Mo' Money!

The Shape of Happiness, Part 2

One of the great pleasures in life is a pint of Cherry Garcia. Even though B&J are fake socialists, they make the best ice cream (sorry Texans - Blue Bell is several notches below B&J). I can easily eat a pint in a single sitting. B&J’s ice cream is rich and creamy, and they always have clever and interesting add-ins. A pint of B&J adds significantly to my happiness. See the graph below:

If we put the number of pints of ice cream on the X axis, and the amount of happiness I get from eating some number of pints of ice cream on the Y axis, you can see that I get H(1) amount of happiness from eating the first pint of ice cream. That’s a lot of happiness. But you know what is better than one pint of ice cream? That’s right - two pints of ice cream! If I eat two pints of ice cream, I get H(1) + H(2) happiness. But notice that the additional happiness I get from eating the second point (H(2)), is less than the amount of happiness I got from eating the first pint (H(1)). A second pint adds to my happiness, but not as much as the first pint did.

The additional value that I get from one more pint of ice cream (or one more of anything) is called the marginal value. And a third pint adds to my happiness, but less than either the first or second. The marginal value of the 3rd pint (H(3)) is less than the marginal value of the second pint (H(2)). This is logical because, even though I love B&J, three pints of ice cream is a lot to eat. The fact that each additional pint after the first pint adds less happiness is called diminishing returns (the marginal value is positive, but decreasing). Almost all goods generate some positive amount of happiness initially (if they didn’t, they wouldn’t be goods - they would be bads), but additional units of the goods result in diminishing returns. For example, if you offered me one new BMW, I would be really excited. If you offered me two, I would still be excited, but maybe not as much as the first one. If you gave me two, I would drive one and I would give my wife one (our “new” car is a 2012 Honda Pilot, so she would be perfectly happy to have a new BMW, too, never mind the Adventure Van). If you gave me a third one, we might use it as our weekend car, but now we’re starting to run out of room at the LHH. I have a pretty big driveway, but three cars is about all that it can comfortably fit. Like the ice cream, the marginal value is falling. A fourth BMW might actually start to cause the happiness curve to not only flatten, but bend downward because now, if I can’t sell the fourth car, it actually starts to cause me problems (the marginal value turns negative). The fourth BMW would actually be a bad, not a good. And, although it is hard to believe, there is even a point where additional pints of B&J would become a bad. 

Last week I talked about two kinds of happiness - life-satisfaction and experienced well-being. Ice cream gives us the experienced well-being type of happiness, less so the reflective, life-satisfaction kind of happiness. Experienced well-being is especially subject to diminishing returns. We can think of the shape of happiness as a diminishing returns curve, like the one above, for most things. It has been conventional wisdom that there was diminishing returns even to income, such that at about $75,000 in annual income, there was relatively little additional happiness generated.

The intuition is that with about $75,000, you can address most of your needs and have some degree of financial security. The idea that there is diminishing returns to income, whether at the $75,000 level or higher, makes sense to me. I don’t feel like I would be all that much happier if I were to increase my income much beyond where I am today. And yet, new studies have shown that this intuition is actually incorrect. In fact, it has been shown that happiness, both experienced well-being and life satisfaction both continue to increase as income increases. The shape of happiness with respect to income is continuously rising, not diminishing. 

This is a graph from a 2021 paper by Killingsworth. 

A 2023 follow-up paper by Killingsworth, Kahneman, & Mellers confirmed the slope of the experienced well-being curve. Kahneman had previously been an advocate for the diminishing returns model of happiness with respect to income.

The 2021 study by Killingsworth was very interesting. He had people reporting their state of happiness throughout a day, indicating if they were happy or unhappy. What he found was that everyone experiences some unhappiness (shocking!) but wealthier people experienced fewer moments of unhappiness (negative feelings) and more moments of happiness (positive feelings). 

This makes sense if you think about it. Poor people are constantly trying to solve problems of basic existence. With very limited incomes, you are juggling paying for food, paying for rent, paying for medical care - usually with one or more of those things falling through. At high levels of income, you just don’t have to worry. You can buy whatever you want. Get a flat tire? No problem - just call a tow truck and get it fixed. 

Something I was mulling over is, why does money have a rising rather than diminishing curve? The answer is in the nature of money. Money itself is not a good - it represents a generic, convertible resource. So with money I can buy some B&J Cherry Garcia, and when I have enough of that, I can switch my spending to something else that has a high marginal value. We don’t value money for money’s sake, we value money because it gives us access to additional goods and services of an infinite variety. For example, instead of buying more B&J, I could buy another kayak. Who knows how many kayaks it takes until you get to the point where the marginal value would turn negative? Kayaks are really just a boat-shaped manifestation of happiness, after all. My very wise, soon-to-be son-in-law acquired a new kayak for me from a yard sale a couple of weeks ago (no one wanted it and the owners were just going to give it away - so he brought it to me - wise young man). I have now discovered that the marginal happiness associated with a fourth kayak is strongly positive. It’s very exciting!

So it makes sense that the shape of happiness with respect to money (income) is indefinitely rising because its fungible nature provides security and solves problems. 

I do think it’s an incomplete story, though. More income can’t give you back time. I deliberately chose an academic life because I value time more than money. In this case, the marginal value of time for me exceeds the marginal value of more money at about my current annual income. My job gives me time for contemplation and study, which I value, and am willing to pay for by giving up income. 

We all value time and money differently. It’s one of the dimensions of diversity that shapes many of life’s outcomes. Consciously or not, we are all solving these optimization problems. As far as we can tell, the shape of happiness with respect to money is continuously rising (always retains a positive marginal value), but the marginal value of time is something we also consider and balance. 

Have you thought about the shape of your happiness with respect to money and time? What other goods have strong, positive marginal values?

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