Optimal Treating

Warning: Don't Read This Post! It's too scary...
...because it's so pointless and long...
So if you're too afraid to enter the "House of Long, Boring Post-Horrors," just read the conclusion at the end.

The phrase "Trick or treat" has been said so many times by so many kids that the once obvious threat has become just an arbitrary bundling of syllables. It's interesting to think that if we take an offensive or even threatening sentence and make a bunch of children say it, suddenly it's cute.

Imagine if millions of children around the country were going door to door saying, "I'll cover your house with toilet paper if you don't give me some amount of money between 5 cents and a dollar!" While it's the same thing as "trick or treat," I think people would be put off by knowing specifics.

So sure it's cute to see kids repeating the same phrase, dressed up as invented creatures, unoriginal as they are, but should we really be rewarding children for hiding their faces, coming to our houses and threatening us?

Trick-or-treating is clearly akin to robbery. While so many other bastions of childhood, such as toy guns, chewing-gum cigarettes, games of Cowboys & Indians, playing in the street and riding a bike without a helmet have all been replaced with "better," more concerned-parent-friendly alternatives, trick-or-treating somehow has slipped through the cracks. At the very least, the phrase "Trick or treat," could have been replaced with "Please, dear neighbor, may I have some candy?" But no - parents have destroyed countless other traditions based on safety concerns or political correctness, but trick-or-treating lives on. How did this happen? How does a traditional Halloween survive when engaging in socially unhealthy behavior is a gigantic no-no for the children of today's overly-coddling parents?

Not only does it survive, but it's more popular than ever. We're spending more than $5 billion on Halloween this year, and it's been growing at a rapid pace over the past few years:


So why is this? I think it's because people are convinced that trick-or-treating IS socially healthy behavior. And it kinda seems like it, doesn't it? I mean, it's a lot like working a real job: You have to leave your house and meet up with your associates, and you travel around your assigned territory trying to convince people to pay you for some hard-to-measure amount of labor. Only in this case the particular labor involved is dressing up, ringing a doorbell and asking for candy.

And even considering that, you get a pretty low return on your investment.

As much as we enjoy dressing up and running around the neighborhood with our friends, the monetary costs - taken by themselves - of trick-or-treating are pretty significant compared to the benefits. How significant, you ask?

Thanks for asking. Here we go:

A kid needs, usually, a mask and a corresponding costume. I had to look this up, but it appears that the average mask costs about $20 to $50 dollars (so average at $35), and the rest of the costume ranges, apparently, from $14 to more than $100. I'm sure a lot of people make their own costumes, though, but the minimum cost has to be at least $10 (the price of ruining a white sheet plus candy bucket). The maximum cost can run in the hundreds.

Based on these costs alone, it seems that the average kid would have to get at least $14 to $80 worth of candy in order to recoup his parents' monetary investment. Let's further assume that it's possible for a kid to 'hit' one house every three minutes for the three hours between 6:30 PM and 9:30 PM - which is really pushing it, if you ask me...

So that's 60 houses. If we take the average of the two figures above ($14 & $80), we get around 47 bucks. This means that the kid has to get about $0.80 worth of candy from each house in order to justify the investment. Considering 60 houses is a lot to visit in one night, I'd say it's damn near impossible to come out ahead if you play the averages...


So how do you come out ahead?

Well, what we're going to figure out now is how much you, the treat-giver, should spend on Halloween candy to give out to the trick-or-treaters, and how much you should spend on a Halloween costume for your kid in order to maximize both your return-on-costume investment, your return-on-candy investment and also the value you get from your community participating in Halloween traditions.

Here are some assumptions with which you cannot disagree:

1. You appreciate Halloween and its traditioniness and are willing to pay some cost for its continuation.

2. You want to minimize the above cost, as well as all other costs associated (costume & candy costs).

3. You want to maximize your kid's happiness: This includes wanting your kid to be creative and have learning experiences, but also to receive a maximum take of Halloween candy from the neighbors.

4. This one's important: The work and/or money that the AVERAGE kids put into their costumes is directly correlated with the amount and quality of the candy they receive. This means that if all the kids just start throwing sheets over their heads and going door-to-door, the neighbors will start giving away 2-cent candies instead of more tasty, and more expensive, chocolate.

5. The cost of candy determines its tastiness and therefore its popularity with the trick-or-treaters. But equally as important: kids aren't that picky about free candy...

