Week 10 Lecture_Price_Discrimination

Week 10 Lecture_Price_Discrimination - Week 9 Price...

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Week 9 Price Discrimination
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Applications of 2 nd  PD A chocolate seller can choose the “niceness” (q) of  the packaging of a box of chocolate. High type values a box at 9q + 20 Low type values a box at 5q + 20 Seller cannot tell the types apart. Seller estimates that the probability of high type is 1/3  and that of low type is 2/3. Cost of creating “niceness” is ½*q 2 . Cost of the  chocolate itself is 10. What is the optimal pricing scheme, assuming that  the seller can choose q ≥ 0?
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time Seller maximizes    λ (P H  – 1/2q 2 H ) + (1-  λ )(P L  – 1/2q 2 L ) with the constraints: 1. θ q H  – P H  =  θ q L  – P L  and 2. θ q L  – P L  = 0 q* θ H ,  q* = ( θ -     λ θ )/(1-  λ ).   q* = 9   ,   q* L  = (5 – 1/3*9 )/(2/3) = 3. Price for packaging is: P* = 15. P* = 15 + 9*(9-3)  = 69.  Price for chocolate is: 20. Seller cannot extract all the surplus of the high 
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Week 10 Lecture_Price_Discrimination - Week 9 Price...

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