The Price of Happiness (2024)

Harvard has been running longitudinal studies for several decades:

* https://en.wikipedia.org/wiki/Grant_Study

and their findings lean towards good relationships with family and friends are highly correlation with happiness, health, and many aspects of financial success. The released a book summarizing many results a few years ago:

* https://www.goodreads.com/book/show/61273746-the-good-life

* https://archive.is/https://www.theatlantic.com/ideas/archive...

A classic paper worth a read:

If money doesn't make you happy, then you probably aren't spending it right

by Elizabeth Dunn, Daniel Gilbert, & Timothy D. Wilson

https://www.sciencedirect.com/science/article/abs/pii/S10577...

Includes explicit recommendations (even in the short abstract)!

Was this AI written? It seems confusing to me but I'm not an economist. I think another way to look at happiness and money is that while money doesn't necessarily buy happiness, it avoids unhappiness. So you remove a negative factor -- not having money, which is a position nobody wants to be in. This is similar to your overall health, friends, love, etc.. It's not that you need tons of them , but not having any of them is a problem, especially health.

"When you don't have any money, the problem is food. When you have money, it's sex. When you have both, it's health. If everything is simply jake, then you're frightened of death."

I wonder how much any of those associations are with income per se versus career satisfaction per se?

I imagine people who are making more money are probably a better fit for their career, feel more needed, and so forth and so on. I do imagine there's some relationship with income and accumulating more money per se, but I wonder how strong that relationship is once you remove the effects of career satisfaction independent of monetary gain, if such a thing is even possible.

I guess it's hard for me to interpret these effects because there's so much going on in the background in terms of meeting life goals, feeling welcome where you're at and feeling like you're able to contribute what you're best at, and so forth and so on.

The other thing is the ordinate axis is hard for me to make sense of. Like, in Figure 1, life satisfaction goes from say, 2.7 to 3.2 on a scale of 1 to 4? That seems like a relatively narrow range to me, even if it is statistically significant, and my guess is those dots are hiding a lot of variability.

So maybe that's what people mean by diminishing returns? Not that there's no actual continuing increase, but that the increase is incredibly small on some absolute scale of happiness? It's hard to know what to make of the happiness numbers — if, say, consequential changes in some measure of happiness occur far below anything on that ordinate axis, none of these increases with income are of any practical significance.

Every Thursday, the ice cream man comes down our street. The price is usually around ~$20 to buy happiness for a family of 4.

> What is the shape of the relationship between money and happiness, and what are its implications?

1. money != income.

2. Zip codes.

3. Age.

4. Social class.

a) 65 year old professor living in Woodside, CA, with a net worth of $250,000K

b) 35 year old HVAC business owner living in Fresno, CA, with a net worth of $2,000,000

First is poor, second is rich, but the study conflates both into the same bucket if they both make, say, $400K/yr

It is difficult to know when you 'have enough' money because like death, you never know what is around the corner. Most of us earn, save, and spend money during our working lives so that we can retire comfortably; but it seems like there is no magic number for when we have arrived.

How long will we live? What will our health be like? Would we like to travel? Leave the kids an inheritance? Give it away? All of these can influence the number.

The secret to amassing wealth is to always live beneath your means; but don't forget to enjoy yourself as you make the journey towards retirement.

Great analysis, but I would probably add that most (but not all) of those who end up with the six- and seven- figure salaries are smarter, more well-connected and socially adjusted, optimistic etc. Most _not_ all. And some are just really good bullshitters, of course.

Ever been to a third world country and seen happy people who make just a couple hundred bucks a month, yet are very healthy and happy? I have. It's very life changing.

Who are the historical figures that you revere the most? Did their positive influences upon your life originate from making and having money?

Money provides freedom, not happiness.

I think as long as you're not depressed because you don't have enough money I've seen people with much much less happier than extremely wealthy people.

I know someone extremely wealthy and he continuously says that he's bored, is depressed yet wants to make more.

Meanwhile I work daily with people on a normal/content wage and I feel like they're generally happier people?

I know people really struggling financially and they're constantly depressed.

People work hard for academic and career success. This will take decades. The plan is to make a lot of money with that success, have costly things/hobbies and derive happiness. It is driven by money as social status, which allows you to buy costly things and signal to others about your success.