6. People's current choices are not currently surplus-maximizing, but they would prefer them to be. (We have to assume this so I have something to write a post about...)

OK - are we all clear on the assumptions?

Now to find the optimal amount of money to spend on treats, as well as the optimal amount to spend on a costume. We'll tackle this problem by testing the extremes:

Let's pretend everyone chooses to minimize all their costs. This means throwing a sheet over the kids' heads, providing a paper sack for the treats and kicking 'em out the door. With such careless and unconcerned investment, how do the neighbors respond? If every kid that came to your door was some sort of cheap ghost, would you continue to hand out expensive candy? Of course not, but you also don't want trick-or-treaters to stop coming altogether, so you'll hand out the cheapest candy you can find just for symbolic value, which is, of course, $0.01-per-piece candy. (It's got to exist somewhere...) So, if you spend $2.00 on the paper bag and the sheet for your kid's costume, you're pretty much guaranteeing a failed trick-or-treat experience, not because you individually are minimizing costs, but because everyone is acting like you and minimizing their costs as well.

But there's a value of Halloween and its traditions (assumption #1). Consumers are willing to pay to make sure the holiday doesn't suffer. So in this crazy imaginary world where everyone is minimizing their costs, is there an incentive to spend more on your kid's costume and/or trick-or-treaters' candy?

F-yeah there is.

If all the kids are cheap ghosts, and all the neighbors are giving out cheap candy, there is disproportionately large value in handily beating the neighbors in your candy offering, and having your kid be the "talk of the town" with his slightly-better-than-cheap-ghost costume. So for spending a few extra dollars, your house will become Halloween-central and your kids will be incredibly popular.

So clearly cost-minimization is not a stable equilibrium, as everyone has an incentive to "cheat" and start competing with each other. This is obvious, of course, since if people suddenly didn't want to compete, we'd be spending less money on Halloween each year instead of more...

But how much will people compete with each other?

Well, the value of that first extra dollar is clearly substantial. If all the other kids have $1.00 outfits but yours has a $2.00 outfit, your kid is - by definition - twice as awesome.

At the end of the spectrum, though, the marginal value of an extra dollar should be zero. And at what price is this the case? It's different for every person, of course, but I think we can generalize: If all the kids have $100 costumes, is there any incentive (in terms of optimization) to spend $101? What about if all the kids have $25 outfits, but your kid's cost $26 - is that a substantial enough difference?

No. First off, homeowners on Halloween most likely suffer from a free rider problem. Essentially, if five amazingly intricately-designed and scary looking zombies and ONE crappy ghost comes to your door, you'll give them all the same quality and amount of candy - the ghost that spent $5 on his costume "rides for free" off the zombies that spent $50. If you disagree with the fact that you'd give them all equal shares, you're a bastard. I'm assuming people aren't bastards... (Also, don't forget assumption #4: that kids' costume expenditure is directly proportional to the candy they receive as a group, but not as an individual...)

So this means that parents are faced with a trade-off: They can maximize their kid's candy to costume-cost ratio, OR they can maximize their Halloween tradition value. If parents choose the cheap & lazy costume route, they'll reduce their own (and their neighbor's) payoff and pleasure from Halloween. If they put too much emphasis on that Halloween payoff, though, they'll more likely over-spend and minimize their joy from profit maximization. (This is assumption #2 - And don't tell me maximizing profit is not awesome...)

The answer to this trade-off problem would normally depend on a world of opinions, but not in a world where the cost of candy can be used to determine the answer: That's right - there's a constant in this problem that helps determine optimal amount to spend on your kid's costume (and subsequently on Halloween candy.)

Remember that one of my assumptions was that it's possible, at most, to trick-or-treat at 60 houses in one night. Also, we've all learned from experience that it's not necessary to spend $0.80 per trick-or-treater when you're giving out candy, right? In fact, kids will come to your door (year after year) if you give out candy that's just slightly better than crap. It turns out that kids prefer quality, but they will be return because they don't dislike your candy offering. So here's the biggest assumption of all: Smarties cost about 6.5 cents per "roll" (piece). In a competitive world, we could conclude that beating this cost by just a little would be enough to satisfy kids and keep 'em coming back every year.

So let's round up to $0.10 per trick-or-treater and assume it's definitely more than enough to keep kids coming back (based on the fact that even Smarties are pretty tasty, and you're beating that cost by at least 50%).

