An Economic Model of Loneliness and Being Extremely Online

Bo Burnham is a comedian and musician who, like so many of the artists I enjoy, produces art that I can only describe as extremely specific to him. His newest special on Netflix features a song, “Welcome to the Internet” (some NSFW lyrics), that I liked so much I thought it was worth writing as a formal model.

No, really. Hey, we all need a hobby.

The whole song is a meditation on the overwhelming nature of the internet and is, in my opinion, fantastic. I think if we zero in on two pieces of refrain in the lyrics, we can get some traction in what Burnham believes is the underlying problem, if not outright crisis, that resides within the internet and those that are “extremely online”:

First, the lure:

Could I interest you in everything?
All of the time?
A little bit of everything
All of the time

This is the value-add of the internet and why we can never, and will never, leave it behind willingly. This is also the “cognitive overload” hypothesis of why the internet is bad. Sure, for the infovores of the world there hasn’t been a bigger technological shift since the printing press, but there certainly exists the possibility that most human minds (if any) aren’t built to handle the deluge of information they are drowning in. That’s one theory, but I think that’s the kind of problem that isn’t actually a problem. Some will consume more of the internet, some will consume less, c’est la vie.

It’s in the second half of the refrain, however, that we see the actual problem.

Apathy’s a tragedy
And boredom is a crime
Anything and everything
All of the time

And therein lies the rub. You can’t opt out. But is that true? Well, that depends on who you are and how you live your best life i.e. how you optimize your utility function. So let’s do it. Let’s write down the utility function that lives inside the song. What we’re going to do is this- we’re going to lay out the simple components as natural language, then turn it into formal math, and then bring it back to natural language.

In our Burnhamian mode, people need two things: Private goods like food and shelter and Social Goods like friendship and camraderie. How much Utility you enjoy will always be increasing in both, but the optimal mix will depend on your constraints (wealth, time, accessible population) and the mathematical function determining how much Utility you get from a mix of Private and Social goods i.e. are they additive, multiplicative, or something else. Utility equal to zero is equivalent to death.

Let’s add one last layer of complexity. Let’s say that your Social goods are a function of two kinds of elements: Friends and Clubs. Friends are direct, one-to-one relationships. Clubs are large social groups. We will define and differentiate between the two as such: if you cease to be part of a friendship (whether between 2,3, or 5 people), then that friendship no longer exists in the same form. If you drop out of a club, on the other hand, that club will persist without you.

So what a person has to do is, within their constraints, try to optimize how much of their resources they invest in their Private goods, their Friends, and their Clubs.

The first line is our base model, the second is an expanded version with our two-input model of Social goods. The function we are using is called a Constant Elasticity of Substitution utility function. The key parameter, α, determines how Private and Social goods interact. If α=1, then they are what economists call perfect substitutes. All that matters is how much you have in total of the two inputs, and if you want you could specialize in just one of them. They are perfectly additive. If, on the other hand, α=-∞ (negative infinity), then they are perfect complements, like right and left shoes. There is no point in adding even one more unit of Private goods until you have another unit of Social goods to pair with it. In a sense, they are multiplicative, meaning if either value is zero, then your utility is zero. The value of α will tell us whether the best life requires more of a mix of Social and Private inputs (if they are more complementary), or simply the most of whatever is the easiest to come by (if they are good substitutes for each other).

We’ve nested in our Friends and Clubs production of Social goods as a CES function within the second equation, with a similar story, only here β will determine how much of a mix of Friends and Clubs we want, or whether we can specialize more in one over the other. In the third and last line of the model, we’ve reduced it down to the underlying questions that will tell our story represented by addition and multiplication signs:

Are Private and Social Goods complements (multiplicative) or substitutes (additive) when we internally produce utility? Are Friends and Clubs complements or substitutes when we internally produce our Social goods?

Assumption 1: α= -0.1 Private and Social goods are weak complements. What this means is that there are diminishing returns to Private and Social goods, you need some of both, but you can have less of one or the other and its fine. Let’s just assume wealthy people need other people in their lives to stay sane while, at the same time people with rich social lives and supportive communities still need food and shelter. You can specialize a bit more on one side, depending on what’s available, but you can’t live without at least some of both.

