## Saturday, 11 April 2009

### Models of consumer value estimation and price choice

Experimentally, we know that the following phenomenon can be observed:

Offer consumers two bottles of wine, priced at £5 and £9. A proportion will not buy at all; of those who do buy, a proportion (70% would be typical) will buy the £5 bottle and the rest (30%) will buy the £9.

Repeat the experiment with three bottles on offer, priced at £5, £9 and £15. A similar proportion will still not buy; of those who do, the propensity to buy the £9 bottle is much higher than previously. It would not be surprising to see the proportions exactly reversed: 30% at £5 and 65% at £9. Barely anyone will buy the £15 bottle, but a majority of buyers are influenced by its presence.

This experiment violates the assumptions that conventional consumer theory is based on. Rational agents "should" have an context-independent demand curve for each product: they are supposed to evaluate the utility of each option, apply a constant exchange rate between utility and cash, compare the result to the price of each product, and maximise consumer surplus. If the value of the £9 bottle exceeds that of the £5 bottle by more than £4, they buy the £9 bottle. Sensible assumptions about the distribution of the utility function among consumers and the effect of diminishing returns together allow us to derive the standard demand curve.

The switching effect caused by the presence of the £15 proves that this is not the process that's going on. Instead, some more subjective decision is at play.

We would like to find a mechanism that explains this. It's one thing to simply say "people's judgment is influenced by the range of options available to them", but much more powerful to be able to explain the strength of that influence, and predict how it will be affected by changes.

For example, will the effect be stronger with a £12 or £20 bottle of wine instead of a £15 bottle? What if there are four options instead of three? And will more, or less, people actually buy a bottle - and does this outweigh the additional profit from the switching effect?

In this article I'll propose a model which could explain the effect. It won't yet be able to answer the questions of the preceding paragraph, but it will hint at where those answers could come from. And it should give some idea of the sign, if not the magnitude, of the answers.

Suppose that consumers are highly uncertain as to the utility they will gain from a bottle of wine. This is plausible - even under rational decision-making, there are many factors contributing to utility which cannot be predicted at the time of purchase. The quality of the wine, the exact time and place you'll drink it, the mood you'll be in and the people you'll be drinking with. Taking the simplest of these, quality: it is not precisely measurable even if you have bought the same bottle of wine before. If you enjoyed it last time, this could have been a result of the other factors; perhaps I enjoyed it because of the woman I shared it, or the food I ate, and not because the wine was great.

Given this uncertainty, which bottle should you choose? The only choice we can have a direct insight (and a limited one at that) into is our own. But I propose that the following model of decision-making is consistent with this effect:

The buyer (probably subconciously) recalls the main categories of their experience of drinking wine. For most of us, there are a small number of high-end experiences - a special occasion, an expensive bottle and meal, perhaps with special people, and an intense experience filling the mouth and nose with distinctive, delicious aromas. A more common experience of enjoying a refreshing glass of wine, either on its own or with dinner, completing an enjoyable experience of afternoon or evening. And an occasional recollection of some really rough vino which went down harshly, stained our teeth and left a bad hangover.

With three ranked bottles of wine in front of us, we can perfectly superimpose them on these three different kinds of experience. Naturally, we want to achieve one of the first two - and most commonly the middle one. To achieve that, we pick the £9 bottle.

But with only two bottles, if we try to superimpose our memories of wine we are forced to include our third choice - to have no wine at all. This becomes associated with the lowest-ranked experience; the £9 bottle becomes the special one; and the £5 bottle the refreshing everyday choice.

In each case we use pattern-matching to associate the choices in front of us with memories of past experiences - probably because those are more easily accessible, more credible and more concrete than the hypothetical experiences we might have in the future.

So the models of decision-making we build may be closely associated with memories of past experiences. There are a number of analytic or practical conclusions we could draw from this:
• That consumers should be more likely to buy wine when there are three choices than when there are two.
• That the effect may be weaker with white wine than red - because far fewer people have memories or even an image of very special experiences of white wine. This, and the previous effect, should be testable.
• The price of the most expensive bottle should be in a range that the consumer might at least consider buying, but sufficiently above the middle price that it is clearly in a different category. This would indicate that the effect might work less well at £12 but also would not work at £50 - probably £15-25 is the optimal range.
• That four options may work less well than three. I have an intuition that three simple, broad categories are about as far as the subconcious will go (in a field where we are not expert, and this effect is not aimed at experts in any case). Four will probably push us back towards rational choice, and I suspect that the effect would be diminished.
• More generally, that there is a specific kind of correlation between experience and choice - for example, people who are new to a product category may be less influenced by framing effects than those who have used it before.

I would not put this forward as a concrete model of decision-making without further testing, but it's an interesting place to start. If you can think of other explanations, please feel free to comment.