#3: The Intensive vs. the Extensive Margin
Using backwards induction to navigate awkward social situations
Hi everyone! I’m pausing the “How to Do the Math” series this week because I am (yet again) traveling.
I’m in an airport right now, on my way to spend three months in a place I have never been before. I know exactly one person here, I don’t speak the language, and I’m scared of being away from my family and friends for so long.
Me feeling a lot of feelings? A five hour layover with nothing else to contemplate? You know what that means: time to hyper-fixate on my finances!
Being in airports, the hellscape of forced spending, price discrimination1, and socioeconomic segmentation2, always gets me thinking about the primary framework I use when making a spending decision: the intensive vs. the extensive margin.
Definition: Intensive and Extensive Margin
In economics, the intensive and the extensive margin are the two ways in which a factor of production can be adjusted. In normal people terms, adjusting your spending on the intensive margin means you’re “inside” the spending already, and are now trying to decide how much to spend. The extensive margin has you “external” to the spending, deciding whether or not to spend at all.
Here at the airport, I’m trying soooooo hard to focus on the extensive margin: not buying anything at all. I can survive four hours in Charles De Gaulle without food, right? I wasn’t planning on spending, since the airline so generously gave me a potato salad at what felt like 3AM, and so my spending here in the airport should be a flat zero.
[two hours have passed]
Okay, okay. In between writing the paragraph above and this one, I gave up, and turned to the intensive margin: how much can I spend and what should I get? I decided to buy something to eat at the airport – but what? Paul and Starbucks each have a petit déjeuner for 15€. I could pay for a lounge with a buffet (75€). I could get a sandwich at Relay for 6.90€, or a different sandwich for 7.80€, or even an Onigiri for 3.90€, and also what is the conversion rate for euros to dollars again?
There are so many options. Given that I have no shortage of time and feelings I need to avoid, I naturally visited every shop and café in my terminal, weighed my hunger and my time and my seating options, and in the end went with… a croissant and an espresso for 3.60€.
My point is: It’s a lot harder to make an intensive margin decision than it is to make an extensive margin one. Had I kept on saying no, I’d be sitting still – a bit hungry, of course, but less annoyed. I also wish that, knowing I was going to say yes, I’d just like, budgeted out 15 euros or something to spend on whatever I want, saving myself the math of trying to somehow optimize the calorie-to-price ratio on two hours of Basic Economy sleep.
Application: Splitting the Check
I always enjoy Charlotte Cowles’ My Two Cents over at The Cut, but the column covers my least favorite financial advice topic a bit too frequently for my taste: splitting the bill and spending with your friends.3 I think something about the splitting-the-check issue tickles the advice columnist’s brain: it’s a social relationships issue more than a financial one, there isn’t an obvious solution, and it’s really fun to dunk on our richer friends for not being more generous or our poorer friends for taking advantage. It’s not often you get to combine FOMO, salary jealousy, and self-righteousness.
I’m not above that. Here’s my take!
For situations where the amount I will spend is uncertain but also will determine how happy I am afterwards, I use backwards induction to turn the tricky social situation into math. I ask myself two questions, in this order:
In the (financially) worst case scenario, how much will this outing cost me?
Given my answer to #1, do I want to go?
Question #1: The Intensive Margin
In the (financially) worst case scenario, how much will this outing cost me?
In the letters sent to the advice columnists above, the letter writers usually complain about chronic problems: a friend group who always wants to split the bill evenly, a friend whose wallet is always “missing,” a family where fighting over the bill is expected. That means the letter writers — and you — can probably kind of predict the outcome.
If I go out with my consultant friends, I know they will want to split the bill evenly. How much is an entreé, a glass of wine, and an appetizer? Someone probably has a Sapphire Reserve and will volunteer to cover the bill. What do I think is the most that person will Venmo request me after the fact?
If I go out with my extended family, I know I’ll be pulled into a fight-over-the-bill game. What is the most that dinner for my aunt, uncle, and cousins might plausibly cost?
If my friend wants to go to a spa for her birthday, we might split the cost of her bill betweetn the other four of us. What is 1.25 times the cost of a spa day?
If I go out with just one other friend, we’ll probably naturally order the same amount and split the bill evenly. What do I want to order? Will I feel an urge to treat her to the dinner? How much would that be?
The Math: take the situation you’re presented with, and do a rough calculation of the cost in your personal worst case scenario.
Question #2: The Extensive Margin
Given my answer to #1, do I want to go?
It’s called backwards induction because we’re working from the latest point (after all the food and services have been consumed, at the moment of splitting the check) back to the present (before the plan has been confirmed).
In Question #1, you learned the maximum the outing might cost you. Now, work backwards to the present, when the plan can still change. Does that cost seem worth the outing to you?
If yes, proceed! In the moment, you can allow yourself to be pleasantly surprised if the outing is cheaper than you imagined – the bill isn’t split evenly, or I lose in the fight-for-the-bill games, or my friend and I realize we aren’t that hungry and just split an appetizer. But if it isn’t, and you do meet your worst case scenario – well, you’ve already rehearsed for that in your head, and have decided that it was worth the cost. Enjoy without fear and resentment!
If not, pause! Right now is your chance to choose a different path, and a different worst case scenario. I know I can’t afford to split the bill evenly with a group of consultants. Since it’s early on, I have a lot of options right now!
Suggest a cheaper place
Take cash to cover my share
Offer to host at my home
Skip the event
Some of these options are more socially awkward than others – but all are, in my opinion, less socially awkward than sitting at a table, still hungry after consuming just a salad, biting my tongue or arguing with my friends.
A note on hosting at home: a friend of mine recently lamented that everyone in New York seems just a little bit embarrassed about their apartment and therefore social life ends up centering around outside places that cost money. For what it’s worth, I’ll speak for myself and hopefully more people here: if you’re my friend and I ask to hang out, I’m willing to climb to your sixth-story walk up and sit on your floor drinking a grocery store beer if that’s what it takes to spend time together.
The goal of Doing the Math on the intensive vs. the extensive margin is to better understand whether our social plans are actually helping us stay connected to our loved ones — a value I’m sure every reader shares. On the intensive margin, we have to be honest about what our social life costs. On the extensive margin, we get to recognize that we have choices about how to construct that social life and hopefully, choose the outcome that minimizes resentment and surprise and lets us simply feel good about our time together.
Exercise: Make an Extensive Margin Choice
This week, I challenge you to make a choice on the extensive margin and spare yourself the self-negotiation of the intensive margin. Some examples:
Instead of trying to budget at the grocery store, consider skipping this week and eating what you have at home.
Change a restaurant plan to an at-home plan.
Skip the “research” of trying to find the cheapest-yet-ethical-and-perfect piece of clothing or household item, and see if you can do without for a little longer.
For my part, I have not yet been inside a café in this new country, despite my jet lag demanding an espresso. Happily, I have found a free espresso machine in my new office. Leave a comment letting me know what you chose!
“Price Discrimination” is broadly defined as the practice of charging different customers different prices for the same good or service. It’s partly legal, partly illegal, and we can discuss its effects in a future newsletter!
A fun statistic for you: Thanksgiving 2023 broke records as 3 million people flew within the U.S on November 26th, 2023. That’s the same number of passengers – 3 million – who take the NYC subway on an average post-pandemic weekday.
74 comments on this last link! Clearly, we all have a lot of feelings about the issue.