The Orange company has introduced a new music device called the J-Pod. The J-Pod

Question

 The Orange company has introduced a new music device called the J-Pod. The J-Pod is sold through Good Buy, a major electronics retailer. Good Buy has estimated that demand for the J-Pod will depend on the final retail price p according to the demand curve   Demand D = 2,000,000-2,000P  The production cost for Orange is $100 per J-Pod.   a. What wholesale price should Orange charge for the J-Pod? At this wholesale price, what retail price should Good Buy set? What are the profits for Orange and Good Buy at equilibrium? b. If Orange decides to discount the wholesale price by $40, how much of a discount should Good Buy offer to customers if it wants to maximize its own profits? What fraction of the discount offered by Orange does Good Buy pass along to the customer? 

Explanation / Answer

Demand function is given as:

D = 2,000,000 - 2,000P where D is Demand and P is Price

The Production cost for Orange is $100 per J-Pod

The Objective has to be Maximization of Profit which is Revenue - Cost, therefore

Profit = P*D - 100*D = 2000000P - 2000P2   -100( 2000000 - 2000P )

Taking first order derivative of Profit function with respect to P and equating with zero we get

   2000000 - 4000P + 200000 = 0 which means P = 550 gives the maximum profit because the second order derivative is negative (-4000)

Therefore the optimum level of wholesale price be $550 if the Demand and Cost functions are for the Orange company as stated above. In case the Demand and cost functions are for Good Buy retailer than $550 should be the retail price.

Nothing is mentioned about the relationship between wholesale price and retail price and or profit margin sharing between the Orange and Good Buy

Let us assume Wp is the whole sale price charged to Good Buy then Profit for Good Buy is given as

Profit (Good Buy) = 2000000P - 2000P2 - Wp(2000000 - 2000P) where P represents retail price

Profit ( Orange company) = ( Wp - 100) * D = ( Wp-100) * (2000000 - 2000P)

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