Pricing HW5.docx - Question 1 a If customers are not forward looking and will at most buy the product once we want to make the highest profit so we will

Pricing HW5.docx - Question 1 a If customers are not...

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Question 1 a) If customers are not forward looking and will at most buy the product once, we want to make the highest profit so we will compress the consumer surplus and make the price right at their willingness to pay. For fashion oriented customers, we want them to purchase at the price of 750 and for the not-so fashion oriented customers, we want them to buy at the price of 375. So, we will set the price at $750 at the beginning of the season and set it at $375 in the end of the season. In this case, our profit is maximized like the following equation: Profit = 750*100 + 375*100 = $112,500 b) If customers are forward looking and they can know whether the firm will optimally drop the price when it is in its interest to do so, we have the following three choices to set price in order to generate the same maximized profit: 1). Beginning: $750, End: $375 Profit = $750*0 + $375*200 = $75,000 2). $750 over whole season Profit = $750*100 = $75,000 3). $375 over whole season Profit = $375*200 = $75,000 Thus, we can set the price as above and make the maximized profit. c) If the segment sizes are changed to be 150 and 50 respectively. For the answer of question a, we still want the fashion customers to buy the product at $750 and want the not-so fashion customers to buy it at the price of $375. So, the profit will be: Profit = 750*150 + 375*50 = $131,250 For the answer of question b, if customers are forward looking, we need to calculate different value of profit in different price settings: 1). Beginning: $750, End: $375 Profit = $750*0 + $375*200 = $75,000 2). $750 over whole season Profit = $750*150 = $112,500 3). $375 over whole season Profit = $375*200 = $75,000 Therefore, we will set the price at $750 and generate the profit of $112,500.
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Question 2 a) 225*1/3 + 200*2/3*1/2 = 141.67 225*1/3 + 150*2/3 = 175 200*2/3 + 150*1/3 = 183.33 Therefore, set $200 as the initial price. If no sale occurs, drop the price to $150. Expected Profit: 200*2/3 + 150*1/3 = 183.33 b) 275*2/10 + 225*8/10*5/8 = 167.5 275*2/10 + 200*8/10*7/8 = 195 275*2/10 + 150*8/10 = 175 225*7/10 + 200*3/10*2/3 = 197.5 225*7/10 + 150*3/10 = 202.5 200*9/10 + 150*1/10 = 195 Therefore, set $225 as the initial price. If no sale occurs, drop the price to $150. Expected Profit: 225*7/10 + 150*3/10 = 202.5 c) Question A sets $200 as the initial price, while question B sets $225 as the initial price. It is because of the different possibility distributions of consumers’ willingness to pay in these two situations.
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