Total Human Earth Utility

Eventually, the sun will die out and with it, our species. That is, unless we extend our existence by colonizing space (likely) or arranging a non-solar energy source (plausible), or unless we shorten our existence by something along the lines of climate change or nuclear winter (plausible). However, to put things into perspective, we present a simple, "back of the envelope" calculation of the total utility humanity will get from the sun on Earth.

Note: I am using the short scale for names of numbers. Thus, 10^9 is one billion and 10^18 is one quintillion. For more on this see Long and short scales.

The simplest form is:
  u = p * a * t
Here u is total utility, measured in QALYs. p is average population, measured in number of people. a is average individual utility level, measured in QALYs per person-year. t is total time Earth will be hospitable for humans, measured in years. Reasonable estimates are:
  p = 10^10 (10 billion) people, which is approximately where the world's human population is projected to level off at later this century (link)
  a = 0.6, which is the average human life satisfaction from HPI normalized (divided by ten) so it would be on a scale from zero to one.
  t = 10^9 (1 billion) years, which is approximately the lifespan of Earth's biosphere (Caldeira, K. and J.F. Kasting. The life span of the biosphere revisited. Nature 360: 721-723)

Using this model and these numbers, we get
  u = (10^10 people) * (0.6 QALYs per person-year) * (10^9 years)
  u = 6*10^18 QALYs

Thus, the total human Earth utility should be on the order of 6*10^18 or 6 quintillion quality of life-adjusted years.

How accurate do I think this value is? Barring any major disasters, it seems reasonable to expect that we'll bump that value for average QALYs per person-year (a) up from 0.6 to at least 0.8 or 0.9 as we improve the human condition across the planet. It is at least plausible that the given value for average population level (p) may actually prove accurate given our recent tendency to maintain population levels below carrying capacity in wealthier, more urban parts of the world. Finally, assuming the geoscience is correct (it probably is, but I'm no geoscientist), the total time (t) should be accurate. However, given the likelihood that our species does not end when the sun is no longer supportive (see below), the exact value for (t) is of little relevance to contemporary decision making.

Increasing (a) is a sound goal and an uncontroversial one by today's standards.

Increasing (p) is a trickier matter. These days, we're more likely to hear concern about overpopulation or overcrowding. Furthermore, it remains unclear what the Earth's long term human carrying capacity will be given today's rapidly changing situations for resources (generally worsening) and technology (generally improving). In addition, we may personally (i.e. selfishly) prefer maintaining a population well below carrying capacity, as is the case throughout today's wealthier, more urban population. We may eventually want to restructure our society to encourage more procreation as is already done in France (link) and perhaps elsewhere.

Increasing (t) is out of our hands. But remember, (t) is total time Earth will be hospitable for humans. Whether we make it that far or farther is very much in our hands. Given today's rapid rate of technological advancement and the billion or so years we have to work with, it's fair worry more about making it that far than about making it farther. If short term threats don't end us, we'll be well positioned to survive post-sun.

For more on ensuring the long term viability of humanity, see Reducing the risk of human extinction by Jason Matheny (key quote: "We review the challenges to studying human extinction risks and, by way of example, estimate the cost-effectiveness of preventing extinction-level asteroid impacts.") and the Lifeboat Foundation, which discusses a wide range of threats to humanity.