For example, saving a life adds 60 years to that life. Then, with an average population fertility rate of 5 per woman, we get 2.5=5/β2 additional people born, each living 65 years. Then, in 15-30 years, the fertility rate reaches 4 per woman, and each of the extra 2.5 children born go on to add to 2=4/β2 more, giving 5 grandchildren, each living 70 years. Then in another 20-30 years each of those 2.5*2=5 grandchildren go on to add 1.5 more (fertility rate of 3 per woman), each living 70 years. And so on.
Just the terms considered so far, up to and including grandchildren, gives a multiplier of >16=1+2.5+2.5β2+2.5β2β1.5 relative to the value in the life directly saved. We can consider both the value in those lives themselves, and how they affect others.
For example, saving a life adds 60 years to that life. Then, with an average population fertility rate of 5 per woman, we get 2.5=5/β2 additional people born, each living 65 years. Then, in 15-30 years, the fertility rate reaches 4 per woman, and each of the extra 2.5 children born go on to add to 2=4/β2 more, giving 5 grandchildren, each living 70 years. Then in another 20-30 years each of those 2.5*2=5 grandchildren go on to add 1.5 more (fertility rate of 3 per woman), each living 70 years. And so on.
So, we added
60 years+2.5β65 years+2.5β2β70 years+2.5β2β1.5β70 years+...Just the terms considered so far, up to and including grandchildren, gives a multiplier of >16=1+2.5+2.5β2+2.5β2β1.5 relative to the value in the life directly saved. We can consider both the value in those lives themselves, and how they affect others.