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Quantity versus Price

A new paper in the Journal of Marketing by Akshay Rao of the University of Minnesota shows that people have a hard time with the following sort of question:
When offered the possibility of 33% off a product or the same product with 33% more quantity, which would you choose?

As the Economist puts it, "Consumers often struggle to realise, for example, that a 50% increase in quantity is the same as a 33% discount in price".

These calculations are directly analogous to the calculations needed to estimate savings in mileage and in gas consumption. A 50% increase in mileage is the same as a 33% reduction in gas use.

In an earlier post, I proposed a simple formula for converting from percentage increase in mileage to percentage savings in gas consumption:
GPM% = MPG%/(100+MPG%)

For example, a 100% increase in MPG reduces GPM by 50%. A 50% improvement in MPG reduces GPM by 33%.

This same formula will work for price and quantity conversions:
Price% = Quant% / (100+Quant%)