inverse demand function for Moosecake’s music as a function of x, the number of tapes sold.
(a) What is the first-order condition for profit maximization? For future reference, let x∗ be the profit-maximizing amount produced and p∗ be the price at which it sells. (In this part, assume that tapes cannot be copied.) _______.
Now a new kind of consumer digital tape recorder becomes widely available that allows the user to make 1 and only 1 copy of a prerecorded digital tape. The copies are a perfect substitute in consumption value for the original prerecorded tape, and there are no barriers to their use or sale. However, everyone can see the difference between the copies and the orginals and recognizes that the copies cannot be used to make further copies. Blank tapes cost the consumers c per tape, the same price the monopolist pays.
(b) All Moosecake fans take advantage of the opportunity to make a single copy of the tape and sell it on the secondary market. How is the price of an original tape related to the price of a copy? Derive the inverse demand curve for original tapes facing UPUR. _______.
(c) Write an expression for UPUR’s profits if it produces x tapes. _______.
(d) Let x∗∗ be the profit-maximizing level of production by UPUR. How does it compare to the former profit-maximizing level of production? From the two profit functions, one sees that _______.
(e) How does the price of a copy of a Moosecake tape compare to the price determined in Part (a)? _______.
(f) If p∗∗ is the price of a copy of a Moosecake tape, how much will a new Moosecake tape sell for? _______.