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Economists Whose Jobs I Don’t Envy, Christmas Price Index Edition…

December 1st, 2012 · 1 Comment
Econ 101 · Just For Fun · Macroeconomics

I have no doubt that most of the nerdy among us have wondered at one point or another how much the gifts in the 12 Days of Christmas song actually cost. (Or at the very least the song brings to mind the storyline in The Office where Andy gifts Erin all 12 days of items via secret santa, with disastrous consequences of course.) Apparently the job of actually calculating this belongs to some poor sap at PNC Financial. Of course.

As if this isn’t bad enough, I am now going to take this opportunity to talk about inflation and the Consumer Price Index. Inflation, as you likely know, is a measure of the change in an aggregate price level in an economy. That said, there are many ways to calculate an aggregate price level. One way would be to add up the prices of one of each thing in an economy. Another would be to weight each item in the economy by how much of it is produced and sold. And so on. (For real examples of such things, you can check out the GDP deflator and the Producer Price Index.)

In order to determine what measure of aggregate price is most appropriate, it’s necessary to think about what we are trying to use inflation to measure. In many cases, inflation is used to measure the cost of living for an individual or household. Therefore, it makes sense to count the things in the economy that consumers typically buy. In addition, it makes sense to weight the goods by how much of them consumers actually purchase. This gives a representative basket of goods that is used to calculate the Consumer Price Index (CPI). Inflation, as it is typically reported, is then the percent change in the CPI from one month to the next or one year to the next or whatever. (You can see more about the Consumer Price Index here.)

The Christmas Price Index essentially does the same thing. If it were the case that the items in the 12 Days of Christmas song were in fact the items that a representative individual bought for his sweetie (dear men of the world: please don’t), then we get the following:

This year, buying one of each gift will cost you $25,431.18, a 4.8% increase over last year’s total.

But wait- we also said that it made sense to weight the index by the amount purchased, so this is probably a better measure:

But for the “True Cost of Christmas” — each gift multiplied by its associated number in the song — you’re looking at $107,300.24. That’s 6.1% higher than in 2011.

So the relevant inflation in Cheesy Christmas Carol Land is 6.1% per year. In case you’re curious, the most comparable figure for the Consumer Price Index is 2.2%. (Also, if you’re curious, you can check out some sort of interactive feature offered by PNC.)

Like the real CPI, the Christmas Price Index probably overstates increases in the cost of Christmas for two reasons. First, the Christmas Price Index only looks at prices and doesn’t take quality and productivity into account. For example, today’s maids-a-milking are likely much more productive than maids were when the song was created, so, yes, you’re paying more, but for a better product. This should make the relevant cost increase lower than what the CPI calculates. (The opposite would be true for productivity decreases.)

Second, the Christmas Price Index assumes that a person buys the same basket of gifts each year regardless of prices. This would imply, for example, that an individual would always purchase seven swans a swimming and only three French hens even if the price of swans increased disproportionately to the price of hens. (Granted, I’m not enough of an ornithophile to know whether swans and hens are suitable substitutes, but just go with me here.) Instead, a rational gift giver would at least consider exchanging some swans for hens in the face of such a change, making himself (and hopefully his giftee) better off than if he had stayed with the static basket of goods. This ability to substitute also means that the effective increase in the cost of gifting is less than the Christmas Price Index would indicate.

Or, you could just make things easier and give one Widget for Christmas:

Update: Ben Popken adds some insight as to the logistics of actually purchasing the basket of Christmas goods, including bundling (did you know that you have to purchase partridges in groups of 30?), advance purchase, etc.

Tags: Econ 101 · Just For Fun · Macroeconomics

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