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.

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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- Fall '15
- Marketing, Pricing, Consumer Surplus, Sales, Beauregard, everyday fair pricing