Income and Wealth inequality is a long standing problem. It is harmful to society in various ways that one can imagine. Allow me to share with you a Social Epidemiologist take on the subject matter rather than an economist view point.
Please spend the next 15 minutes to watch this TED Talk by Richard Wilkinson, Co-Author of the Spirit Level (2010), a book that raised a lot of eyebrows simply because the statistical observation apparently didn't meet the technical scrutiny (here). Both the Authors responded to all their critique and launched The Equality Trust (here), a social movement with a goal to improve quality of life in the UK and reducing economic inequality.
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Fast forward to 2014, when the Non French speaking people of the planet finally got their hands on Capital In the 21st Century by the French Economist Thomas Piketty.
The voluminous book central idea lies in this chart