2 Questions About Income Inequality

Since income inequality in the USA has been in the news lately, I have a couple of questions about it:



1) Since it is generally accepted that intelligence is normally distributed and presumably ability is also normally distributed, if income inequality were primarily the result of differences in intelligence and ability should it be expected that income should also approximate a normal distribution?



2) If income inequality is primarily a result of the higher income earners working harder than the lower income earners, should income inequality remain stable, or only have a slight trend, over the long term? This question is based on the reasoning that an increase in income inequality implies that the financial reward for working harder is increasing, which would be expected to motivate more people to work harder with the result that there would be more people sharing the increased reward for working harder which in turn should cause the income inequality to decrease. This is analogous to what happens when demand pushes up the price of a product and leads to more producers producing the product, which in turn puts downward pressure on the price of that product.

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