Economics of Santa

Its that time of year. The emporium jingles of George and Mariah are resurrected — I’m reminded of this delightful essay I came across in middle school about the physics of Santa’s Christmas Eve undertaking. Been trying to dig it up on the web to no avail but did find something from the year 2000 where a Stanford researcher recreates a summary of the same essay — it seems he too was unable to find it again. Here’s the link.

He calculates that portly St. Nic carrying a “350,000 ton load traveling at 650 miles per second would subject him to the same forces as a spacecraft re-entering the earth’s atmosphere causing him and all his reindeer to be vaporized within 4.26 thousandths of a second.” I don’t remember much more from the original piece which was more detailed except in the end it said, “If Santa ever existed, he’s dead now.” Ha ha.

This got me thinking — Santa may have his work cut out with the laws of physics, but he’s still got to fund the whole operation. Since ‘tis the season, why not take a crack at how that might work.

Market Sizing

We’re going to need to update some of the demographic assumptions from 20 years ago. So 31.5% of everyone on earth is Christian. A further 16.3% are deemed “unaffiliated” with any religion according to the PEW Research Center. Let’s say around the same proportion of these heathens live where Christmas is a thing. That gives us around 36.6% of the world that presumably celebrates the Christmas holiday.

Now it’s likely the demographic age structure varies from religion to religion but for our purposes, this fun little feasibility need not get too meticulous. We are going to assume that Santa’s addressable age bracket is between 2 and 8. Translation — everyone born from 2014 to 2020.

140 million babies are born annually at prevailing fertility trends of around 18 live births per 1000 people according to UN estimates. Some die — the Unicef’s U5MR — or mortality rate for kids aged five or below per 1000 live births stands at 37. To simplify lets apply that rate across our age bracket. That’s 840 million kids; about 809 million that survive. Santa’s got a monster market of around 296 million odd Christian / Heathens (lets call them Cretins) aged 2–8.

But, Santa ain’t Karl Marx and the naughty or nice list dictates rations here. This is a tough one to estimate so lets assume it entails kids with crack / booze / fentanyl etc. addled parents who have destroyed all the innocent whimsy of a happy childhood. Santa’s not showing up if you don’t believe in him. This is how the Matrix is designed.

Since all bad things are positively correlated to poverty, we can discount our market by 11% — or the US population living below $33K in annual household income. Below this level it becomes harder for mama and papa bear to lay off the pipe.

The number of households is fairly similar to the 108 million computed in the original paper. This is important as it dictates the number of stops Santa has to make.

This gives us a grand total of around 263 million little Cretins who will be expecting Santa to come up with the goods when they go to bed tonight. That’s roughly around the same number of people that have a Visa card in their wallet. Big market — Santa’s in for a windfall.

Production

Except, these little freeloading bastards aren’t paying Santa shit. But he still has to produce and deliver 263 million toy units between the 24th and 25th of December. That is a LOT of toys. To put it in perspective that’s about the number of Monopoly board game sets EVER sold.

Only one company comes close as a benchmark — LEGO. The world’s largest toy company that sells roughly 220 million Lego sets every year. This too represents just about the right price point. Santa certainly isn’t, or shouldn’t be doling out 263 million iPhones this Christmas.

So, lets begin estimating how much it would cost to replicate Lego’s production. We don’t have to go very far for this. Despite being a private entity Lego is kind enough to publish its audited financials.

The figures are in DKK or Danish Krone the FX conversion for which is around 7 DKK / USD. Now we should be clear about what Santa actually has to pay for.

Raw materials / consumables. Check.

Licensing fees — potentially. Doubt the villainous corporate overlords in charge of producing Barbies and Silly Putty will forgo a piece of Santa’s operation if they could. But how would they enforce it? Surely dragging Santa into arbitration would be the worst PR disaster in history. Santa gets a pass on this one.

