First of all, let us understand what is Kuznet's curve. Simple google search results that Kuznets curve is a hypothetical curve that graphs economic inequality against income per capita over the course of economic development. According to this hypothesis, as an economy develops, market forces first increase and then decrease economic inequality.
Kuznet Curve-
(reference - Wikipedia)Frankly, I never thought about reasoning/explanation of this curve. But one day, this question was asked in Macroeconomics course exam. Though I was only auditing this course, but multiple conversations with my friends intrigued me to think about this phenomenon.
Original Question - Income inequality in growing nations is very high but it goes down once the nation is developed. Income inequality seems to be low when the nation is poor and also when the nation is developed. If we draw a graph with income level on the x-axis and income inequality in the y-axis we get an inverted U curve. None of the growth theories explain this behavior of income inequality. Come up with your own theory where this behavior is explained. Your theory should not only explain this behavior but growth shouldn't be possible in your theory without income inequality becoming high.
Here was my answer - A neoclassical model of Kuznet Curve using Schumpeterian entrepreneurship
Note: This answer was developed based on ideas initiated by Christopher Olk (my course-mate).