Problem 1. You are a monopoly MP3 produces with a technology to produce MP3 players with capacity between 0 and 3 GB. That is, the quality of an MP3 player, z, can vary from 0 to 3. You face two types of consumers in the market. Type 1 consumers value MP3 players with a capacity of z at V1 = 80(z 1). Type 2 consumers them at V2 = 40z. The marginal cost of an MP3 player, regardless of its capacity, is zero. You know that the market consists of 900 type 1 consumers and 600 type 2 consumers.

1. Suppose that at the point of sale you are able to identify which consumers are type 1 and which are type

2. If you are a profit maximizing monopolist, what quality do you offer to each type? 2. Again, assuming you are able to identify the types of each consumers, what price do you charge each type?

3. Suppose you only knew that there were 900 of type 1 and 600 of type 2 consumers but were unable to tell which type you are selling to (e.g. at the point of sale) How much are Type 2 consumers willing to pay for quality z2?

4. If you want to type 2 consumers to buy the good with quality z2, what is the highest price p2 you will charge for an MP3 player of quality z2?

5. Suppose you also offer an MP3 player with quality z1 > z2 at price p1 > p2. If you want type 1 consumers to by the MP3 player of quality z1, what is the most you can charge them for it? Would you ever want to charge them less? Explain why or why not.

6. Is it optimal to offer 1 or 2 types of MP3 players?