Let Us Do Expected Value Math on $0 Price

Once again the power of $0 price is in the news. This time in The Wall Street Journal, featuring research published in Journal of Consumer Research. It is the previously famous Hershey’s experiment from Dan Ariely’s work,

“In one of their experiments, participants were offered a choice between a cheaper lower quality chocolate (Hershey’s) and a more expensive higher quality one (Ferrero Rocher). The price of the chocolates was manipulated between subjects in the following manner: two cents & 27 cents, one cent & 26 cents, and zero & 25 cents. Results showed that whereas there was roughly an even split between the two chocolates in the first two conditions, 90% chose Hershey’s when it was free, indicating a discontinuity in the cost-benefit evaluations. In other words, consumers over-reacted to the free chocolate.”

As it had been said before, “something magical happens at $0 price”.   So a strong case is made for giving your product away for free regardless of the experimental conditions and its applicability to your particular scenario. You are told that Free is Free marketing. But no one bothered to do the math for you on what is the expected value of free. Let us do just that here.

Let us assume the costs are all sunk since you already bought the chocolates. From the text in bold above you can see that:

  1. When the price was 1 cent for Hershey’s and 26 cents for Rocher,  the choice was even, that is 50%. So the expected value of the customer is  (0.5 * 1 + 0.5 * 26) =  13.5 cents
  2. When the price was 0 cent for Hershey’s and 25 cents for Rocher, the choice was 90% Hershey’s and 10% Rocher. So the expected value is (0.9*0+0.1*25) = 2.5 cent

So which option would you choose? One that has an expected value per customer of 13.5 cents or 2.5 cents.

If you believe the free customers generate other revenue, then each one has to make up additional 12.2 cents from whatever means it is.

Just by giving up the 1 cent on the price you could lose much more than 1 cent. In this case, you lost  11 cents and left with the hope that you will somehow make up for it.

What does this say about the wildly famous Freemium model? The Freemium model is about having a free version to get users and hope that they will convert over to paid premium version. Simple calculation from Hershey experiment shows presenting a free version is much worse than presenting a low priced version alongside premium version.

Isn’t it time you do some hard math and reject fads and pseudo economics of social media gurus?

See also:

1. Opportunity cost of $0 price.

2. Dan Ariely cautioning on the dangers of $0 price.

16 thoughts on “Let Us Do Expected Value Math on $0 Price

  1. Yes, people measure what is convenient and available. That is is why you see metrics like HHI and RMS.
    Apple has less than 5% of market share in mobile phone market but has more than 30% of profit.


  2. Christian
    You are correct. I am not selling my articles but using them as part of my Marcom tactic, like BCG Perspectives.

    If the option to give away free does generate incremental profit over not having free option, by all means one should do it but not before doing the math.


  3. Another one of my favourite quotes is “there is no bank in the world that will accept a deposit of market share” …which is what free will give you.

    I have another comment – Behavioural Economics. Great stuff. Been around for 30 years now. But those of us involved in pricing have been doing behavioural economics since Joseph (with his coat of many colours) was sold into slavery by his brothers!

    But these chocolate experiments (etc) are always done with undergrad and grad students. When is Dan Ariely at al going to get out and do some experiments on other (real) people. Who here is going to base their pricing strategy on the behavior of some Duke University students?


  4. Great point. But I would say you also have to consider how similar the product offer is. In this case the product is a chocolate bar – and then I 100% agree with you calculation.

    But one could also argue that you yourself are using a freemium model; free blogposts on effective pricing, and then pricing consulting as a premium.
    For me the breaking point is how similar the “free” and “premium” product offer are..


  5. Free is intoxicating. The idea of releasing a free version of something can be hard to fight against because the upside is that user growth can be truly phenomenal.

    I’ll mention to someone how many customers we have and 20-30% of the time the response will be “Yeah, but how many of those are paying customers.” It’s a funny interaction that’s reinforced by glorifying users #’s instead of glorifying customer and revenue growth.


  6. Joseph
    Thanks for the comment.
    Pricing is not all art. The known unknowns of pricing is science and only the unknown unknowns is art. You will see that from my many articles on Effective Pricing.


  7. Jon
    Thanks for participating.
    You are correct, it s not a pricing strategy and yes if they are not paying they are freeloaders and not customers.
    Free is not a marketing strategy but a clueless tactic.


  8. Lets not forget that free is not a pricing strategy! Its a marketing strategy. Its an advertising strategy, its a ‘free-rider’ acquisition strategy (can’t call them customers if they’re not paying…can we?)


  9. Thanks a lot for this write up. It’s definitely interesting how 1 cent can change behavior. Pricing is such an art. Finding the perfect price sweet spot is a journey in itself.


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