Labor — Now I’m not exactly sure as to the going market wage for Leprechauns. Wait, what are they? Hobbits? Smurfs? Vietnamese kids? Helpers but… just “helpers?” Who live on the North Pole. So, what are they going to do with money right? Most of the year they’ll ice-fish and play hopscotch in the arctic tundra. Food and entertainment sorted. Bunk at the toy factory. So lets say they’re free. Excellent.

Depreciation — Santa may never age. But his setup will. He’s going to need to account for upkeep to shell out toys in perpetuity. But lets adjust out about US$ 10 million in impairment of intangibles.

CAPEX — Assuming the population keeps growing it makes sense he’d need to pay for upgrades to the production facilities. Lego spent about $440 million on new PP&E last year.

A production facility at the north pole would certainly need lots of heating. But to keep it simple lets say he has an energy efficient system included in the overall fixed assets on Lego’s balance sheet. At some point Santa would have ponied up $2.4 billion (adjusted from Lego’s fixed assets) to pay for the production facility. But that’s just a drop in the bucket as we will soon see.

Santa need not indulge in any sales & marketing activities. Nor R&D. We will keep operating costs at zilch considering we will cover the cost of distribution in detail later. He’s got no bank borrowings nor is he liable for taxes. He may need a communications department to handle correspondence with 263 million little whippersnappers. But that just entails some IT infrastructure run by some of his slaves… sorry — helpers.

SO — the above mentioned costs are estimated at US$ 1.846 billion in the context of producing 220 million Lego so if we do a quick unit adjustment for 263,497,601 units on Santa’s docket, the production cost for this year stands at around US$ 2.2 billion.

Now lets figure out how he’s going to get them down all those chimneys.

Logistics & Transport

We estimated around 105 million households — kids are bundled into homes which on average hold 2.5 each in 2022.

Time zones give him 24 hours + however much time kids in the age bracket need to sleep which is apparently 10–12 hours. Let’s say kids are on average asleep by 9pm and awake by 9am. Providing for some wiggle room either side, Santa has 34 hours to pull this off.

We are assuming Santa is not climbing down any chimneys, not stopping for cookies; he just has a super efficient mechanism where presents are whipped out of his sack into any available orifice in every home. This endless void of a sack incidentally, weighs 131,500 tons. (1 pound per present).

There are a couple of ways to approach the distance to be covered:

1. Use the 75.5 million miles estimated by the original article as a function of number of households spread evenly across the earth. Adjust this distance to account for land area (21%) instead of total planet area. Giving us 21.9 million miles.
2. Use the 87,832.4 miles calculated by a Wolfram Mathematica geo-computation to estimate the shortest path through all the world’s capital cities. Adjust this distance for a multiple of cities assuming an average of 2 million households per major city (source: WCCF). Which gives us 4.611 million miles.

Source: Wolfram Mathematica

We’re going to need some flexibility going forward so lets keep both options on the table for now. Now we estimate the speed at which he needs to be travelling. If we revisit our 2 estimates of distance in light of his 34 hour window we get the following:

For context:

• Speed of sound: 767 mph
• Lockheed SR-71 Blackbird: 2,200 mph
• 1% of the speed of light: 7 million mph

The fastest vehicle on earth would not cut the mustard. And even at that speed the G-force would turn Santa’s cheeks the color of his beard as blood pooled into his boots. But lets disregard all that — Santa’s veins run thick with eggnog and gravity and physics and all that nonsense doesn’t apply to him.

Those speeds are achievable for Santa and he’s got a NASA Heat Shield that costs around $50 million to keep Rudolph and co from turning into charred venison. But how much is it going to cost to get him to speed.

Fuel

Where oh where is Santa going to generate all that thrust? The Sleigh? The Reindeer? Some external force? Let’s consider all three:

1. Shrunken Hadron Collider

• Since the required speeds in every scenario are under the cosmic limit of 67 million mph, a speed to which the Large Hadron Collider can propel matter. We must adapt the 27 km ring that took 10 years to build, so that it putters Santa along smoothly. If only we could shrink it and put it on the back of his sleigh…
• Lets say Santa’s sleigh is a souped-up 50-foot beast of a thing. Lets say he can even handle a 100-foot Hadron Collider engine attached to the back. Theoretically you could use a reverse of Moore’s Law to denote a doubling in cost when the size is halved. The LHC cost $10 billion. So if we shrink it to a hundred feet that’s… a geometric sequence of 10 doublings resulting in $10.2 trillion which isn’t really a reasonable amount of money even for Santa.