We’re all different in how we build our social lives and, in turn, how we internalize the internet in our lives. I think we can gain some insight into this process by working out the stories in this simple model through our second parameter, β. Let’s consider three broad types of people.

Person Type 1: Friends and Clubs are Strong Substitutes (high β)

These people are either relatively offline (e.g. they still use their phones as phones to make phone calls) or extremely online (e.g. they get a panic attack unless they have 80% battery and a charge pack on their person). These are the people who can become hyper-specialized in new clubs if they are extricated from prior social networks or club settings. This is why cults recruit people who move to new places where they don’t know anyone. This is how your diehard hippie socialist friend grew up to be a conservative evangelical after they moved to the Texas suburbs.

With regards to our original question, people who hyperspecialize in their club and club identity will be constantly contributing grist to the club’s identity: evidence of the necessity of the club and it’s mission, rage at non-members, disappointment in members who aren’t committed enough, and constant vigilance in the monitoring of everyone else’s commitment. They are in it, they are of it, and they are ready to purge.

Apathy’s a tragedy (You must care about everything the club cares about)
And boredom is a crime (All of your time must be allocated to the club)
Anything and everything
All of the time

Type 2: Friends and Clubs are strong complements (low β)

These are the people that I think Burnham’s song is targeted at, for whom he has the most sympathy, and with whom I suspect he would count himself. These are people for whom the internet is the most taxing, the most exhausting to navigate.

Type 2 folks want to have personal friendships and friend groups while still feeling a part of something bigger, whether it’s a community, a political movement, or spiritual affiliation. Type 2 people will have preferences towards one or more social identities manifested as clusters on the internet, but they don’t want to purge people who don’t share those preferences from their circle of friends. Type 2 folks are interested in civil rights and social justice, but they want to diversify their emotional and material resources across their personal relationships and private wellbeing as well.

The deluge of the internet, with its stark images, focus on extreme outcomes, battle cries, and public reputation mauling, are constantly admonishing and shaming Type 2’s. Type 2 people are tired. Perhaps most importantly, the pandemic has been especially hard on Type 2’s. While Type 1 club-specialists have thrived by focusing the totality of their efforts to the online arena, their voices have been tearing the Type 2 social-portfolio diversifiers to shreds.

Type 3: Friends and Clubs are weak complements (middle β)

Type 3 people are a lot like Type 2’s, but it is easier for them to compartmentalize the production of their social goods. Type 3 people are often in clubs, but they are rarely of clubs. They’re not joiners. Whether you’re looking at sacrifice-demanding religious cults or extremely-online political culture warriors, if the social associations of the world demand too much of Type 3 people, they are happy to half-ass their contribution or opt-out entirely. They might be on Twitter or Facebook, but they don’t need to reply to anyone. They might go to church on Sunday with the family, but if the minister tells them their sister is going to hell for their sexual preference, it’s just not that costly to stop going. For them clubs will always remain a luxury good, never a necessity.


To be clear this post is an exercise in building a toy model of something big and complex and important. It’s a gross abstraction and shouldn’t be taken too seriously. The process of formalizing your thinking on a social mechanism, however, is something that I think you should take very seriously. Formal models are useful because there is no hiding what your idea actually is. There’s no “sorry, you misread me” or reliance on obscure jargon. Formal models force you to clarify and reveal your thinking to everyone, including yourself. They can open up new avenues for explorations and even generate empirically testable predictions. Formal models have in many ways been the principal force behind economic imperialism in the social sciences. Not because the math is perfect or all encompassing or even correct. It’s because it’s all out there, ready to be judged and dissected and tested. That transparency makes it a useful.

I don’t know if my interpretation of Bo Burnham’s theory of the internet is correct or even necessarily what he intended it to be. But this is one way we can take it a step forward and see what we can actually learn from it. Which is pretty much all I want to do for the rest of my research life, on every topic, all of the time.

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