Fact Fans! It’s time for another round of WTF? (With math!)

The income inequality debate has been going on for quite some time in the United States. Ever since the 1970’s, income growth has split into three tiers, and the pattern continues today. This leads to a multitude of different arguments, some on income inequality, some on income growth inequality, and some on inflation and wage inequality. These arguments are often found thrown together in mix, with everyone referring to them as the same argument. But as any reader here will know, things are not always what they seem at first glance.


Let’s look at the first argument:

The claim here is that the top earners make far more money than the middle or lower earners, and that this is a recent problem (as in, this is not the way it has always been). These two arguments have to be looked at separately  as even if the first is true, it is no simple task to show that it is improper aside from relativistic thoughts about fairness. Since we deal with facts here, we will not be making the moral arguments.

Factually speaking, in 1970 the median incomes were divided as such:
(Source: US Census Bureau, adjusted for inflation)

Data 1970
20th percentile $15,126
Median (50th) $35,832
80th percentile $60,148
95th percentile $95,090

In 2009 they were a little different:

Percentile 2009
20th $20,453
50th $49,777
80th $100,000
95th                                                               $180,000

As you can see, income differences have existed for a while, in 1970 having less of a gap than in 2009.

Difference           1970            1970        2009          2009
95th-20th $79,964 15.91% $159,547 11.36%
95th-50th $59,258 37.68% $130,223 27.65%
95th-80th $34,942 63.25% $80,000 55.56%

This means the income gap is growing, as claimed. There has always been an income gap, also as counter-claimed. This argument only establishes that there is a gap and it is growing. The next part may help to explain why this is so.


The above graph shows the increase in income over the years. In the later 70’s, the top earners continued to grow in their income while the lower percentiles almost flatlined in growth. This continued until the 2000’s, where that growth still rose more but only slightly. Income also did not go down as much for the top earners as for the rest during the recession.

This brings us to the other two points: has there been a change in income growth (and how much), and how does it affect the ability to purchase relative to inflation and private economic growth?

Looking back at the data, we can see the growth for each group:

Difference 1970-2009                         Amount                               Percent
20th percentile $5,327 35.22%
Median (50th) $13,945 38.92%
80th percentile $39,852 66.26%
95th percentile $84,910 89.29%

Keep in mind that this is over a span of 39 years, or about 0.9% a year for the poor, 1% for the mid, 1.7% for well off, and 2.3% for the rich. There is most certainly a difference here, and it is quite large (more than double growth in wages for rich versus poor).

Note also that this is not about how much one earns, but how much what they earn grows per year. This in and of itself is obviously unequal, but it gets worse still. See, 2.3% of $10,000 is much less than 2.3% of $100,000. Not only is the growth more by percent, but as the discrepancy grows so does the wage gap.

This is readily apparent from the chart above. While the median income only gained $13,000 in real income, the upper income earners increased their incomes 3 times that and the top earners increased their incomes 6.5 times that. As this trend continues, that difference will only increase. If this trend continues for another 39 years, the following will be the resulting income difference:

2009-2048 Amount 2009 Percent growth Amount 2048 Difference $
20th percentile $20,453 35.22% $27,656.55 $7,203.55
Median (50th) $49,777 38.92% $69,150.21 $19,373.21
80th percentile $100,000 66.26% $166,260.00 $66,260.00
95th percentile $180,000 89.29% $340,722.00 $160,722.00

In short, if this trend continues, in 2048 the poor will have increased their income by $7,000, and the median will have increased 2.5 times that, the rich would have increased almost 10 times that, and the upper rich would have increased 23 times that. This is the numerical reality that many conservative authors will not acknowledge when they deny there is a non-justifiable income gap.

Lastly, we need to look at inflation rates to see if these increases in salary keep up with it. The optimal inflation rate is 2%; above it, and we start to see people not able to afford basic items, below it, and we start to see a devaluation of the currency and its buying power (unemployment also goes up since businesses can’t afford to pay workers). Mostly, the USA stays around 1.5-2%, and it’s worked out nicely for the economy so far.

In the following chart we will look at wages adjusted for inflation from 1970-2009:

1970 2009 Difference Difference per year
Median Wages
(Inflation Adjusted)
$45,146 $52,195 $7,049 $180.74

Not bad right? Who wouldn’t want to have an extra $180 in their pocket a year?

Oh, except let’s look at standard commodities in 1970 versus 2009. Remember, these values are adjusted for inflation, so any increase of price is on top of inflation:

1970 2009 Difference Difference Per Year
Price per Gallon
(Inflation Adjusted)
$1.514 $3.608 $2.094 $0.054

Gas expenses per year:

Average gallons a year Price 1970 Price 2009 Difference Difference per year
789 $1,194.55 $2,846.71 $1,652.17 $42.36

Rent per year:

Average rent (Adjusted) 1970 2009 Difference Difference per year
Per year $4,980.00 $8,160.00 $3,180.00 $81.54

Uh oh, that cut quite a bit of our winnings away, about $123, leaving us with a much smaller $57 a year boost. Well still, that’s fine, a good rai-

Average Utilities (Adjusted) 1970 2009 Difference Difference per year
Per year $595.00 $3,171.96 $2,576.96 $66.08

Crap. Now we are losing money. Thankfully, the food prices have dropped some:

Average Food (Adjusted) 1970 2009 Difference Difference per year
Per year $7,696.00 $6,604.00 -$1,092 -$28.00

Which means we are in the green! By around $19! A year! Ok, not pretty, but sti-

Average Healthcare (Adjusted) 1970 2009 Difference Difference per year
Per year $1,074.56 $4,824.00 $3,749.44 $96.14


I think I rest my case.