My latest business venture, The Crumbs, has been getting some traction recently. I go to school at Dartmouth College, where students without a car have difficulties grabbing necessities. So I started a local delivery service in part because I want to help students have easy access to Walmart, CVS, and a number of fast food chains. (The main reason is to donate all proceeds to a local homeless shelter, where I've been a volunteer for many years.)

As much as I love running the business, this post is not about The Crumbs.

Instead, I want to write about Chicken McNuggets.

Three and a half weeks ago, when I added a fast food component to The Crumbs, I pulled the initial prices off an online compendium of fast food prices. When the Team went into our local McDonalds, the actual prices of Chicken McNuggets were as follows:

10pc - $6.40
20pc - $6.40
40pc - $11.51

In New Hampshire, McDonalds charges the exact same price for 10pc McNuggets and 20pc McNuggets.

Initially puzzled, I began to search for explanations.

There are countless explanations (20pcs is too much for some people, for instance) that almost work, but a good number of them are knocked down by asking "Why doesn't McDonalds just lower the price for the 10pcs McNuggets, or raise the price for 20pc McNuggets?"

The following are three, more elaborate, attempted explanations, pulling in everything from social psychology to behavioral economics.

Attempted Explanation #1: The Decoy Item

In Dan Ariely's Predictably Irrational, a fantastic book about behavioral economics, the Duke economics professor mentions a curious psychological trick used on subscriptions for The Economist. Readers were initially offered the following two choices:

Web Only: $59
Web and Print: $125

Of the customers that purchased subscriptions, 68% purchased web-only subscriptions, the more economical option.

Later on, The Economist added a puzzling third option:

Web Only: $59
Print Only: $125
Web and Print: $125

The "Print Only" option seemed to be a mistake. It offered a strictly inferior alternative to the comprehensive Web and Print option, at the exact same price.

Yet, with now 84% of customers purchasing the more expensive Web and Print subscription, the numbers proved that the newly added option was far from a mistake.

The point of the "Print Only" option was not so that people would actually buy it; rather, it served as a point of comparison for the "Web and Print" option and made it seem comparatively more attractive. With very little effort, the decoy option resulted in a nearly 50% increase in sales.

In light of Ariely's behavioral economics explanation, perhaps this is what McDonalds is trying to do:

10pc Nuggets: $6.40 (decoy)
20pc Nuggets: $6.40
40pc Nuggets: $11.51

There are noticeable differences to the original Ariely example that pose a challenge to this explanation, however. Instead of attracting buyers to the more expensive option, the decoy seems to attract people to the less expensive option. Along with other psychological pricing tricks, wouldn't that decrease profits?

So I kept searching for other plausible explanations.

Attempted Explanation #2: (Loss) Leading

A Quora post takes a stab at making sense of what's happening:

"A common marketing technique of many retailers, which includes all the fast food chains, is to offer a small group of desirable products at lower gross margins. These products are widely known as loss leaders. ... [Its] only purpose is to get you into the store, with the hopes that you will order other products, preferably the high margin ones which will help to offset the effect of the low margin loss leaders."

A Reddit thread echos a similar explanation.

Even if McDonalds makes little to no money selling you their 20pcs Nuggets at the same rate as 10pcs, you're in the store now. The high-sodium McNuggets combined with strongly flavored dips might encourage you to buy a drink or some fries, both of which are higher margin products.

Yet this too, doesn't make a lot of sense. Shouldn't McNuggets be a high margin product in and of itself? Burger King recently decided to sell 10pcs nuggets for $1.49, implying that the nuggets themselves don't cost that much to make. Perhaps it is a classic case of penetration pricing, but it just doesn't seem right that with huge economies of scale, McDonalds isn't making a good margin from their McNuggets.

Attempted Explanation #3: Paradox of Choice

The secret to our answer may lie in psychology professor Barry Schwartz's carefully researched phenomenon that having a large number of choices may inhibit our decisions to buy. When people take a long time to buy something through weighing options, their expectations are raised significantly, decreasing the chances of making a sale.

Perhaps offering only two real choices instead of three, and making the 20pcs look "resonably good enough", may lead consumers towards a quicker decision and thus quicker sale.

While the Paradox of Choice may be interesting, the rest of McDonalds seems to contradict the hypothesis. With the multitude of sizing, flavoring, and customizable options on the McDonalds Menu, it seems implausible that McDonalds has taken the Paradox into account at all; with so many other options, a meager reduction of overall choices by one would likely make no difference at all.

What do the actual numbers look like?

Unfortunately, because of McDonald's relative opacity surrounding their sales numbers, we can't tap into specific sales data to investigate possible explanations.

But wait! We can. With data from The Crumbs, and an underlying (though very questionable) assumption that our customers form a reasonable representation of McDonald's customers as a whole, we can.

Here's our numbers:

Whaaaaat?

Not only did people buy the 10pcs option, they bought it far more frequently than the 20pcs option, even though both cost the same.

So why is the supposed decoy the most popular option? After hours of research and endlessly staring at The Crumbs' extensive analytics effort, unfortunately I still have no clue.

Perhaps the real solution is a mix of the aforementioned explanations. Maybe the 40pcs Nuggets is an anchor item that isn't actually meant to be purchased, since it is too much for most people to finish. Coupled with the fact that the 20pcs Nuggets the clear logical choice, made more attractive by a decoy, that happens to lead people to the store for more high-margin items... well, maybe we have an explanation here.

Loose End #1: The McChicken Conundrum

I ran some calculations and it appears that the best option for obtaining chicken nuggets at McDonalds... isn't even with McNuggets.

With McChicken patties weighing 63 grams and having a better quality of chicken than McNuggets (a meat score of "C-" compared to "D-", according to Calorie Count), in nearly all 50 states it makes more economic sense to order the chicken equivalent in McChicken patties.

Even if you ask McDonalds to skip the buns, lettuce, and sauce, you're coming out substantially ahead. And if you don't, I guess you now have extra buns and lettuce on top of that. Sure, it's weird to break that chicken patty into nugget sized chunks, but remember to take that price out of your savings.

Loose End #2: There's a Theorem Named After Chicken McNuggets!?

To conclude this article on Chicken McNuggets, this is not the first time in my life when I've taken an interest to this topic. Back in high school when I was studying for the United States of America Mathematics Olympiad, I ran across an interesting looking math problem.

Back then, you could only order McNuggets in groups of 9 and 20. So the question was: What was the largest number of nuggets that you couldn't order?

It turns out, there's a general purpose method of solving problems like these. The Chicken McNuggets theorem states that you can replace 9 and 20 with any two coprime numbers a and b, and the solution to the question is defined by ab - a - b.

Therefore, the largest number of Chicken McNuggets that you can't buy is (20)(9) - 20 - 9, or 151 nuggets. Anything greater, and there exists a combination of 20pc and 9pc orders that has you covered.

So the next time you pull into a McDonalds, give Random Directions a shoutout. Say something to the tune of, "I'd like the equivalent of 151 McNuggets please, in the form of McChickens, and skip the bread and lettuce please!"

You're welcome.