3. (20 points) There is only one firm that produces COOL sneakers, and its product has no substitutes. There are two types of customers in the market for COOL sneakers; type H (Lady Gaga) and type L (you!) with the following demand functions: QH = 2000 5P and QL = 500 20P. If there is no fixed costs and the marginal cost of producing sneakers is $10: (a) What is the price and quantity produced if we charge one price to everyone? (b) What is the producer surplus? (c) What is the price and quantity if we want to charge different prices to each consumer group? (d) Find the surplus from engaging in this pricing strategy and compare your answer to part

4. (20 points) Suppose that Mozart has a utility function of the form U = 10X +XY where X is music notebook and Y is velvet shoes. If price of notebook and velvet shoes are respectively 5 and 10 marks and Mozart has 100 marks to spend: (a) Find Mozart's utility maximizing quantity of notebooks and pairs of shoes using any method. (b) If the king of Germany decides to raise his salary by 100 marks, what happens to his consumption of X and Y? (c) Are X and Y normal, inferior, or Giffen? Explain.