As the old saying goes, "The rich get richer and the poor get poorer". The cause of some people living easily while others live in poverty has been pondered by economists for centuries and has lead to wildly differing opinions about inequality, its nature, and its causes.
Inequality is caused by differing levels of returns on investments. Investments are not necessarily investments of capital, but can also refer to investments made with labor and other key assets (as they also say, "time is money").
While the wages of the working class (the working class's ROI) may only rise by 3-4% every year, the capital of investors (the investor's ROI) typically earns higher than 8% per year. While the working class does get wealthier, it is not nearly as much as the wealth increase as investors gain.
One of the primary objectives of economics in the past two centuries (ever since Ricardo and Marx) has been to try to study how politicians and market forces can influence inequality. This is covered in much further detail in Piketty's book, Capital in the Twenty-First Century.
For most people, economic inequality is not necessarily problematic. There exists great value in encouraging people to promote more to the economy and to be rewarded for that. On the other hand, unsustainable inequality growth (not as sexy as "inequality" for sure) is a much greater problem, and a problem that is faced now in the early twenty-first century, and will continue to be faced for decades.
Unsustainable inequality growth can lead to massive differences between the wealth amassed by investors and the working class. Bezos' total wealth represents the total salaries collected by at least one million Americans in one year. This massive collection of wealth is due to differences in the rate of return on investments, such as by Bezos, or by a common working American.
The solution to eliminating bad inequality is to eliminating unsustainable inequality growth. This means that for inequality to be healthy, growth must be equal between investors and the working class.
Many solutions exist to this problem, but unfortunately many require government intervention. Companies have no true natural incentive to give their employees more. It would take money away from investors, who they need for survival. Sacrificing growth for more equality between workers and investors means potentially sacrificing a company's lifeline.
Despite this, companies could try changing the way they understand their ownership structures. They can replace their Wall Street owners with Main Street owners. This can be done through encouraging greater market participation by the general public, by creating an ESOP (Employee Stock Ownership Plan), by creating a workers cooperative (a step further from an ESOP), or by creating a customers cooperative.
Market-based approaches are much harder than simple government decree, but face much less controversy (especially by those bugging liberals and "free-market advocates"). My ideas regarding government interference to limit unequal inequality growth include
Of course, the most simple government intervention to solve this problem would be socialism but that without a doubt cause a civil war.
In conclusion, the greatest problem regarding inequality, which itself is the greatest problem that most economists try to solve, is unbalanced inequality growth. There are many solutions to it, both market and government mandated, and neither goes without problem or controversy. However, if we want to preserve liberty and equality, more steps will need to be taken to ensure that division does not cripple our world.