Mathematizing Happiness

Altruism and the gift of shade-grown coffee
“No one has ever become poor by giving.” ~Helen Keller “When people make donations to privately provided public goods, they may not only gain utility from increasing its total supply, but they may also gain utility from the act of giving” (Andreoni, 1990: 473).
In my previous blog, I explain how it is practically impossible to formulate happiness. However, there may be a way to theorize it. Shade-grown coffee is the perfect example of how we can try to explain human behavior through mathematical equations. Economists are known (and criticized) for their theories of utility, which quantify how much one thing, a good or service, makes people happy in terms of degree of satisfaction. Indirectly, this is revealed through how much people are willing to pay for that thing. To illustrate: if you pay $5 for a cup of shade-grown coffee over $2 for a standard cup of Joe, this is the indirect way of measuring your underlying preferences that the expensive cup because brings you greater satisfaction, which economists call ‘utility.’ This is the neoclassical way of explaining human behavior. Let’s dig deeper: what is actually different about the shade-grown coffee that makes you willing to pay more? Is it just a cup of coffee, or does it also embody something else like a fuzzy feel-good feeling that you have contributed to a greater cause like protecting the Amazon rainforest and lifting a farming family out of poverty. (For a really great example of marketing with brilliant emotional appeal, see Follow the Frog. Okay, so maybe I actually did that…(and will be doing it again soon). We all want to be good people. We all want to save humanity, save the rainforest, and be Robin Hood of the 21st century. We also—in a very selfish way—want to help ourselves. Intrinsically, we are both selfish and altruistic beings. It’s in our human nature [1]. It might seem like good and helping others break the rules of economic rationality. After all, we could purchase the cheaper cup of coffee, invest the $3 saved, and with the right savings vehicle and the magic of compound interest, eventually strike it rich [2]. Yet, people still opt for the more expensive cup of coffee. Economist, no surprise, have found a way around to clean up this blemish to their equation with theory on impurity. To explain this, there is something called impure altruism [3]. When people act in benevolent ways, like make donations to charity, they are doing so for their own benefit too. Andreoni (1989) developed a warm-glow model that presents a new utility function for impurely altruistic behavior: U=Ui (xi, gi, G) [4] ,[5] Which means that we can drive maximum utility through the following equation: max Ui (xi, gi, G) | xi + gi = wi, G=G-1 + gi Kotchen (2006) has shown that the same model can be used to explain the markets for ‘environmentally friendly’ goods by mathematically illustrating how charitable giving is akin to ethical or green-consumption. I’ll try to explain this through the $5 cup of shade-grown coffee example. Suppose you can measure happiness in one-unit increments, which you can think of as golden utility points expressed in units of dollars. We can break down the intrinsic utility of shade-grown coffee:
  • $2—It tastes good and wakes you up (or xi points as a ‘private good’ which you, and only you, receive)
  • $3—It does good, by sustaining the tropical rainforest with shade cover as opposed to more agro-intensive farming (or G+gi points as the ‘public good’ that benefits the entire ecosystem, and that hypothetically includes you).
Notice that the $3 donation is the sum of G and gi because we treat coffee as a quasi public good [6]. The big “G” is the public good dimension, in other words, the shade-grown effects of coffee as helping the entire tropical rainforest. The small “gi” is your private benefit. After all, you’re part of the global environment too, so if the coffee is helping sustain a rainforest, even if it’s thousands of miles away, that is helping you in some indirect way. Does shade-grown coffee make us happy? By the logic of this formula: yes. But do we really need a formula to know that? Perhaps there’s something more to shade-grown coffee that doesn’t fit neatly into the equation. It makes us feel like we’re doing good. It’s as though we are willing to pay more for shade-grown coffee because it gives us some deeper satisfaction for that “um-good” feeling like psychological umami[7] that we’ve just saved (one leaf of) the rainforest, all through our guilty pleasure of morning coffee.  

Footnotes

[1] Taylor, Ken. “Psychological vs. Biological Altruism.” Philosophy Talk. 2010. < http://www.philosophytalk.org/community/blog/ken-taylor/2015/04/psychological-vs-biological-altruism>. [2] Einstein called compound interest the eighth wonder of the world, and with good reason. As an extreme example, suppose you invested the $3.00 in a stock paying an annual interest rate of 15%, compounded quarterly. Then the balance after 50 years is $4,728.71. If instead the interest rate is 20%, compounded quarterly, then after 75 years you would have a whopping $6,821,988.3. [3] Andreoni J. (1990) Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving? The Economic Journal 100: 464-477. [4] Capital letters indicate the sum or total and lower case letters indicate individuals. So G is the utility for society and gi is the utility for the individual, for the same good. [5] Two extremes would deviate from this utility function. The first is the case of pure altruism, by which the individual does not gain any utility for him/herself from the warm-glow feeling gi=0 such that Ui=Ui(xi, G). The other is the case of pure egoism by which the individual does not care at all about the greater good, G=0, and they act only in self-interest such that Ui=Ui(xi, gi). However, when people are motivated by both self and society interest, i.e. they are impurely altruistic, then both G and gi fit into the utility function. [6] In Econ talk, shade-grown is public in the sense that the environmental benefits are non-excludable. The missing half to be a pure public good is that, on a per-cup basis the coffee is does not fit the criteria as ‘non-rival’ because when you drink from that cup there are fewer sips for another consumer to enjoy. [7] Umami is the Japanese fifth taste that inexplicably explains why food is delicious. The term psychological umami is my own concoction.  

Additional References

Andreoni J. (1990) Impure Altruism and Donations to Public Goods: A Theory of Warm-Glow Giving? The Economic Journal 100: 464-477. Kotchen MJ. (2006) Green Markets and Private Provision of Public Goods. Journal of Political Economy 114.