A counterpoint: some 795 million people in the world do not have enough food to lead a healthy active life. That's about one in nine people on earth. [1]
I do not think that is because of the production capacity of the economy. A little redistribution would go a long way...
But if you want the "glass half full" view - zoom out even further and chart further back into history and measure proportion of global population in absolute povery, poverty, living on $1.25 or less (adjusted) per day, and you get charts like this:
http://s3.amazonaws.com/content.washingtonexaminer.biz/web-p...
and individual cases like China, which are just amazing:
http://iresearch.worldbank.org/PovcalNet/images/ChinaSpecial...
and you're more hopeful that we'll solve global hunger and poverty in our lifetimes.
It wasn't redistribution that caused it - on the contrary the evidence is that previously planned economies opening up reversed their fortunes (no co-incidence on where that China chart begins to show progress).
The major international aid orgs now almost entirely agree that food aid and humanitarian action should be short-term and a stop gap. The solutions are in trade, access to credit, access to markets, food engineering and sustainability, education, empowering the entire population (ie. no sexism, racism, etc.) political stability, etc. [0][1]
It's why I completely agree with grandparent OP that the "division" performed is misleading - the economy isn't a fixed size nor is the distribution zero-summed. We can lift the rest of the world up to our level rather than meeting in the middle.
And in case it's not obvious, consider: Person A just graduated with a law degree from Harvard; they have negative net wealth. Person B is a retiree who lost their retirement savings in a Ponzi scheme; they still have a fair chunk of equity left in their house, but they've already got two mortgages Which one do you think is going to have trouble buying food?
Amartya Sen won a Nobel for helping point out how misleading a simplistic analysis can be here.
Seen in this way, statements about redistributing the monetary wealth of the world are pretty much useless, since people spend money in different ways. It may be that everyone holds $52,819 after the great redistribution, but the value of money and price of goods would have to change drastically such that the number is meaningless and not representative of what such a state of the world would be like (we would have to build a lot more big screen tv's, medium income housing, etc. if the plan were taken to fruition, and a lot fewer opulent dwellings in big cities and yachts).
Furthermore, the very wealthy invest and save a lot more (how else would the great wealth accrue if they spend it as quickly as they earn it?). If the wealth of the very wealthy were redistributed we would quickly learn that what really limits the welfare of your average consumer is the production capacity of the economy-- not the total amount of nominal money they hold.