Optimal Taxes

I know, it's the worst title for a post ever. Bear with me. Let's say we have 8 people who earn 10,000 a year, and 2 people who earn 100,000 a year. Now which tax system would you prefer?

1. Those earning under $20,000 a year gets an earned income tax credit (essentially, a refund) equal to 90% of their income. Those earning over $20,000 pays 36% of their income in taxes.
2. Everyone pays 50% tax on all their income, but then everyone receives a $14,000 grant.

The first scheme appeals to progressive instincts. Those who can pay more should pay more. It transfers money from the rich to the poor. But it isn't necessarily fair because why should we punish one group just for being rich? The second scheme seems fair - it treats everyone identically. But why should people who are already rich receive this block grant? They don't need it, do they?

Here's the kicker. Each tax scheme results in an identical distribution of post-tax income. In either case, each of the poor people ends up with $19,000, and each rich person ends up with $64,000. In the U.S., we operate more like scheme 1), but it doesn't necessarily lead to any greater redistribution than a flat tax and grant scheme.

I'm not sure exactly what my whole point is on this, but I thought it was an interesting thought experiment.