As a country’s income increases, the county’s income distribution flattens. The best mathematical model for income distribution is the log-normal distribution — take the natural log of every individual’s income, and it approximates a Gaussian (“normal”) distribution.
Looking at the data from the Pew Research Center (Figure 4) we can use the median income as-is and fit the rest of the numbers to log-normal distributions. Over the past generation, median household income has increased from $27,036 to $51,777. If the standard deviation of the log-normal distribution had scaled as did the median, there would, in fact, be less income inequality than there is today.
The difference is that those at the 20% mark would be making 3.5% more than they do, and those at the 80% mark would be making 3.4% less. Those at 10% mark would be making about 5.3% more, and those at the 90% mark 5.1% less.