Industrial Organization: Markets and Strategies Paul Belleáamme and Martin Peitz published by Cambridge University Press Part IV. Pricing strategies and market segmentation

Industrial Organization: Markets and Strategies Paul Belleáamme and Martin Peitz published by Cambridge University Press Part IV. Pricing strategies and market segmentation Exercises Exercise 1 Geographical pricing [included in 2nd edition of the book] "Purple Dream"has the monopoly on the production of purple light-emitting diodes (LEDs). It faces geographically separated markets, market 1 and 2. The demands are qA = 1 pA and qB = 1=2 pB, respectively. The transport and production costs are set to zero. 1. Assume that the Örm chooses to set a uniform price across the two markets. What is the proÖt maximizing uniform price? What are the quantities sold on the two markets at this price? 2. Assume that the Örm uses third-degree price discrimination. What are the proÖt maximizing prices and quantities on the two markets? 3. Calculate consumer surplus and proÖt under a uniform price and under third-degree price discrimination. Compare the two situations and comment on the result. 4. Does the result from question 3 hold generally? How would the results change if qB = 1=3 pB? Solutions to Exercise 1 1. ëPurple Dreamí has the monopoly on the production of purple light-emitting diodes (LEDs). It faces geographically separated markets, noted A and B. The demands on these two markets are respectively given by qA = 1 pA and qB = 1=2 pB. The transport and production costs are set to zero. 2. The Örm chooses a uniform price p to maximize  = p (qA (p) + qB (p)) = p (3=2 2p). The proÖt-maximizing price is easily found as pu = 3=8. The quantities sold are qA (3=8) = 5=8 and qB (3=8) = 1=8. 3. Here, the Örm chooses pA to maximize A = pA (1 pA) and pB to maximize B = pB (1=2 pB). The optimal prices are found from the Örst-order conditions, respectively as p A = 1=2 and p B = 1=4; the corresponding quantities are qA (1=2) = 1=2 and qB (1=4) = 1=4. 4. ProÖts under uniform pricing and under third-degree price discrimination are respectively equal to  uni = 3 8 5 8 + 1 8
= 9 32 ;  3rd = 1 2 1 2 + 1 4 1 4 =