revisiting the repugnant conclusion

http://www.science.uva.nl/~seop/entries/repugnant-conclusion/

i was thinking about the economic decision to have a baby, and it seems that derek parfit wants to come up with a theory which avoids a situation which ends up like figure 1, where we transition to a population with larger total utility but each with a very low positive quality of life. As utilitarians, then, it seems that the moral conclusion would be to sacrifice some of our present utility in order to have more babies who will all have shittier lives because the world is overcrowded. 

i just thought intuitively that the figure doesn't make sense, and i thought of a reason why. i realised it looks a lot like classical economic analysis. the repugnant conclusion is simply the same fallacy in economics that goes: if every good achieves some positive revenue by selling it, then the firm should maximise revenue by selling the good until the price is at 0, when we know that that is not true unless the marginal costs are 0. 

you see, you have to model the problem like this. intuitively, an extra baby imposes a negative externality (via the resource budget constraint) on EVERY single other person in the economy. Plot average utility (price) on the y-axis, and total population N on the x-axis, and draw a downward sloping average utility/population growth curve. then the total utility curve is equivalent to the total revenue/expenditure curve , and it is maximised when the average utility elasticity of population is 1. 

Also remember that population growth is an endogenous (private) choice. However, the philosopher wants to look at it from the social planner's point of view. So, if we were on the left of the e=1, then an increase in population would decrease average utility, but maximise total utility. So, the repugnant conclusion still holds for some extent. However, we avoid the conclusion mainly because after e=1, then it no longer makes sense to continue increasing population. If you were to increase it beyond that point, then the externality beyond that point matters (because the resource constraint bites harder, and because the externality hits more and more people as population increase) So, we will never end up at a point B where each person has miserable little utility but the total population is happier. I.E. you cannot compare 100 person each with 10 utility (total 1000) with 1001 people each with 1 utility (total 1001) because it is not possible to get to the second point moving along this utility schedule.  I.E, the repugnant conclusion's worst conclusions are impossible. 

To ensure that the demand curve I have propose is downward sloping, you go back to classic indifference curve analysis. This time, your indifference is between allocating your resource constraint between population (i.e. feeding/creating new members), and increasing your current population's consumption. The utility function for you would be biased towards yourself because people are selfish/impatient, but have reasons for having babies. If you did want the moral conclusion, you could choose the weight so it would be perfectly altruistic, giving them both equal weight. These are your two choice bundles, x1 and x2. an increase in average utility of the current population necessitates a fall in population, while an increase in population would necessitate a fall in average consumption. 

Ok, then how do you explain population growth. On this curve it would be like a shift in technology/tastes affecting the demand curve. It is a shift of the utility curve at every point. Intuitively this happens because you relax the resource constraint. So, a certain average utility is now compatible with a greater number of people because the economy grows. 

To model how exactly this changes, then you shift to the endogenous growth model with population choice. And come on, isn't it intuitively realistic. We are all impatient. And I look at the population growth data, it does seem that the growth so far has come because the resource constraint has been relaxed. I do think that the world might be able to support more people and a higher utility (we are on the left of e=1). But again, this is because now we are able to endogenously control our population choice through contraception, family planning etc. Therefore, because of our impatience in consumption, we do not achieve the social planner's optimal. That is why governments in developed countries are in fact so worried, and paying you to go for the repugnant conclusion. But at the same time they don't want you to reproduce too much. There is an optimal population growth rate implied by the model. 

It isn't a paradox to me anymore until someone points out what is wrong with my analysis. I always thought that the problem was that this was a utilitarian question at its heart, and so it lends itself to some form of analysis, which nobody has seemed to bothered to do. So you can confuse people by proposing unrealistic hypothetical scenarios in language, when the math doesn't allow for it. Then you have these identity arguments etc which just don't make so much sense.

Of course, other branches of moral philosophy, I still have immense respect for. Math touchest not thee.