I can see what you are saying, but I think we can both agree that the literal interpretation of families with 97 children isn't particularly realistic.

A similar objection goes for asymptotic time horizons: we don't have infinite time to work with, this is reality, we have a handful of critical decades. Climate models are typically run to year 2100, where of course the world hasn't ended, but it's probably a +3.5C ... +4C ... scenario, so options are dramatically restricted, and continuing to diminish, for the surviving people.

Another way to think about the population would be to simply consider how we might expect the US and Bangladesh populations to change over a reasonable time horizon, to figure out how many person-years of consumption (and pollution) we get for each individual and half of their descendants.

Here are some parameters and assumptions for a rather simple model:

Parameters:
Bangladesh United States
----------------------------------------------------------------
Fertility rate, births per woman 2.2 (y2013) 1.9 (y2013)
life expectancy at birth, female 71 (y2013) 81 (y2013)
life expectancy at birth, male 70 (y2013) 77 (y2013)
life expectancy mf geom average 70.5 79
average age of first child birth 18 (y2011) 25.4 (y2010)

This data in itself is pretty interesting! The fertility rate for both countries is similar (although on different sides of the 2.0 fence), but the "average age of first child birth" is very different!

Simplifying assumptions:

assume everyone in each country behaves the same:

everyone lives until their birth life expectancy
everyone has same number of kids
uniform life expectancy
divide birth rate by 0.5, everyone gives birth
everyone has children at the same age

all these parameters are stationary wrt time

These are pretty severe assumptions, obviously, but let's see where they take us.

Using these parameters, over a time horizon of 100 years, starting with a 0-year old US person, and a 0-year old Bangladeshi person, we obtain [0]:

Bangladesh: 343.8 person-years of consumption
United States: 214.7 person-years of consumption

If we multiply this by the country specific per-capita per-year rates of CO2 pollution, we get

Bangladesh: 343.8 * 0.3 = 103.14 tons of CO2 pollution
United States: 214.7 * 19.3 = 4143.7 tons of CO2 pollution

The US person (and their descendants), have contributed ~40x the CO2 pollution as the Bangladeshi person (and their descendants) over this time horizon!

We can compare this to a US person who has no children over the same time horizon:

United States, no children: 79 * 19.3 = 1524 tons of CO2 pollution

If we extend the time horizon to look at a ridiculous 900 year period, then we get the following:

Bangladesh: 71650.5 * 0.3 = 21495.2 tons of CO2 pollution
United States: 1308.8 * 19.3 = 25259.84 tons of CO2 pollution

The single United States person (and their finite number of descendants) have still produced more CO2 pollution than the single Bangladeshi person (and their large and growing number of descendants)!

### What, if anything, can we conclude?

Over a time horizon of 100 years, a cartoon typical US person (and their descendants) will be responsible for about 40x the CO2 emissions as a cartoon typical Bangladeshi person (and their descendants).

A cartoon typical US person can reduce the CO2 emissions they are responsible for by around 60% if they make a decision to have no children, over a 100 years time horizon.

Over a 900 year time horizon, ridiculously assuming parameters to not vary over time, a cartoon typical US person will still be responsible for more CO2 emissions than a cartoon typical Bangladeshi person.

[0] via a hastily written python script: https://gist.github.com/fcostin/2225b2a51ad8859b5d1b