Hi!
I am a bit confused on how to solve this problem.
Bain & Company
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Hi Eva,
Happy to explain.
You can tackle this problem in 2 high-level steps:
A. Compute the missing market share of Newcomer & Company 2
B. Use the market shares to derive weighted average prices for each company (incl. Newcomer)
A. Compute missing market shares of Necomer and Comp 2:
- Starting point: overall there are 4 companies - Company 1, Client, Newcomer and Company 2. You know 2 of the 4 market shares -> Company 1 = 35% and Client = 30%; total of the 4 companies must be 100%
- Now you know that the other 2 companies have 35% in total (100% - 65% from Comp1 and Client) and that Newcomer share is 0.75x of Company 2 share and can set the 2 following equations:
- N+Comp2 =0.35
- N=0.75Comp2
- Solving for N and Comp 2 will give you shares of 15% and 20% respectively.
B. Use the market shares to derive weighted average prices for each company (incl. Newcomer):
- Now with that information you can define a new equation that computes the average price of R$188, i.e. 188 = (share of Comp 1 x Comp 1 price) + (share of Client 1 x Client 1 price) + (share of Newcomer x Newcomer price) + (share of Comp 2 x Comp 2 price) .
- You can set a new variable Y for the price of any of the companies and express the prices of the other companies via Y. An easy way would be to define the following
- Company 1 price = Y
- Client price = Y (we know Client = Comp 1 price from the instruction)
- Company 2 price = 0.85Y (as per instruction)
- Newcomer price = 0.85Y - 10 (we know from instruction that it's 10 less than Company 2)
- Now put all of these into a single equation: 188 = 0.35Y + 0.3Y + 0.2x0.85Y + 0.15x(0.85-10) and solve for Y -> Y=R$200 (= Comp 1 & Client price as per 2a)
- Finally, you know that Newcomer price = 0.85Y - 10 -> plug the 200 into that equation and solve for Newcomer price → you will get R$160
Hope this helps.
Let me know if any questions and feel free to PM me.
Regards, Andi
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