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Currently I am reading Samuelson's "Economics" (in a German translation). I found it very enlightening and especially the chapters on the equality of 'savings' and 'investment' in domestic-product.

After introducing this as a bookkeeping equality in discussing the GDP in general, there follow some chapters in which the fact is elucidated, that for a given GDP there is an optimal amount of saving, where the total investment equals the total savings. Not being in that equilibrium either incurs depression, unemployment (when saving is too high and consumption too low) or inflation and overproduction (when investment overshoots).

Now my question: What is the current economic view on the extremely growing (private) wealth (of a small minority of people) in the developed western countries and those countries which are about to reach their economic standard (China, India, South-East-Asia). Is this simply a counterbalance to investments in production goods (new factories in China and Asia, internet-infrastructure around the globe, new investments in the energy sector for wind and solar power, which are quite expensive and other investments (which ones?))? In this case one might see this as a parallel to the enormous investment in railroads and oil pipelines in the 19th century which at that time made their owners rich but also provided a counterbalance of goods to that wealth.

Or are we watching a beginning oversavings crisis in which the wealthy can not invest their enormous wealth usefully any more, because of non-existing profitable investment possibilities? So should the wealthy consume more to keep the global economy running (moon flights, hotels on mars, more private jets and yachts)?

Or is the excessive rise in stock prices the outlet for this oversaved wealth?

Besides direct answers I would also be interested in literature recommendations for that problem, either in book form or on the internet - my edition of Samuelson's book is from the 60s. (Note: I am not an economy student but a mathematician with an interest in economic questions).

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