Question: Mr. Ithaca Video (IV) sells video tapes to adults and to kids. Suppose IV knows the demands in the two groups are as follows:

Adults: Q^A = 10 - P and Kids: Q^K = 8 - P

Suppose IV's marginal cost is constant and equal to $3 regardless of who he sells a tape to and regardless of how many tapes he sells. There are no fixed costs. That is tc=$3Q and mc=$3.

a. Suppose IV can't tell the difference between adults and kids so he has to operate as a simple single-price monopolist, i.e., he does not price discriminate. If you add the demand curves together you get a joint demand equaling: Q^Demand = 18 – 2P. Solve for the complete monopolistic solution; determine what price IV charges as a profit maximizing simple monopolist. How many tapes in total will he sell? How many tapes do adults buy at the simple monopoly price? How many tapes do kids buy? (Note: graphs are nice, algebra is nice, graphs and algebra are even nicer!)

b. Suppose IV figures out a way to tell adults from kids and now can split the market and practice third degree price discrimination. Solve for the 3rd degree price discriminating monopolist solution; what price will he charge adults and what price will he charge kids per tape? How many tapes in total will he sell? How many tapes do adults buy? How many tapes do kids buy? (Note: graphs are nice, algebra is nice, graphs and algebra are even nicer!) Also note, fractional units of tapes can be sold.