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I am studying for an exam in marketing, and there's the following sample question:

The main reasons that people choose products in category X is: 1. Brand 2. Price. Where the importance ranking is 50% Brand and 50% Price. Brand A’s utility is 50 and Brand B’s utility is 30. What is the maximal pricing among the following of Brand B’s product so that it will be preferred by the market if the pricing of A is $80?

a: $54.9

b: $59.9

c: $64.9

d: $69.9

The correct answer is (b). How do they get to this number? My only idea of how to solve this would be to multiply $80 by 30/50 but that's not even an option. Thank you.

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Here you have a possible answer (although I am not 100% sure about it):

You said Brand counts 50% and price 50%. We can consider that with higher brand utilities we get higher chance of buying, while with higher prices we get lower chance of buying the product. Following this idea, I made this equation in which both chances (of product A and B) should be equal, since it would lead us to an equilibrium in which it would be the same for the custumer to buy the product A or the product B:

$U_A - P_A = U_B - P_B$

We substitute according to our values:

$50 - 80 = 30 - x$

We simplify:

$-30 = 30 - x$

Again:

$-60 = -x$

And again:

$x = 60$

So 60\$ would be the price of indifference between product A and B. So we should make it a bit lower if we want people to buy product B: 59.9$, the correct answer of your problem.

I hope it helps.

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