Problem 2

Your company has a monopoly on a wristwatch digital cameras Market research has shown that demand for these cameras is P(Q, z) = z(48 ? 2Q) Where z is the quality of the camera measured in megapixels The cost of designing a camera with z megapixels is F(z) = 18z2, but once designed, there is no marginal cost to producing the cameras Only one type of camera can be produced

Problem Set #5 2

1 Write down the profit function for the camera as a function of z and Q

2 What is the optimal quantity of camera's to produce?

3 How many megapixels should you offer?

4 What are the company's profits?

5 Suppose you had the option of producing multiple types of cameras Given the information provided in this question, is it worthwhile to offer more than one type of camera? Explain your answer

Problem 3

A monopolist can 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 There are 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 The market consists of 750 type 1 consumers and 250 type 2 consumers

1 Suppose you are able to identify which consumers are type 1 and which are type 2, what are the optimal qualities to offer to each type?

2 Again assuming you are able to identify the types of each consumers, what are the optimal prices will you charge to each type?

3 For the rest of the question, you are not able to identify the difference between types Assume you will offer a quality of type z2 intended for Type 2 consumers, what is the price p2 you will charge for this product as a function of z2?

4 Suppose you will offer a second level of product quality to type 1 consumers with a quality of z1 and a price of p1, what constraints must hold to ensure type 1 consumers purchase this product?

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

6 What are the optimal price-quality offerings in this market, what is the maximum profits the monopolist can achieve