# How much does it cost to be ‘that true love’ of Christmas?

The **Christmas Price Index** is a (somewhat comical) economic indicator maintained by *PNC Wealth Management*.^{1} It tracks the cost of the gifts described in The Twelve Days of Christmas.

It all started in 1984 as a ~~ploy~~ marketing effort by *Provident Bank* to engage the bank’s customers during «*the traditionally light holiday weeks*».^{2} The general idea is to keep track of two numbers:

**Christmas Price Index**
- The cost of buying one set of each of the gifts described in the carol. This is equivalent to the cost of buying only the gifts of the twelfth day.
**True Cost of Christmas**
- The cumulative cost of following the instructions on the carol,
^{3} for a total of 364 gifts

## True Love requires an assistant

But an economic indicator is nothing without numbers. So, **how do you get prices on partridges, pear trees and Lords a-leaping?** Believe it or not, True Love requires a financial advisor, someone who will do the dirty deed of shopping. Since 1986, that person has been Rebekah McCahan, investment strategist for PNC. She shares with us in an interview:^{4}

The National Aviary in Pittsburgh provides the cost of the doves and swans. The partridge price came from a national game bird supplier; the hen price, from a hatchery; and the cost of geese from a waterfowl farm. A national pet chain provides the price of the calling birds, or canaries. The pear tree price comes from a nursery in New Jersey. A national jewelry chain provided the cost of five 14-carat gold rings, and PHILADANCO, a modern dance company in Philadelphia, provides the price of the ladies dancing.

The Pennsylvania Ballet gives the price of the lords a-leaping. Prices for the musicians in the song—the drummers and pipers—are provided by a Pennsylvania musicians union. Lastly, maids a-milking are the only unskilled laborers in the Index, and as such, they reflect the minimum wage. Year after year, the sources for the prices remain the same for the most part for consistency, but they have changed on occasion because of changes in the market or business landscape.

## How many items?

According to the mathematical facts of the lyrics, the True Love buys gifts according to the following algorithm:

- On day 1, he buys 1 of
*n*_{1}. 1 item today, 1 item total
- On day 2, he buys 2 of
*n*_{2} and 1 of *n*_{1}. 3 items today, 4 items total
- On day 3, he buys 3 of
*n*_{3}, 2 of *n*_{2} and 1 of *n*_{1}. 6 items today, 10 items total.
- …

In general terms, the number of items True Love will buy on the *n-th* day is given by the formula ^{5}

*a*(*n*) = (*n* × (*n* + 1))/2

While the total number of items (*m*) bought up to the *m-th* day is given by the formula^{6}

*a*(*m*) = (*m* × (*m* + 1) × (*m* + 2))/6

## Other important considerations

One must also consider the problems that come with sending and receiving this many gifts. **Consider the following**:

The pear is not a particularly big tree. Wikipedia says it reaches 10–17 metres^{7} tall. GardeningKnowHow cites pear trees as needing about 20ft of clearance between trees. Then we can imagine a tree as a 20x20 ft square in order to calculate total area. A simple 60x80 ft garden is enough to plant the 12 pear trees bought during this time. This garden gives the 12 partridges more than enough space to nest… on the ground.

The 22 doves can fit on this garden: it’s easy to imagine every tree having 2 doves.

The modern Faverolles chicken is apparently no longer fit for consumption or egg production. A posh group of bird nuts has determined that the hens are somewhere in the 3.4–4.3 kg range.^{8}

But the number of chickens may become troublesome. A few weeks ago, news broke of a man in Australia who “accidentally” bought 1,000 chickens when he thought he was buying only a few. When discussing this piece of news, I came upon the wisdom of MetaFilter user “loquacious”, who identifies large numbers of chickens as being connected to strange macro-scale quantum effects.

loquacious writes thusly

Man, just 20-30 full grown hens running around free range is like having little bug-eating dinosaurs everywhere and I mean everywhere. Somehow they’ll get up in trees and on roofs and go places cats don’t even dare go… maybe because cats are mammals with forebrains and chickens are, well, they’re chickens.

Also above a certain number of free range chickens it they seem to start behaving with macro-scale quantum effects like they are photons or electrons or something (…) they’ll phase right through walls and start exhibiting some pretty spooky and alarming behavior.

The 36 “calling birds” are quoted as canaries from Petco. One advantage of these species is that they live well on cages and aviaries. Now, I’m no expert, but it seems like 36 of these can comfortably fit on 12 trees, although the number of bird species is growing and we haven’t got to the most troublesome of the lot. At this point, you have 12 + 22 + 30 + 36 birds and their faeces should start to be a concern, both for its acidic effect on the ground and for your lovely garden walks. I’d forget about having a nice nap under a tree, unless it’s under some sort of protective tarp.

The gold rings seem, in general, like a good idea, given that it tends to keep its value over time. A few minutes on Google tell me that the price of gold has generally increased since the 70’s. No problem here.

42 geese. Now here’s trouble. One goose can wreak havoc in even a small population, as evidenced by recent media. Now imagine having 42 of the little devils! At this point, your garden is their property and by law you should fence it and place warning signs around so as to avoid liability.

42 swans. Although less evil than geese, these are still a force to be reckoned with. And not just because of their fierceness, but because of its cost: PNC has determined that the (financial) cost of the swans is the most unpredictable element of the index, and indicates so by calculating a separate “Core index” without the swans, making it a more stable figure for calculations.

In 2019, for example, the regular CPI (buying one “set” of every kind of gift) is $38,993.59 USD, but the swans alone are valued at $13,125 USD (~33.6% of the total).

This difference only gets steeper when calculating the **True Cost of Christmas**. In 2019 it’s valued at $170,298.03 USD, and the 42 swans represent $78,750 of it (~46.2% of the total)

Humans. Oh, humans. Managing 40 maids, 36 female dancers, 30 male ballet dancers,^{9} 22 pipers and 12 drummers is no small feat. Organizing all of them into any kind of consistent, artistic demonstration will take lots and lots of man-hours. I’d recommend having two separate directors for the dancers and the musicians and letting them figure out how to integrate the two groups.

Also, the song doesn’t specify whether these are being hired for a single evening or are given as some sort of slaves. The implications of either solution are left to the reader as an exercise.

All in all, managing all these gifts seems too much work, even for *my true love*. I’d stick to a nice Xmas card and a thoughtful, practical present like a skillet.

## See also

Now known as PNC Financial Services

Apparently the bank’s usual customers didn’t have any kind of end-of-year fiscal responsibilities, never made inventory and didn’t have to juggle work responsibilities, holidays, transport schedules and regular shopping.

One partridge and one pear tree on day 1; two turtle doves, one partridge and one pear tree on day 2 and so on.

How much for 10 Lords-a-leaping?

Astute readers will recognize this as the Sequence of Triangular numbers, entry A000217 on The On-Line Encyclopedia of Integer Sequences

Astute readers… Tetrahedral numbers, entry A0000292 on the OEIS

33–56 ft

7.5–9.5 lb

Yeah, the nine ladies’ salary is an estimate from The Philadelphia Dance Company and the ten lords’ estimate is from the Philadelphia Ballet. Why quote two companies instead of one is beyond me, but the price difference is notable. The “Nine ladies dancing” estimate is $7,552.84 USD (or ~$839.2 per individual dancer), while their male counterparts are estimated at $10,000 USD ($1,000 per dancer)