The individual rationality of buying small cokes/chippies

One of the most vexing questions in economics has to be why the price of a 330ml coke is often only slightly less than the price of a 1.5l coke. This issue generalises to other products such as chippies.

Now there are a number of good responses, namely:

1. Strongly diminishing marginal utility for fresh coke and a very low value on saved coke (or a relatively high cost of storage),
2. A 330ml bottle is easier to consume than a 1.5l bottle – as a result the value of the 330ml bottle may be higher for people on the move, and so they are priced to service different markets.
3. The cost of producing a 330ml coke is far more than a 33/150th of the cost of producing a 1.5l coke

These answers seem to satisfy me when I think of coke. However, when I think of chippies I find this explanation sadly lacking.

Downstairs I can buy a little bag of chippies for $1.50 or a far bigger bag of chippies (x3) for $3.00. I always buy the little bag.

Now I will do this each day, and don’t get any less value from 3 day old chippies than I do fresh chippies. Furthermore, I am eating them at work – implying that there is no storage cost and no convenience benefit.

No-one steals my chippies if I get a big packet so its not that. Am I passing up a free lunch here (and thereby not being a utility maximiser as my shirt says) – or is there a reason I buy the small bag instead of the big bag.

Other reasons for choosing small

There is actually a reason why I buy the small bag instead of the big bag – marginal pricing and pre-commitment.

Even though the big bag is three times the size of the small bag it does not imply that I will consume those chips over three days. When I have a whole big bag of chips in front of me I just consume them until the marginal cost of doing so is equal to the marginal benefit. As the marginal cost is virtually zero, I keep consuming until I get zero or negative satisfaction from an additional chip.

If I buy a smaller bag of chips then I introduce a cost for eating past that point. So for example, even if the small bag was 1/3 of the cost of the big bag, it is likely that I would still end up eating less chips – as I have to pay to get each 1/3.

The optimality of this relies on the assumption that the last set of chips I eat (say for simplicity I would eat the whole big bag – then we are talking about the last 1/3) is actually worth less than the appropriate proportion of the price (1/3 in the example case). This is me paying for the introduction of marginal pricing.

On the precommitment side I realise that I am viciously time inconsistent with chippie eating. Before eating the chips I think that the optimal path would be to only eat a few chips. When eating the chips I want all the chips. Once I’ve eaten the chips, I wish I hadn’t, as I’ve got to go and play hockey – damn you hyperbolic discounting!

By buying fewer chips/limiting my choice set I can pre-commit to eating less chippies (h.t. Rose Colligan). As it is my choice to do so prior to the chippy eating game between my past, present, and future selves, I know that the choice will be optimal.

With the advantage of marginal pricing and pre-commitment provide two more reasons why the small packs of chippies and small drinks at the supermarket are not much cheaper than the big ones!