The 1% Question

In my vacations last week, there were, obviously, lots of economists and a fair amount of conversation that would only appeal to economists. (Though less so than you might imagine- I've found that my group of economist friends are much more capable of having non-economist conversations. This was pointed out by some others during the trip. But I won't be presumptious enough to claim that our "non-economist" conversations would be interesting to anyone else just because they don't involve arguments about how fast diminishing marginal returns set in...) However, we did have one conversation that I thought might be interesting to the massess.

We started off trying to kill time by answering questions like "If you had to be an office supply, which would you be?" (my answer: a TI-83 graphic calculator) and "Fill in the blanks: Oregon is the ____ of ____?" (I won't reproduce my answer...). But we eventually got to a question that evolved into this:

If you faced the choice of increasing your income by $1 million per year in perpetuity or increasing the income of everyone in Country Z (we settled on China after a while) by X%, how big would X have to be to make you choose to raise the incomes of others?

Some notes:

1. This assumes that if X=0 you would choose the $1 million.
2. The increase in income is proportional. So if X=1%, then someone earning $500/year would see an extra $5, while someone earning $1,000,000/year would see an extra $10,000. That is, the Gini curve would be unchanged.
   
3. You can do whatever you want with your $1 million/year- spend it, invest in, give it to charity, send it to China, whatever.
4. If you choose to raise incomes in China by X%, no one would ever know that you did that.

After a while (as the result of various people's initial answers), we ended up debating what you would choose if X was equal to 1%. (Hence, the "1% Question.")

Some issues that came up in our debates:

1. Would you really notice a 1% increase in income? Or, as it was put at the dinner table (which may not be the right way to look at it), if you had 1% more food at each meal, would you notice?
2. How valuable is it to see the effects of your charity? For us, at least, we wouldn't witness those income increases in China. If I chose the $1 million, I could do a lot of good locally, and see the impacts. (Is this a "Think globally, act locally" question?)
3. And, of course, how selfish are you? That is, in the utility function you are maximizing here, what's the relative weight of others vs. you (and your family).

Without (yet) revealing where I came down on this, let me tell you that answers ranged from X= very, very small (i.e. less than .1%) to X= at least 10%, but not sure. Part of the issue is that we lacked some facts about China which made the difficult question even more difficuly. So here's some China facts:

1. The size of China's economy is $8.8 trillion in GDP in 2005, with GDP/capita equal to $6,800.
2. The distribution of income in China: a Gini of .415 in 2001, and the bottom 10% of the population earned 2.4% of income and the top 10% earned 30.4% in 1998.

In our debate, I think we thought China's GDP was $7 trillion, so 1% more income meant $70,000,000,000 or a ratio of 70,000 to 1, relative to the $1 million you'd get. Thus, even at 0.1%, you have a 7,000 to 1 ratio. But, of course, you don't get it and you don't even get to really see it.

Tough question.... If there's any readers left after that long absence, I'd love to know what you think. I'll give you my answer in a bit. (ETA: Here it is.)

ETA: Oops, Bryce let the world know our question first!