I wanted to share two rather incredible nonlinearities in the world of personal finance that have rather profound implications for how we treat money.

Nonlinearity 1: Avoiding Lifestyle Creep

1. Suppose that Dave takes home $65,000 a year after taxes, and spends $60,000 a year maintaining hislifestyle - retirement savings, rent, food, transportation, travel, etc. Dave’s able to save $5,000 a year, which covers one month’s worth of expenses. My old roommate used to talk about earning runway, not dollars. Dave’s earning a month of runway per year. After 12 years (if Dave doesn’t invest at all, and ignoring inflation), Dave could go without income for a year.

2. Now suppose that Dave gets a raise to $75,000 a year (post-tax). His overall salary went up by $10,000, or about 15%. What happens if Dave doesn’t change his lifestyle at all? He’ll now be savings $15,000 a year; 3x as much as before. Dave’s runway accumulation rate is now 3 months per year (or 0.25 years of expenses/year), it’ll only take Dave 4 years to earn a year’s worth of security.

3. But what if Dave did in fact adjust his lifestyle, such that he now spends $70,000 a year? With a modest spending increase of 17%, he’s still saving $5,000 a year as in the beginning, but his runway accumulation rate is now only 0.07 years of expenses/year.

4. If we go back to the beginning, and Dave is earning $65,000 a year post-tax, but he finds a way to cut $10,000 of spending per year, then Dave is able to save $15,000 per year, as in point 2 — but Dave is now earning runway at a year of 0.3 years of expenses/year.

Even modest percentage increases in income or expenses can have massive impacts on the percentage change in your runway accumulation rate.

Nonlinearity 2: Diminishing Marginal Returns

One of the most important concepts in economics is diminishing marginal utility, the idea that the first thing (a car, a meal, a backpack, whatever) might you make quite happy, but the tenth likely less so. It’s intuitive, then, that a study that tried to answer “does money buy happiness” found that emotional well-being tended to saturate at income levels of around $75,000, and a logarithmic relationship between income level and life satisfaction (the nuances of what emotional well-being is versus life satisfaction can be found here - also, it’s tough to conduct research on money and happiness, not just because studies are difficult to replicate, but also due to how easy it is for popular media to misinterpret results). Increases in spending may not actally much you that much happier; certainly a 15% increase in income is unlikely to make you 15% happier [1]. I’m curious as to whether the relationship is cleaner when you look at people’s household spending versus emotional well-being and life satisfaction (though that data is likely hard to come by).

[1] This probably doesn’t hold true for the lower ends of the income scale, where more money is legitimately the cure to most problems.