23 Mar 2011

A thought on happiness

NB: This post describes how economists think about (and fail to see) the real world; I am still learning.

Economists say that people choose actions to "maximize their utility," which raises two questions. What's utility and what's included in its definition?

"Utility" can mean many things, but it basically means happiness, and it includes everything that makes people happy. That can mean making and spending money, but it can also mean watching the sunset.

This inclusiveness helps us understand the problem with programs or policies that contribute to GDP (monetary activities), to the detriment of non-GDP activities. Thus, we may see policies to help moms work (and hire nannies) as "good" for the economy, when they may not be good for utility. (Note that I am talking about changing incentives to participate in these activities, not voluntary participation.)

I was thinking a little more about utility and came up with the following definition:

Utility = peopleαproductionβconsumption1−α−β

This is the first time I've used math on this blog in nearly three years, but this notation uses the classic Cobb-Douglas function, which has two useful characteristics (given that α and β are positive and sum to less than 1). First, we can see that a value of zero for any of people, production or consumption means that utility is zero. Second, more of any of these increases utility according to the values of α and β.

In non-mathematical terms, the main idea is that balance is good, but more is better :)

Now the definitions of people, production and consumption are also interesting.

People includes friends, family, lovers and strangers. Different people attach different weights to each of these subgroups. Both a family man and a swinger can put high values on α, even as they assign different priorities to different subgroups.

Production is easier to understand, as our output of paid and unpaid goods and services. Likewise, consumption involves a combination of goods and services -- everything from a cup of coffee to bungee jumping at Victoria Falls to the 22nd Rolls Royce. People obviously put different weights on different types of consumption and production.

It's important to note here that many economists consider time spent in production as "lost" to leisure (a type of consumption), making production a bad. This simple idea can be resolved by dividing production into fun (additional consumption) and work (lost consumption), but that often-overlooked nuance means that many economic models are not very accurate.

Production as a positive source of utility, OTOH, clarifies the reason that many of us work and choose jobs; less-attractive jobs have lower β value.

Bottom Line: We are the same in our pursuit of happiness but different in the way we find it.


  1. Utility to whom?

    From an individual's perspective, I would not consider production as part of my utility function (except as you argue, the fun part which would be consumption). `People', when defined more specifically (e.g. time spent with family and friends) can be considered consumption too. And whoops, we end up being consumers.

    From a government perspective, aren't you double counting with both consumption and production in there?

  2. I like the model in general. I would suggest you show it graphically (hard to do w/ three goods). X_i could be seen as time as well or resources spent on good i. But your summary is already good David.

  3. The requirement that superscripts sum to one implies that a doubling of inputs doubles utility, but that's not really necessary. They can sum to less than one (utility doesn't double) or more than one (it more than doubles).

  4. @Erik -- an individual. Your simplification to consumption alone commits the fallacy I am trying to avoid: confounding consumption with happiness without considering "non-consumptive" tasks of production and people. (Yes, you can define all food in terms of atomic matter, but some people like to keep hot dogs separate from ice cream.) Double-counting happens with your definition, not mine.

    @JM -- these can be consumed via time or money; time may be a better base unit.

    @TF -- decreasing marginal utility holds as long as all coefficients are <1, but I'd prefer sum to <= one, since it's hard to imagine real examples of doubling all more than doubling happiness.

  5. As you probably already know, this is an issue that has received increasing attention in recent years. Amartya Sen, for one, has written persuasively about our need to separate "happiness" from traditional economic measures (e.g. GDP), and improve our understanding of (holistic) quality of life.

    On that subject, and since you are in The Netherlands, have you come across related research from this organisation?

    PS - Nice model.

  6. David,

    For the sake of finding a complete definition of utility, where would you place natural resource stocks and maintenance? Personally, I would gain utility from just knowing that there are sound resource policies being implemented around the globe. In general, where would non-consumptive utility-increasing values fit into your model? Would they go under people, labeled as actions undertaken by strangers?

  7. This is an excellent topic. Books should be written about it. I've long argued that economics is the study of maximizing utility (happiness). To quote Bret Maverick, from the old TV series, "Money is just a way of keeping score."

  8. @Stickman -- no. Not seen NWO. the Dutch are pretty good at quality of life :)

    @Dan -- There's a difference between a stock and flow. If the fish (or coal or trees) are just THERE, then there's no consumption (or production), but planting trees, walking among them or cutting and using them are flows that correspond to consumption activities. This matters if one person wants to fish (consumption and/or production) but another person wants to watch them (consumption). They are at odds, and there's no "utility-math" to reconcile those desires. They can be reconciled in either markets or politics.

  9. I understand you point regarding the distinction between stocks and flows. Given your response, however, it seems as though utility should not be so vaguely equated with "everything that makes people happy". If I derive happiness from simply knowing that a healthy salmon population is THERE (vegetarian?), then there is no consumption/production, but my happiness is greater than it would be had those fish not been there. Should utility should be more precisely defined as "happiness derived from people, the production of goods (or bads), and the consumption of goods (or bads)"?

  10. The model is a great conversation starter, but I think what you say elsewhere on your blog about the use of math in social sciences (mathturbation is the word you use to describe it, if I remember correctly) is still true for a conversation about utility or happiness (maybe even more so).
    I would argue that we, as individuals and as a society, would be a lot better off if we thought more about the difference between means and ends. It seems that money (GDP) has become an end in and of itself for many individuals and society at large, which is where, in my opinion, a lot of the trouble starts. Problematic policies that focus on GDP instead of quality of life follow from this wide-spread confusion. Clearly, some might argue that having money in their pocket makes them very happy, and getting money is therefore a justifiable goal in itself, but I believe this stems from a close cultural association of money with pleasure (buying food, beer, vacations, etc.) and a feeling of security. Still, I would argue that most people would admit that what makes them truly happy are the things and services money can buy (and “free” things, like sunsets). Another reason for this means-ends confusion is the fact that money is easy to define and quantify, while happiness is much harder to define and measure, which only makes this an even more important conversation topic.
    One policy question I would love to see discussed is whether governments should just maximize the sum of all of the citizens’ happiness, or whether they should try to make sure that there’s a basic “happiness safety net” for everyone (I mean in a purely theoretical way, as I realize that this would pose a measurement problem yet again). Is a state in which everyone is somewhat happy better off than a state with a small number of extremely happy citizens and a large number of miserable citizens (the total happiness of the later state is larger than that of the former). Also, I would love to hear comments on how to maximize happiness for all given that some individual derive a lot of satisfaction from other people’s unhappiness (e.g. beating people up for fun, rape, child molestation, the pleasure of seeing someone get hurt in a you-tube video, etc.).
    And just for fun, how would you incorporate utility from other people’s disutility in your model?

  11. @Sabine -- I totally agree on the means/ends confusion and the problem with policy that aims at GDP instead of happiness -- much of which cannot be quantified (I am VERY happy listening to "free" streaming audio now, but there's no GDP bump...)

    Utility from disutility? Pleasure from others' pain? Just use "-happiness_{-i}" as in the opposite of happiness of others (-i means not you :)


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