Imagine a world in which we could take care of our friends’ kids when they need to pop out, because our friends live a stone’s throw away. A world where any time you wanted to head out for a quick drink there would be a friend within ten minutes’ walk to go with. A world where you can easily get a pal over to set up a barbecue, or where you can play board games or have supper with friends on the slightest whim. Why don’t we live in that world already?

I live in London, a pretty large city. When I want to see my friends I often have to travel 45 minutes or an hour across town to do so. This level of latency is pretty annoying. Imagine how many Friends plotlines would have been broken if they hadn’t always been agglomerating across the hall from one another or in Central Perk.

Acquaintances who come from or live in smaller settlements will say something like ‘the benefit of living in a small city is that your friends live close by. If you want to have a pint with someone, you need only walk ten or fifteen minutes and you can do so.’ Obviously, as a matter of pure fact, this is true. But the scales have been artificially weighted: the person in the small city must choose from a much smaller pool – the pool of people living within fifteen minutes’ walk!

This would also be true if we demolished all of the neighbourhoods of London except the ones near the one I live in now. I would have either to choose to have no friends at all, or make friends with those people within a short walk of me. I could achieve the small town ideal just by refusing to be friends with anyone who lives further away.

Think how some complain that they could find no one like them in a small settlement, and had to move to the big city. By living in a smaller settlement you are constraining your friendship choices in a way that is likely to be imperfect, unless it is some sort of intentional cluster of people like you.

The small town question did get me thinking, though. Why don’t my friends and I live closer to one another? I think I have come up with a highly abstract and simple model that explains it. Basically it’s all about externalities.

When you choose where to live in a city, you choose based on a list of priorities. For me, it’s proximity to job, safe and pretty neighbourhood with good amenities, proximity to family, and proximity to friends. Imagine there was a cluster of your friends – everyone lived in Brixton, say. Then imagine your job was in Shoreditch and your parents were in Greenwich. Your ideal point would not be Brixton, but a midpoint of your parents in Greenwich, job in Shoreditch, and friends in Brixton, perhaps London Bridge or Bermondsey.

If everyone decides like you, then the cluster peels apart as quickly as it got together. The positive externalities that would be created if your entire group of friends lived in the same place – childcare, pub visits, evening activities, meetups on a whim – all disappear because there is no institution or incentive to compensate people for choosing a slightly suboptimal location for themselves that benefits everyone overall.

This is what I seem to experience in the real world: almost no clustering of friends at all, despite everyone regularly bemoaning and lamenting how difficult it is to do things on short notice.

From experience, people my parents’ age tend to have totally new sets of friends from their youthful schoolmates, university pals, or old work colleagues, largely based around their childrens’ schools and local areas. After all, friendship is very substantially an in-person thing.

Of course, this is made worse by the difficulty of the housing market. If property was a quarter of the cost then people could afford to leave flats empty for four months and move towards each other, or blunt some of the force of location, location, location.

But even if we had a housing market with no scarcity at all and we were all much richer I expect this situation would still obtain, because of the uncompensated positive externality you generate for your friendship group, an externality that I can’t see any institution for accounting for.

It would seem weird for your friends to pressure you to live closer to them – something that would help solve the problem – and it would be even weirder for them to pay you to do so.

Even if we didn’t feel this awkwardness it would also open the situation up to free riders, because the positive externalities are distributed widely. So it’s probably not worth enough to me to pay the full amount necessary to get Sam to move to me. Between me and ten of Sam’s other friends it would be worth it, but I would have to get them all to move before it would be worth it to them to pay him. It only works if we all do it at the same time.

So what can we do? Is there anywhere around the world or anywhen in history that solves this problem?

P.S. Check out the new issue of Works in Progress.