NatBike, a bicycle manufacturer, has identified two customer segments; one that
ID: 351620 • Letter: N
Question
NatBike, a bicycle manufacturer, has identified two customer segments; one that prefers a customized bicycle and is willing to pay a higher price and another that is willing to take a standardized bicycle but is more price sensitive. Assume that a customized bicycle costs $400 to manufacture, whereas a standardized bicycle costs $300 to manufacture. Demand from the customized segment has a demand relationship of d1 = 40000 – 40p1 and demand from the standardized segment is d2 = 60000 – 75p2.
What price should NatBike charge each segment if its goal is to maximize profits? What is the total profit? If NatBike were to charge a single price over both segments, what should it be? How much increase in profits does differential pricing provide?
Explanation / Answer
(1) Profit function of customized segment F(p1) = Demand * ( Price - Cost) = d1*(p1-400)
= (40000-40p1)*(p1-400)
= 40000p1-16000000-40p12+16000p1
= 56000p1-40p12-16000000
For profit maximization, first order derivative (slope) of profit function must be equal to 0
d(F(p1))/dp1 = d(56000p1-40p12-16000000)/dp1 = 56000-80p1 = 0
=> p1 = 56000/80 = 700
Profit function of standardized segment F(p2) = Demand * ( Price - Cost) = d2*(p2-300)
= (60000-75p2)*(p2-300)
= 60000p1-18000000-75p22+22500p2
= 82500p2-75p22-18000000
For profit maximization, first order derivative (slope) of profit function must be equal to 0
d(F(p2))/dp2 = d(82500p2-75p22-18000000)/dp1 = 82500-150p2 = 0
=> p2 = 82500/150 = 550
Price of each segment for profit maximization are following
p1 = 700
p2 = 550
Total profit = (40000-40*700)*(700-400)+(60000-75*550)*(550-300) = $ 8,287,500
(2) Let single price be p
Total profit = (40000-40p)(p-400)+(60000-75p)(p-300)
= 40000p-16000000-40p2+16000p+60000p-18000000-75p2+22500p
= 138500p - 115p2 - 34000000
First order derivative of the above profit function = d(138500p - 115p2 - 34000000)/dp = 138500 - 230p = 0
=> p = 602.17
Total profit = 138500*602.17 - 115*602.172 - 34000000 = $ 7,700,540
(3) Increase in profit differential pricing provide = 8287500 - 7700540 = $ 586,960
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