Best car deal based on mileage and price.

[El Demente]

Hi guys,

I'm comparing car deals based on their mileage and price. I understand that other factors involved, but for the sake of this exercise let's concern ourselves with only these factors. Obviously, the lower the mileage, and the lower the price the better.. but I just can't wrap my head around which formula to use.

Example	Miles	Price
A	200,000	4000
B	200,000	8000
C	100,000	4000
D	100,000	8000

Obviously example C is the best deal. But which formula can be used to demonstrate this? If I divide Miles by Price, then example C is neither the lowest nor the highest result. Same as if I divide Price by Miles.

I appreciate the help!

 

[Steven G]

If you divide miles by price then assuming the same price the higher mileage car will yield a higher number. For example 200,000/4000>100,000/4000 but the 200,000 mile car is not a better deal.
You need to decide how much better a 100,000 mile car than a 200,000 car. IF you say that it is twice as good, then you can multiply the miles by the price and the one with the lower number is a better car.

 

[HallsofIvy]

You will need to tell us what weight you want to give "mileage" and "price". Certainly both a higher mileage and higher price reduce the value so you want to assess value as a/mileage+ (1-a)/price for some a between 0 and 1. But the value of a depends on your preference.

 

[Dr.Peterson]

My initial thoughts were like Jomo's: if value is inversely proportional to both mileage m and price p, then you can go by the lowest product of mileage and price. But there is no good reason to make that assumption.

Another (still oversimplified) model would be to suppose that a car had a fixed life, say M miles. Then you could determine the value in dollars per remaining mile as p/(M - m), looking for the minimum. I doubt that this is at all useful in real life.

 

[El Demente]

Thank you all for your help. You all have conveyed to me the proper way to think about it. I was trying to force it into a ratio, however the weight in value assigned to mileage and price in proportion to each other is rather arbitrary and subjective.