At 60 houses, this adds up to about $6.00 worth of candy for a hard working trick-or-treater. Now here's the problem: You can't get a good costume / candy bucket for less than $6.00, now can you? If you tried - and if everyone else tried, too - we'd reduce the value of Halloween to the point where only the kids would want to participate; parents would face substantial costs by themselves, while everyone else gets the benefits. In other words, we'd have a long-term equilibrium with parents subsidizing the majority of Halloween costs while non-parents pay just a few dollars for candy.

Since Halloween can't survive solely on parent subsidies (neighborhood participation & incentives are required), the community value of Halloween must therefore include non-parents spending at least an amount above and beyond the $6.00 that - when multiplied by about 60 - comes close to equaling (but not necessarily as much as) the amount that parents spend on their kids' costumes.

So we're essentially faced with a simultaneous move game - non-parents have to make candy expenditure decisions at the same time that parents make costume expenditure decisions (and candy decisions...) without each other knowing what the others' choices are.

Acceptable costumes cost, at a minimum, about $14 (according to my sources). So we can plug this and the other numbers into the general formula to figure out the answer:


[Cost Per Piece of Cheapest Acceptable Candy] < [Non-Parent Per-Piece Candy Expenditure] < ([Minimum Acceptable Costume Cost] - [Cost Per Piece of Cheapest Acceptable Candy] * [# of Houses 'hittable' in One Night]) / [# of Houses 'hittable' in One Night]


So with our values plugged in:

$0.10 < [Non-Parent Per-Piece Candy Expenditure] < [$14 - ($0.10 * 60)] / 60 And simplifying:

$0.10 < [Non-Parent Per-Piece Candy Expenditure] < $0.133


So we end up with our optimal answer for the non-parent: In order to both minimize your monetary costs and maximize your Halloweeny benefit, you must pay some part of the Halloween kid-costume-subsidy. To make the value per piece a little easier, we'll assume it's a whole cent value greater than 10 but no more than 13, which leaves $0.11, $0.12 or $0.13 per piece of candy you give away. I'd argue, though, that it's not really necessary to subsidize the parents too much, so $0.13 is probably out of the picture. That leaves 11 or 12 cents per piece. In other words, if you expect to get 100 trick-or-treaters, you should reasonably expect to spend about $11 to $12 on candy. If you normally get a trick-or-treater every minute for a full three hours (as I've seen before), this means Halloween should cost you no more than $22.


Parents, on the other hand, face both the costs of giving out candy to the kids on top of the cost of furnishing their own kids with a costume. Fortunately for people who are still reading this post, I'll just assume that these two costs are mentally separated in the minds of parents. If they weren't separated, though, the formula for non-parents' candy expenditure would depend on parents spending a different amount on candy, in order to keep the "Total cost of Halloween" concept in tact. Since I'm making the assumption of compartmentalization, though, parents should spend around $14 on each kid's costume and .11 (instead of the higher possibility - $0.12) per piece of candy.

So for a household with two kids that gets 100 trick-or-treaters, this would lead to a total Halloween cost of about $39.

(This time it's a picture of The Guz a few years ago trying to hit a piece of a pumpkin with a hammer...)

While I've covered everything from the diminishing marginal return on costume investment to the minimum acceptable price and quality of a piece of candy, I had to make a lot of assumptions that I didn't explain entirely. The way I see it, you can either trust me on these things or you can ask that I make this post twice as long as it already is... I think we all know the answer to that one...

Anyways, on to the
Conclusion

If every household in America has about 1.7 kids (quick Google search results), and there are about 120 million households (Census estimate), this means we should be should be spending about $4.2 billion on Halloween each year in total. If you look back at that graph, you'll see we started barely exceeding this number in 2006, meaning we OVERSHOT OPTIMALITY!!!

So what is the significance of that? Well, if we suddenly start assuming people will regress to some sort of "optimal mean," then Halloween spending (and subsequently celebration) is due for a decline. Of course, people are hardly rational and will hardly play the Halloween game optimally, so maybe we'll just keep getting more Halloweeny, more obsessed with decorations and candy and keep gaining weight every year during the quarter-long holiday season from October to January.

More importantly, though, is that as an individual household you can actually maximize your Halloween consumer surplus by taking my advice: Remember, $14 per kid on costumes and 11 to 12 cents per piece of candy should not only maximize your own personal Halloween surplus, but also maintain the value you get from the community being just as Halloweeny as you.