The marginal benefit of legs

Saving shelter dogs, limb by limb

Ever since I read a 2018 Forbes article about the “importance of humanizing your brand,” I’ve been worried you might not believe I’m a human. So just to be safe, I’m starting this piece by talking a bit about myself:

Hi. My name is Peter. I am definitely a real life, human man. I am full of bones. If you need proof, I have pictures. And I have arms, I can assure you of that. Big, fancy arms.

Here’s a few more facts about me, a human man:

• I have a tendency to sneeze with such force that I’m a bit worried I’m going to blow the teeth out of my mouth

• I recently learned the word “catachresis” and won’t stop trying to use it in a sentence

• I don’t take Viagra because I take nitrates for chest pain and this may cause an unsafe drop in blood pressure

• I love the band Frightened Rabbit

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Also my wife and I foster shelter dogs from time to time. We’ve probably had about a catachresis of those bad boys over the years.

I know what you’re thinking. “Woah. This guy is smart, funny, AND rescues dogs? Is this guy Jesus?”

Last I checked, Jesus didn’t foster dogs nor [sort of] know what the word “catachresis” meant. More of a middling carpenter who wasted his weekends arguing with the Pharisees, amiright? #NailedIt

“Don’t get crucified by shoddy craftsmanship” - Jesus Christ

To be fair, my wife is the dog rescuing evangelist—I’m just a guy who tripped into the wild world of animal rescue. My wife is my sweet, kindhearted better half—whereas I’m about as affable as an anal fissure.

But this post is not about my wife’s gentle nature or my throbbing fissures—it’s about dogs. Specifically, three-legged dogs.

Somewhat recently, a three-legged pup came up for adoption at our local animal shelter and something peculiar happened: people lost their g-d minds. Waves and waves of people were tripping over their bipedal selves trying to get their hands on this three-legged guy. The dog wasn’t a particularly desirable breed or a conventionally cute puppy—he just happened to have one less leg than what we’ve come to expect from these things.

And this made me wonder: what might be the marginal benefit of legs?

To answer this, let’s revisit our freshman year Econ 101 course:

In economics, marginal basically means additional. Economists believe that the average Joe Shmoe goes about his life trying to maximize his net benefit (which is the total benefit minus the opportunity cost). So an economist assumes Mr. Shmoe will go ahead with something if the marginal benefit exceeds or is equal to the marginal cost. Confused? Just consider the “an apple a day keeps the doctor away” proverb:

One apple a day? That’ll keep the doctor away. Two apples a day? You betcha. Five? I could see that, yes. Ten? That’s a realistic amount. Eleven apples? Perhaps. Fifteen? I could see that as a very real possibility.

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495,000 apples a day? I’m no doctor, but probably not. At some point, the marginal cost of consuming an additional apple is higher than the marginal benefit of consuming that additional apple.

Marginal benefit: the amount by which something increases the total benefit
Marginal cost: the, uhhh… opposite of marginal benefit

What the fuck does this have to do with a three-legged dog?

I’m getting there. Below is a chart showing the marginal benefit and marginal cost curves of dog legs: 

The point at which they intersect is where the net benefit is maximized. Let’s start with the marginal benefit curve. The marginal benefit of the first dog leg is massive—a zero-legged dog is basically a shitting potato with fur. As the number of legs increase, the total benefit increases (dogs have more mobility, a greater likelihood of getting adopted, less likely to be mistaken for a rock, etc.) but the marginal benefit decreases. The marginal benefit decreases a bit from one leg to two legs, two legs to three legs, and so on—and, at some point, an additional dog leg will yield no benefit at all. 

“And, at some point, an additional dog leg will yield no benefit at all” - The This is bullshit guy (and Paul Krugman, probably)

Now let’s consider the cost of dog legs: a roving dog can get into mischief, it can injure its leg, you’ll need to cut the dog’s nails at some point, etc. But unlike marginal benefit, the marginal cost of an additional dog leg increases over time (meaning the total cost increases). More legs means—among other things—more nails to cut, a greater possibility of injury, and an ever-increasing amount of nightmare fuel.

Economic theory says that three dog legs are Pareto-optimal.

This is all to say—three legs appears to be the sweet spot for shelter dogs. According to microeconomic theory, it’s the optimal amount of dog legs. With three legs, the dog can still walk normally. And it’s a novelty but not too much of a novelty. Three legs gives your dog a touch of uniqueness

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without greatly increasing the overall cost of dog ownership or inversely impacting the ability to walk (and hence: optimizing the adoptability of the dog). That’s my dissertation. Three legs: good. More or less legs: bad. I’m thinking about titling it: An Exploration in Pareto-Optimality on the Mechanism of the Animal Welfare System.

Now you might be thinking to yourself: What about leg location? What if the dog has three legs but they’re like, inside him somehow? And I hear you, I really do—but that’s not really the point I’m trying to make here.

So what do we do with this information? Hard to say. Nobody wants to be the guy who suggests we start ripping off shelter dog limbs—but I mean…

How much do you want a loving family, Bonnie?

Bonnie is actually up for adoption, by the way 😬

Dogs are cool. Just think about the dogs who get one of their legs amputated. They go to sleep with four legs, wake up with three legs, and just go about their lives—unsure if they ever actually had that fourth leg. What a way to live.

During my time in dog rescue, I’ve noticed that a lot of people crave a good adoption story. They think the dog they’re adopting needs a unique narrative that resonates with people. And they want the dog to “pick” them. They want some kind of bizarre we locked eyes and he mouthed, “I will love you for ever, whatever happens. Till I die and after I die, and when I find my way out of the land of the dead I'll drift about for ever, all my atoms, till I find you again...”

But that’s not really how it works.

So I guess the second part of my dissertation is just: give shelter dogs a chance. Let them open up. Dog shelters are insanely stressful. We expect these dogs to have non-stop positivity, as if they’re a guy explaining to you why getting fired from his dream job and having his entire family abducted by the Navarro Cartel is actually the best thing to ever happen to him. 

Bringing a shelter dog home and being disappointed when they struggle to immediately assimilate into your household is like going on a first date, stabbing the guy in the chest, and then complaining to your friends that he didn’t have a great sense of humor.

“I dunno, Beth, he just seemed really preoccupied with something.” - you, probably

There’s about 70 million stray dogs and cats in the United States. If each of you would just open up your homes to about… 233,000 of these poor creatures, the stray dog crisis could end. I know that seems like a staggering amount of dogs per subscriber—but that’s just the reality of having a really small email list.

What I’m ultimately getting at is that I don’t have many subscribers. I need more subscribers. Like, millions more.

So please. Share this post. Do it for the homeless pets. Be the change. 🙏🐶

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1. I also—oddly enough—take great pleasure in frightening actual rabbits.

2. See: Dwight’s survival food plan

3. From your perspective, since dogs aren’t sure how many legs they should or should not have.