2. Jet Fuel

• Let’s just assume Santa’s Sleigh is the Millennium Falcon incarnate and all it needs is regular Jet-A Fuel (Kerosene). We’re going to assume the fuel efficiency of a Boeing 747 which can transport 455 tons of cargo while burning 3,600 gallons of Jet Fuel per hour. Or, 5 gallons of fuel per mile. We are going to entirely ignore the effect that an increase in speed has on fuel consumption.
• So when we adapt this to Santa’s itinerary — i.e. a cargo load of 131,500 tons travelling a distance of [either 22 million or 4.6 million miles] over a period of 34 hours — Jet Fuel at current prices will cost anywhere from $1 trillion to $215 billion — lets go with the cheaper estimate to give this feasibility a fighting chance.
• Unfortunately that doesn’t quite take into account the extra 226 million tons of fuel to carry which dwarfs the original cargo and pushes the fuel cost to $ hundreds of trillions. We’ve gone backward.

3. The Reindeer

• Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, Blitzen, and Rudolph would need roughly 800,000 additional friends to lug around a load of 131,500 tons at a regular clip. Reindeer can cost anywhere from $1000 to $3000 so for these special flying species we’ll put up a premium and say $5000. That’s $4 billion to buy reindeer every decade or so — doable! BUT, we need to supercharge these suckers and once again fuel is going to be a drain on Santa’s coffers.
• Reindeer can typically run for around 50 mph for about an hour — impressive! They can achieve this on a diet of around 15–25 pounds of vegetation every day — shrubs leaves, herbs, grass, moss etc. But we found some reindeer feed online for $10 per 25 pound bag. That should do. Some quick (and faulty) math tells us that to soup up 800,000 reindeer to run at 135,618 mph for 34 hours you would need to feed each one 2.3 million pounds of feed. In which case Christmas morning may bring a fresh coat of snow and caribou crap.
• The cost to fuel all 800,000 supercharged reindeer for the trip — $738 billion. The most reasonable figure so far.

Right — to sum up:

• Santa needs $2.2 billion to produce 263 million units of toys.
• Another $50 million for a new heat shield every year (the sleigh is an indestructible family heirloom)
• $4 billion to buy new reindeer every decade — $400 million a year.
• And a mere $738 billion to power the deliveries.

A grand total of $740.65 billion in annual operating costs.

That is roughly the size of Abu Dhabi’s sovereign wealth fund (ADIA). It is also about twice the annual fiscal expenditure of India.

But, since Santa doesn’t earn anything, this has to be funded by an existing pool of capital. Which — by any estimate — should make it the single largest pool of capital ever known. So, how much dough does Santa need to have in order to service 3/4 of a $ trillion in annual liabilities?

Well, firstly — he can’t exactly keep those shekels in risk assets. What happens in a down market? Christmas is downsized? The route is cut in half? The naughty or nice criteria becomes very stringent? Well lets assume he takes that risk and the cash is in the S&P 500. In 2021 the total return was 27% but lets set it to a more expected bull-cycle annual level of 15%. This would entail Santa’s holding about $5 trillion in stocks and ETFs.

That’s crazy. He could secretly be Blackrock’s biggest client accounting for a third of their assets. The far more likely scenario is — being the guardian of Christmas — he’s probably a little more risk averse. Say his cash is in 30-year Treasury Bonds and he eats the 4% coupon to fund operations every year. This would entail Santa’s holding about $18.5 trillion in Govt bonds. Making Santa the largest debt holder of the United States — holding about 2/3 the entire bag, and twice as much as the Fed itself.

However you slice it, Santa’s got some serious cash money..

Ho Ho Ho!