On Patreon, we ask supporters to occasionally toss questions over to us that they want answered that are a little bit harder to get an answer to than something you might ask on Quora. For this, the introductory piece in our new series You Asked, we’re tackling an economic question.
This is the best question ever, though, and so this might be the last installment in this series.
In Roald Dahl’s book Charlie and the Chocolate Factory, the titular Charlie Bucket gets a tour of the secretive Willy Wonka’s chocolate factory because he finds one of five “golden tickets” hidden inside his signature Wonka Bars.
Spoiler warning: Spoilers for Charlie and the Chocolate Factory, a fifty-year old book for which there are countless film and television adaptations, follow.
Why does Wonka do the “golden ticket” scheme?
Dahl was inspired by the rivalry between the two predominant British chocolate makers, Cadbury and Rowntree’s. Both would routinely send spies to each other’s factories disguised as new employees and eventually began implementing strict rules to keep that kind of thing from impacting their own businesses. This secrecy became the basis for Willy Wonka, who closes his chocolate factory to the public to prevent industrial espionage.
The premise of the book, revealed at the end, is that Wonka is looking for someone to inherit his factory as he has, presumably, no heirs nor shareholders. To become his heir, you need a goodness of heart and not a degree in business.
But is Wonka himself a good businessman? Is it possible that the “golden ticket” scheme is more about raising some dough than it is about finding an heir?
Veruca Salt, one of the winners of the contest, is known to have obtained her ticket through brute force probability: her father purchased thousands of Wonka Bars, at a cost of fifty pence apiece, and had employees at his factory unwrapped them until they found a golden ticket.
Today, around 350 million Cadbury Dairy Milk bars are sold annually. We’re led to believe that Wonka is a pre-eminent brand, so if they sold roughly the same number of bars, and the duration of the contest is about six months, the chance of winning the contest is 5:170,000,000.
Why do we think the contest runs six months? Violet Beauregarde has chewed the same piece of gum for at least three months and began chewing it after finding her ticket. Most business things occur in quarters, which are three months long, conveniently – indicating that Violet began her search at least a full quarter before the tour. The likely explanation is that the contest is two quarters long.
The Five Winners
If Veruca Salt has normal probability, her father needs to purchase one-fifth of the chocolate bars – 35 million of them – in order to be sure that he’ll find a winning ticket. In 2020 dollars, that’s around $92.7 million. Presumably, Mr. Salt stops opening the bars once he finds a winning ticket, which doesn’t necessarily have to occur at bar #35,000,000; he can resell the remaining bars to recoup some of his costs, but Wonka likely makes a tidy profit; even if his wholesale price is half the retail price, Mr. Salt has to purchase $46.4 million in chocolate bars.
Veruca is the only one to obtain her ticket in this manner. Augustus Gloop, a gluttonous child, eats several candy bars a day. The current world record for most chocolate bars eaten in one minute is three; let’s assume, in the world of Charlie and the Chocolate Factory, that record is held by Augustus and represents his hourly chocolate intake. Assuming Augustus sleeps for the recommended seven hours, he consumes fifty-one chocolate bars in his seventeen waking hours. We don’t know how many days pass between the contest announcement and Gloop finding the ticket (assuming, again, that the contest was held in 1971 and that he found his ticket in chocolate bar 35,000,000, it would be sometime in the year 3851 when he found it), but we know that Gloop is the first person to find a ticket. If Gloop finds his ticket in his last chocolate bar of the first week of the contest, he’s eaten 357 bars, or $929 worth.
Violet Beauregarde finds her ticket when she briefly switches from gum to chocolate. We know that she finds her ticket three months prior to the tour. Beauregarde is an obsessive and it’s reasonable to assume she ate chocolate bars nonstop while looking for the ticket, which had to have taken at least slightly longer than Gloop. For… health reasons, we’ll call Gloop’s three-bar-per-hour habit “nonstop.” It takes her a full three months to find a ticket, clocking it at a stunning $12,077.
Mike Teavee never reveals how he got his ticket in the book, but in the 2005 film it’s said that he developed an algorithm to find the ticket, the kind of thing you might write as an explanation if you don’t know how algorithms work. In the film – which, I should mention, I haven’t seen, so I’m relying on this old Reddit thread for the basics – Teavee uses the manufacturing date and then some information that would be meaningless. The most likely explanation, if we’re taking this seriously, is that Teavee uses industrial espionage and claims the algorithm as cover. An employee smuggles a winning bar to Teavee, who then spends $2 to purchase a bar at a local retailer and claims this is the winning bar.
The same goes for Charlie – well, not the industrial espionage bit, but that he buys a single bar.
Total Cost for the Winners: $46,413,010
The Countless Losers
We used a baseline assumption that the number of bars produced during the contest duration was 175 million. Currently, around 31% of food is thrown out at the retail and consumer levels uneaten. If 31% of Wonka bars are regularly thrown out at the retail level, some 54.25 million bars would go uneaten during the contest period, a loss for the Wonka company of around $141,252,000.
During its annual Monopoly event, McDonald’s sees same-store sales increases of 5.5%. That same increase for Wonka’s prize would mean the number of eaten bars would drop to 47.6 million bars. That’s 6.65 million extra chocolate bar sales, worth $17.3 million in 2020 dollars.
Without knowing what happens to the Salts’ bars, it’s hard to know what impact they had on the global Wonka market. The Salts are wealthy, though, so maybe they just throw them away. If so, their $46.4 million investment is in addition to the regular sales, which would mean that Wonka sales increased by $63.7 million.
The 1971 average U.K. wage is £28 per week, or $519 in 2020 U.S. dollars. This is probably what Wonka pays, since he imports foreign laborers for anti-espionage reasons and not cheap labor reasons. There are 165 Oompa Loopmas in the 2005 film, for an annual payroll of $4.45 million. Increasing sales by $63.7 million probably had a big impact on Wonka’s bottom line even if he had to double the number of Oompa Loompas on the payroll.
Well, that’s that. Wonka’s search to find an heir likely generated over sixty million dollars for his chocolate business. Wonka’s chosen heir, Charlie is like eleven and definitely not old enough to inherit a chocolate factory, which really raises doubts that the whole point was to find an heir and not just a one-time boost to sales.