Instead, find joy in cheap hobbies and ignore the status markers. Just do things for yourself, not for others.

> a linear association between happiness and Log(income) implies that the marginal utility of additional dollars diminishes exponentially, though never mathematically plateaus

And income (or wealth increase) can go up exponentially with wealth, so hitting the point where wealth just grows = linear increases in happiness relative to time?

Sometimes is a miscalculation why people are not happy with what they have, mostly because they see another bigger number.

This may be a very tone deaf thing to say, but what really helps me is to just tell myself I am happy. It's certainly not fool-proof when faced with genuine problems, but I often find myself unhappy or annoyed for no particular reason. In those moments I just tell myself I have everything I need and life is great, and then it just feels better.

That said all the findings that these studies seem to gravitate towards like close relationships also align with my experiences as being powerful effectors.

related: https://www.astralcodexten.com/p/contra-pritchard-on-liberal...

Money definitely buys happiness for me. But I resent the amount of competition and how much bs I have to put up with to get it. It's definitely eroding the happiness. Especially when you engage in all the bs for years and still don't get much more money.

As always, correlation is not causation, so it's very possible that the people who tend to be happier also tend to maybe fit into society better and thus get higher paying jobs, not that you necessarily need to make X/year to be happier.

It is still interesting to see how the actual numbers shake out though, especially the section on how the income quintile groups actually scale linearly instead of log linearly with reported happiness.

I've held the notion that money behaves in a log-linear way for decades, so it's nice to see that formalized finally. A river exhibits different behavior than a lake or the ocean. It's interesting that Daniel Bernoulli (famous for the Bernoulli effect) had a similar instinct in 1738. Compared to the talking heads in news and politics today, he was an intellectual giant to say the least.

I did a deep dive on finding how well tax brackets correlate with a log-based tax rate, but couldn't find much. I'll just summarize the results of my AI-assisted research:

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https://www.fidelity.com/learning-center/personal-finance/ta...

https://www.reddit.com/r/AskEconomics/comments/1iri8nf/tax_b...

By plotting the 2026 single filer tax bracket thresholds against their marginal rates, we can fit them to the classic logarithmic function:

  log-linear equation for slope of line (y = m * x + b):
  tax rate = m * ln(income) + b

The ideal fit yields the parameters m = 0.0672 and b = -0.5121. The table below outlines how closely the mathematical log formula predicts actual statutory tax rates:

  income    tax rate  ln() tax rate  deviation
  $12,400   12%       12.10%         +0.10%
  $50,400   22%       21.52%         -0.48%
  $105,700  24%       26.50%         +2.50%
  $201,775  32%       30.84%         -1.16%
  $256,225  35%       32.44%         -2.56%
  $640,600  37%       38.60%         +1.60%

US federal tax brackets match a base-e natural logarithm (ln) model surprisingly well, boasting a statistical correlation R^2 of approximately 0.962.

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The general public might have a hard time understanding logarithms, so I investigated using base 2, base 10 and base e (ln) to explain them (the base doesn't affect the computed tax rate). Here are the two simplest rules of thumb for a log-based tax system:

  a) base 2 log: every time your income doubles, you pay 4.7% higher taxes on the total
  b) base 10 log: every time you add a 0 to the end of your income, you pay 15.5% higher taxes on the total

  income          tax rate  taxes paid    approximation

  a) base 2 log:
  $8,192          9.37%     $768          ~10%
  $16,384         14.03%    $2,299        ~15%
  $32,768         18.69%    $6,124        ~20%
  $65,536         23.35%    $15,303       ~25%
  $131,072        28.01%    $36,713       ~30%
  $262,144        32.67%    $85,642       ~35%
  $524,288        37.33%    $195,717      ~37% (current top marginal tax rate capped above this point)
  $1,048,576      41.99%    $440,297      ~40% vs 37%
  $2,097,152      46.65%    $978,321      ~45% vs 37%
  $4,194,304      51.31%    $2,152,097    ~50% vs 37%
  $8,388,608      55.97%    $4,695,104    ~55% vs 37%
  $16,777,216     60.63%    $10,172,026   ~60% vs 37%
  $33,554,432     65.29%    $21,907,689   ~65% vs 37%
  $67,108,864     69.95%    $46,942,650   ~70% vs 37%
  $134,217,728    74.61%    $100,139,847  ~75% vs 37%
  $268,435,456    79.27%    $212,788,786  ~80% vs 37%
  $536,870,912    83.93%    $450,595,756  ~85% vs 37%
  $1,073,741,824  88.59%    $951,227,882  ~90% vs 37%

