For almost 40 years, inequality within the top percentile of the income distribution, measured as the ratio of income share of top 0:1% to the income share of top 1%, has been increasing in the US. The income of super-rich people increased more than the income of rich people. In this paper, we show that improvements in automation technology (the number of tasks for which capital can be used) is an important factor contributing to this inequality. We consider a model in which labor has a convex cost and capital has a linear cost. This leads to a decreasing returns to scale profit function for entrepreneurs. As capital replaces labor in more and more tasks, the severity of diseconomies of scale diminishes, hence the market share of top-skilled entrepreneurs increases. If entrepreneurial skill is distributed according to a Pareto distribution, then top income distribution can be approximated by a Pareto distribution. We show that the shape parameter of this distribution is inversely related to the level of automation. Finally, we rationalize convex cost of labor using the theory of efficiency wage.