Thursday, November 29, 2007

Market Failure in Christmas

A model:

Denote the degree to which advertisers push christmas by 'Push'. This includes seasonal music playing in malls, Santa set up in said malls well before christmas, advertisements mentioning the number of shopping days remaining, etc, etc, etc.

Partition the set of all consumers into two groups. Group 'Elf' includes those whose utility is an increasing function of Push. Group 'Humbug' includes those whose utility is a decreasing function of Push. (Full disclosure: I fall into the latter category.)

Claim: Elves spend more money on christmas than do Humbugs. This seems a reasonable assumption; and is stated without proof. (If there is survey data on this, I would love to see it.)

Assume advertisers set Push in order to maximize profits, which we will take as analagous to sales. Consumers react to this advertising as we would expect, given their utility functions. Elves purchase more holiday merchandise, Humbugs purchase less. However, since Elves spend more, is it not reasonable to suspect that an increase in Push would, in absolute terms, elicit more spending from Elves than it would dissuade from Humbugs? This is true, for example, if each reacts equally to Push in terms of percentages. I further suspect that this could true because below some minimum standard, it's very difficult to decrease one's holiday spending; e.g. your significant other still expects presents, even if you can't stand venturing into the Push-filled malls.

But, just because spending contains an asymmetry does not imply that utility does. The amount of Push will be set higher than optimal because those financing the Push are responding disproportionately to the desires of Elves because Elves control a disproportionate amount of spending in the market place.

For example, assume we have 5 Elves spending $1000 on Christmas and 5 Humbugs spending $500 on Christmas. Each has utility of 100. Normalize Push to 1. Assume Push rises by 10%. The Elves increase their spending 10%, to $1100, and the Humbugs decrease their spending to $450. But the utility of the Elves rises, say, 5 utils to 105, and the utility of the Humbugs falls 5 utils to 95. In this manner, there is an incentive to continue increasing Push until the cost of the increase is equal to the spending induced.

In this manner, retailers will not only increase inequality among society, but expend productive resources on increasing Push, which does not improve the utility of society. Note that even if the Elves outnumber the Humbugs - irrespective of by how much - there still exists a point at which more Push has no net effect on the utility of society, but at which advertisers will increase it, given certain indifference curves, or given pretty much any indifference curve, if you believe my argument about it being very hard to substitute away from christmas spending below a certain point.

NOTE: This argument is severely hamstrung by the lack of equation ability inherent to blogger. I'll have to LaTeX it formally over the holidays.

UPDATE: The more I look at this the more I feel that utility should be removed from the equation, and we should simply assign monetary benefits to the gains/losses from exposure to Push, which prevents one from wading into the which-welfare-function-is-right debacle. I'm fairly utilitarian, but ceteris paribus, I prefer less inequality to more - to a certain point.

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