The reason why we need to worry about income and wealth inequality is that it leads not only to divided societies and kids being born either "lucky" or "unlucky" but it also distorts democracy. The rich have the free time and money to lobby for what they want, own news media to present their distorted views of the world, enter politics and ingratiate themselves with the powerful elites. While the rest of the population is preoccupied with working hard to provide the basics of life for them and their families. It is this distorting effect on democracy and policies that I think is a major cause for concern. Just look at the graphic below the top 3 wealth US citizens, Warren Buffet, Bill Gates and Jeff Bezos now have more combined wealth than the bottom 50% of the US population.
There are three really good websites that deal with these issues.
1) Inequality.org which as been tracking inequality-related news and views for nearly two decades It is a project of the Institute for Policy Studies since 2011 and it has many useful insights into inequality and how the issue can be tackled.
2) WID.World The World Inequality Database is a superb resource for tracking and graphing the evolution of income inequality around the world. You can plot graphs by country over time and also compare countries. You can select the shares of various income groups like the top 1% and the bottom 50%.
3) inequality.stanford.edu Stanford University Center on Poverty and Inequality tracks the growth of inequality in the United States and provides research, policy analysis and some very useful datat relating to the issues of poverty and inequality.
There are many dimensions to inequality, income and wealth, differences between countries, differences within countries, difference between regions of the world, trends over time, differences by category such as men and women, by religion. The causes are equally complex ranging from the degree of capitalism, to political factors such as the extent that countries are controlled by oligarchs. Economics needs to address this issue more fully than it currently does as it influences the extent to which macroeconomic policies work. For example, economic theory suggests that it is better to cut taxes on the poor rather than the rich to stimulate to stimulate aggregate demand in an economy. The argument for progressive taxation is also based partly on the idea that financing public services is better done by taxing the wealthy. When we come to dealing with the large costs of the coronavirus pandemic I have no doubt it will be the rich that will eventually be made to pay for a lot of the costs because the poor and newly unemployed will simply not be able to be taxed to pay for it and indeed they will be the most reliant on that State to help them survive the crisis and beyond. Expect to see a lot more focus on the issue of inequality in the years to come.