Wednesday, September 22, 2010

Taking things too seriously at lunchtime

This PhD Comic from two years ago presents a model of predicting how good food will taste. As the cost of the food approaches 0, it doesn't matter how hungry you are or what quality the food is, it's going to taste really good. So far, so sensible.

BUT. This flies in the face of research that tells us people think wine (for instance) tastes better when people are told it costs more - even though the wine tasting was free. If both relations hold, then, this one only holds for some foods or for foods below a certain cost.

Let us study the other implied relationships to see if this is a reasonable formulation of the relationships between variables. If you hear someone describing how good some food was and you want to determine its actual quality, you might try transforming the above equation to read:

Quality = Taste * Cost / Hunger

This would lead you to ask the person how much the food cost and how hungry they were. If they were particularly hungry, you would discount their tasty tale appropriately. Sounds pretty reasonable. If you also ask the person about the cost, you're playing a game well-known to The Little Prince (see quotes 6 and 7). This is probably the most sensible transformation of the equation.

Now let's pretend instead you are a perfect monopolist who is able to prevent anyone from reselling your food and you wish to extract the maximum consumer surplus possible. You know how hungry your customers are and how good the food will taste to them. By using the Law of Free Food, you derive

Price = Quality * Hunger / Taste

You should charge your customers more for high quality food than for less and you charge them more when they are hungry. Sensible enough. The better tasting the food, the ... Lower the price?? If this were true, you would serve everyone very high quality petroleum products and caster oil.

Let's try this again. Suppose you are trying to decide if you are hungry enough to eat the food in front of you. You must be at least as hungry as:

Hunger > Taste * Cost / Quality

This tells us that you have to be very hungry before you consume expensive food but cheap food is fine for snacking when you have the munchies. Okay, this is about not wasting high cost food, I can maybe see that. In a similar vein, you have to be very hungry to eat trash while you don't have to be very hungry before you eat high quality food, all else equal. However, the better tasting the food is, the hungrier you have to be before you're willing to eat it. Hunh? I would say the opposite is truer: you have to be very hungry to eat terrible food but you don't have to be that hungry for someone to convince you to have a chocolate.

These applications show us that the Law of Free Food is a quite troublesome relationship as specified. It may be the case that Taste = F(quality, hunger, cost) and that the first derivatives go in the hypothesized directions over a certain space. But the inverse functions clearly demonstrate that the particular specification is rejected by economic research, theory, and common sense. At best, the author needs to claim over what (limited) variable space the above equation is expected to hold.

No comments:

Post a Comment