## Partridges and pear trees: The math behind the 12 Days of Christmas!

This is not a drill: Holiday season is finally upon us. December is a hectic month for everyone: moms, dads, Santas and students.

While using online gift shopping and Christmas music as distractions from math homework, the obvious question (other than solving for X) becomes:

# How much would it cost to actually purchase everything in the 12 Days of Christmas ?

Before we can appreciate the total price (hint: it’s not cheap), we have to understand the broad math concepts behind the market that sets the price.

At Yup, our tutors provide help with your math homework, but we also believe that you should be able to draw real-life applications from math as well. The same goes for physics and chemistry: we teach you how to solve the problems, not just give the answer.

Here’s a little crash course in economics. We break it down to the tune of “The 12 Days of Christmas”, so you can show off your math chops the next time you have to sit through the overly repetitive “six geese a-laying”.

According to PNC’s Christmas Price Index,  the total for this season’s gifts, including 11 pipers piping, is \$34,363.49.

# So how do the numbers break down?

According to PNC’s yearly index, here are the individual costs for 2016:

A PARTRIDGE IN A PEAR TREE

### \$209.99

(-2.3%)

This gift’s price decline from last year is fully due to the Partridge which fell 20% from \$25 to \$20, due to oversupply of game birds. The Pear Tree will set you back \$189.99 – the same as last year.

TWO TURTLE DOVES

### \$375.00

(+29.3%)

Supply couldn’t seem to keep up with the demand this year for these popular lovebirds! This gift experienced the biggest spike in price from last year, compared to the rest of the gifts.

THREE FRENCH HENS

### \$181.50

It’s been a quiet year for the French Hens. There was no change in their price, due to steady supply and demand in the past year.

… and so on and so forth. Head over to the article to see the rest of the gifts (including the most expensive item by far).

# What – or who – sets these prices?

There are many factors that explain why the cost of a partridge went down from \$25 in 2015 to \$20 in 2016 (even though the overall cost rose about \$232).  Here are some economic terms to know:

• Deflation: Refers to a widespread decline in prices that also has the potential to undermine the economy by stifling production and increasing unemployment.
• HyperInflation: Occurs when prices rise by 100% or more annually. It can destroy economic stability and even political stability by driving the price of necessities higher than people can afford.
• Index: Is a statistical measure of the changes in a portfolio of stocks representing a portion of the overall market. It is a sample meant to represent the performance of the whole.
• Inflation: A persistent increase in prices, often triggered when demand for goods is greater than the available supply or when unemployment is low and workers can command higher salaries. The US Federal Reserve Bank and central banks in other nations try to keep inflation in check by decreasing the money supply, making it more difficult to borrow and thus slowing expansion.

We still haven’t mentioned one thing… the fact that you’d actually end up buying the same gifts every day for 12 days means that your total ends up being a lot more than \$34,000… check out this video to see what I mean:

Therefore, the index refers to the cost of all the items as they are, while the “true cost of Christmas” refers to each item x 12 for every compounding day of Christmas. When applying this math to each of this year’s items, you get a grand total of \$156,507. That’s \$1,000 more than in 2015.

Basically, the holidays ain’t cheap if you want to walk the walk.

Trends over the past 30+ years that PNC has been calculating the index show us that the 80’s were a very different time. If you’re curious about the costs adjusted for inflation and wages when your parents were youngsters, head over to PNC.