Two different ways to charge for a good

The conventional way to charge consumers for something is pretty simple - they pay for every unit they buy. But, there are alternatives. One is to charge an up-front fee and then refund customers for every unit they purchase below some threshold. Google's new Project Fi has an element of this built into it, as they explain - 'Let's say you go with 3GB for $30 and only use 1.4GB one month. You'll get $16 back, so you only pay for what you use'.

          It is simple to design a pay and refund pricing policy that are theoretically equivalent. For instance, suppose you regularly buy movies from an online website. Also, suppose that you would never buy more than 20 movies a month. Then the following pricing policies are equivalent:

• Pay: You pay £5 for every movie you download.
• Refund: You pay a monthly fee of £100 and receive £5 back, per movie, if you download less than 20 movies. 

For example, if you buy 10 movies in a month then this either costs £10 x 5 = £50 or £100 - 10 x 5 = £50.
          To say, though,  that a pay policy and refund policy are equivalent in theory does not mean they are equivalent in practice. So, which type of policy would you prefer? And which type of policy do you think would lead to most downloads?

           One way of looking at this is to say that paying money for something is coded as a loss. So, under the pay policy there would be 10 times during the month where you 'lose' £5. The abundant evidence for loss aversion tells us that losses are bad. So, 10 losses are very bad. Under the refund policy there is one big loss of £100 and then a gain of £50. Now, a big loss is clearly worse than a small loss. Evidence suggests, however, that we don't consider a big loss as bad as lots of small losses. This, in itself, does not tell us that a £100 big loss is better than 10 losses of £5. But, it does suggest that people might prefer the refund policy once we factor in the additional £50 gain. So, expect people to opt for the refund policy.

           Consider now the number of downloads. With a pay policy each download is a loss of £5. With a refund policy each download reduces the gain at the end of the month by £5. Loss aversion clearly implies that people will download less with a pay policy than a refund policy. Interestingly, this poses something of a conundrum for the company deciding on a pricing policy - the refund policy may be more popular but lead to more usage.  

           If you are not convinced by the above arguments lets churn out some numbers consistent with prospect theory. Suppose that if you lose £x you suffer a psychological cost of 2log(x). Then losing £5 costs 3.22 while losing £100 costs 9.21. This is already enough to tell us that 10 losses of £5 is worse than a one-off loss of £100 (because the 10 losses costs 32.3 compared to only 9.21). Hence, you would prefer the refund policy. Suppose that if you gain £x you experience pleasure of log(x). Then gaining £5 adds at most 1.61 to pleasure which is nothing compared to the cost of paying £5. Hence, you will download more movies under a refund policy.