  b) base 10 log:
  $10,000         10.66%    $1,066        ~10%
  $100,000        26.12%    $26,120       ~25%
  $1,000,000      41.59%    $415,900      ~40% retains current millionaire tax rate near 37%
  $10,000,000     57.06%    $5,706,000    ~50% at mid-millions vs 37%
  $100,000,000    72.52%    $72,520,000   ~75% at $100 million vs 37%
  $1,000,000,000  87.99%    $879,900,000  ~90% at $1 billion vs 37%

  From those tables, it's easy to see how a log-linear flat tax rate would work:

  a) base 2 log:
  4.7% flat tax: tax rate = 4.7% * (number of doublings) - 50%

  b) base 10 log:
  15.5% flat tax: tax rate = 15.5% * (number of zeros) - 50%

  c) base e log (for completeness):
  6.7% flat tax: tax rate = 6.7% * (number of zeros) - 50%

Politicians would set the log-linear tax rate slope (the 4.7%, 15.5% or 6.7% depending on log base) and the tax rate base (50% which might vary between perhaps 45-55%).

After grokking this, we might ask why a non-logarithmic 10% flat tax wouldn't work? The answer is subtle, but it's because it wouldn't incorporate the increased buying power over expenses ratio of higher incomes, so the formula would become tax rate = 0 * (number of zeros) + 10%, making it a regressive tax that penalizes low incomes and lowers taxes on high incomes that don't need the help.

To demonstrate why a 10% flat tax would be regressive, lets calculate the log-linear tax rate that meets the current $2 trillion US tax income:

  tax rate = m * ln(income) + b

  calculation of m for ln(income) derived from current values:

  m = (T - (b * AGI)) / (AGI * ln(u))

  m = log-linear slope to solve for
  T = total US tax revenue (currently about $2 trillion)
  b = -50% (floor held constant as a starting point)
  AGI = annual gross income of US (currently about $15 trillion)
  u = center of mass income of all taxpayers with half of tax revenues above and below (currently about $250,000)

  m = (2e12 - (-0.5 * 15e12)) / (15e12 * ln(250000)) = 0.05096 ~= 5%

  calculation of m for base 2 log and base 10 log for completeness:

  a) base 2 log:
  m = (2e12 - (-0.5 * 15e12)) / (15e12 * log2(250000)) = 0.03532 ~= 3.5%

  b) base 10 log:
  m = (2e12 - (-0.5 * 15e12)) / (15e12 * log10(250000)) = 0.11733 ~= 12%

Lets see if the calculated m slope would lower taxes:

  final tax rates to meet $2 trillion in tax revenue using base 10 log-linear tax at m = 12%:

  tax rate = 12% * log10(income) - 50%

  income          tax rate  taxes paid    approximation

  b) base 10 log:
  $10,000         -2.00%    -$200         ~0%  tax floor/credit for poverty line
  $100,000        10.00%    $10,000       ~10% tax for working class
  $1,000,000      22.00%    $220,000      ~20% for millionaires (37% top marginal tax rate currently)
  $10,000,000     34.00%    $3,400,000    ~35% for multimillionaires
  $100,000,000    46.00%    $46,000,000   ~50% for top millionaire incomes vs 37%
  $1,000,000,000  58.00%    $580,000,000  ~60% for billionaires vs 37%

  notable thresholds:
  $50,000         6.39%     $3,194        ~6.5% tax for median income taxpayers
  $250,000        14.78%    $36,938       ~15% tax for center of mass income taxpayers

It's obvious from the last summary that incomes under $100,000 would pay less under a log-linear flat tax than a 10% flat tax. Millionaires and multimillionairs would pay less than their current 37% top marginal tax rate too. Only top multimillionaires and billionaires would pay higher taxes than they do now.

After running the math, I feel that it's objectively self-evident that a log-linear tax reflects reality better than a 10% flat tax.