Simple arithmetic

Deirdre McCloskey had a piece in the NY Times on Sunday called, "Growth, Not Forced Equality, Saves the Poor."  In it, she wrote "As a matter of arithmetic, expropriating the rich to give to the poor does not uplift the poor very much.  If we took every dime from the top 20 percent of the income distribution and gave it to the bottom 80 percent, the bottom folk would be only 25 percent better off."  That didn't sound plausible to me, so I looked up figures on the distribution of income.  There are lots of sources, but the one that came up first was from the Congressional Budget Office.

Rather than interpreting "take every dime" literally, I calculated what would happen if you gave to the bottom quintile until they caught up with the second, then gave equally to the first and second until they caught up with the third, etc., and stopped when the top quntile had been reduced to the level of the fourth.  I call that the egalitarian formula.  I also calculate an alternative in which the money is distributed equally to the four lowest quintiles, again stopping when the top quintile is at the same level as the fourth.
                 
                       Actual             Egalitarian            Flat-rate            
Top                $188,000            $83,000                $104,000
2nd                  $83,000            $83,000                 $104,000
3d                    $59,000            $77,000                 $80,000
4th                   $42,000            $77,000                 $63,000
Bottom            $24,000            $77,000                 $45,000

The numbers refer to housholds in 2011, and the "actual" are after taxes and transfers.  The average gain in the bottom four quintiles would be a lot more than 25%--the bottom three would gain by more than 25% under either formula.  Of course, if redistribution led to slower economic growth (and extreme redistribution like this probably would) it would not help the poor in the long run, but it would take quite a while for lost growth to offset the immediate gains.  To quote John Stuart Mill again "The relaxation of industry and activity, and diminished encouragement to saving which would be their ultimate consequence, might perhaps be little felt by the class of unskilled labourers in the space of a single lifetime."

Where did McCloskey get the 25% figure?  Given the magnitude of the discrepancy, it can't be a matter of using figures from a different year, or individuals instead of households, or some other technical issue.  If you interpret "take every dime" literally, start with 20 and divide it 4 ways, that gives 5, which is indeed 25% of 20.  That is, she didn't take account of the fact that people in the top quintile of incomes have higher incomes than people in bottom four quintiles.   That's the only explanation I can think of.  That leads to the question of how someone who is not just a trained economist, but a  Distinguished Professor (emerita) of Economics, History, English, and Communication could make this kind of blunder, but I'm not going to try to answer that.