1. Blue company has introduced a new music device called Juke. The production cost (Cm) for Blue is $100 per Juke. Juke is sold through Buy-Buy, a major electronics retailer, at wholesale price of Cr. Buy-Buy has estimated that demand for Juke will depend on the final retail price p according to the following demand curve: D (demand) =2,000,0002.000 p
2. What is the profit function of Buy-Buy? What is the derivative of Buy-Buys profit function relative to retail price(p)? What is optimal retail price (p) for Buy-Buy as a function of wholesale price (Cr)?
3. What is the profit function of Blue? What is the derivative of Blues profit function relative to Cr?
4. What wholesale price (Cr) should Blue charge for Juke? At this wholesale price, what retail price (p) should Buy-Buy set? What are the profits for Blue and Buy-Buy at this price?
5. If Blue decides to discount the wholesale price by $40, how much of a discount should Buy-Buy offer to customers to maximize its own profits? What fraction of the discount offered by Blue does Buy-Buy pass along to the customers?