Problem 2. Your company has a monopoly on a wristwatch digital cameras. Market researchhas shown that demand for these cameras is P(Q, z) = z(48 ? 2Q). Where z isthe quality of the camera measured in megapixels. The cost of designing a camera with zmegapixels is F(z) = 18z2, but once designed, there is no marginal cost to producing thecameras. Only one type of camera can be produced.Econ 3P06: Problem Set #5 21. 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 informationprovided in this question, is it worthwhile to offer more than one type ofcamera? 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 ofconsumers in the market. Type 1 consumers value MP3 players with a capacity of z atV1 = 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 type2 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 theoptimal 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 theprice 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 aquality of z1 and a price of p1, what constraints must hold to ensure type 1 consumerspurchase 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 maximumprofits the monopolist can achieve.

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