Problem 1. FootWear, a shoe manufacturer, has identified two customer segments;
ID: 423496 • Letter: P
Question
Problem 1. FootWear, a shoe manufacturer, has identified two customer segments; one that prefers customized designer shoes and is willing to pay a higher price and another that is willing to take standard shoes but are more price sensitive. Assume that the cost of manufacturing either shoes is $500. Demand from the customized segment has a demand relationship of di - 50000 - 25p and demand from the price-sensitive segment is d2 80000 50p2. What price should Footwear charge each segment if its goal is to maximize profits? What is the total profit? If TwoWheels were to charge a single price over both segments, what should it be? How much increase in profits does differential pricing provide?Explanation / Answer
Part 1: Difference pricing
Demand from customised segment, d1 = 50000 - 25p1
Profit from customised segment, R1 = d1*(p1 - 500) = (50000 - 25p1)*(p1 - 500) = 50000p1 - 25000000 - 25p12 + 12500p1
For profit maximization, dR1/dp1 = 0
d(50000p1 - 25000000 - 25p12 + 12500p1)/dp1 = 62500 - 50p1 = 0
p1 = 62500/50 = 1250
Demand from price-sensitive segment, d2 = 80000 - 50p2
Profit from price-sensitive segment, R2 = d2*(p2 - 500) = (80000 - 50p2)*(p2 - 500) = 80000p2 - 40000000 - 50p22 + 25000p2
For profit maximization, dR2/dp2 = 0
d(80000p2 - 40000000 - 50p22 + 25000p2)/dp2 = 105000 - 100p2 = 0
p2 = 105000/100 = 1050
Price for customized segment = $ 1250
Price for price-sensitive segment = $ 1050
Total profit = (50000-25*1250)*(1250-500) + (80000-50*1050)*(1050-500) = 14,062,500 + 15,125,000 = $ 29,187,500
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Part 2: Single pricing
In this case, p1 = p2 = p
Total profit function, R = (d1 + d2)*(p-500) = ((50000-25p)+(80000-50p))*(p-500)
= (130000 - 75p)*(p - 500)
= 130000p - 65000000 - 75p2 + 37500p
= 167500p - 65000000 - 75p2
For profit maximization, dR/dp = d(167500p - 65000000 - 75p2)/dp
= 167500 - 150p = 0
p = $ 1117
Total profits = 167500*1117 - 65000000 - 75*11172
= $ 28,520,833
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Difference pricing provides Increase in profit = 29187500 - 28520833 = $ 666,667
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