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I am but a humble lay person, but I have a question.

I've been thinking about wealth inequality and the structure of capitalism. It seems to me that the pay rate for workers accumulates in a linear way. That is, during year 1 you make X, at the end of year 2 you've made 2X, at year 3 you've accumulated 3X and so on. You may get raises (although probably not so much in our current economic conditions of a labor oversupply) or switch jobs, but if you stayed at the same firm, and conditions didn't change much, then your savings accumulate in a linear way.

But for the business who hires you, they start out with some money, then they use that money to buy raw materials and pay you to convert them into a product, then they take your finished product and sell it for more money than they started with. Let's say they start off with Y, then at the end of a year they have 2Y. But this is an exponential growth: they then start over the process using their 2Y, and can hire twice as many people and buy twice as much raw materials and sell twice as much, to end up with 4Y at the end.

So while worker worth goes up in a linear way, 1X, 2X, 3X, 4X...the employer's worth goes up in an exponential way, 1Y, 2Y, 4Y, 8Y...So in that case, isn't wealth inequality fundamentally built right into capitalism, and therefore we should expect it to pretty much always get worse as time goes on, unless measures are taken to combat or reverse it after the fact? Am I wrong in my analysis here?

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    $\begingroup$ At the end of year 1 why does the worker not invest his savings X? That much at least could grow exponentially. On the other hand what you describe is a known phenomenon described recently in some detail by French economist Thomas Piketty. You can read discussions about his work on this site or on the internet in general. $\endgroup$ – Giskard Apr 18 '16 at 5:53
  • $\begingroup$ @Tobias, there is no reason why firm's growth is exponential. Why do you think that's the case? It possible that the sales Y are only just enough to pay the wages and raw materials for the next year's production that agan brings in Y. It is obviously true that firms can grow, while people can't 'grow'. But even so, firm's growth doesn't necessarily mean the owners wealth is growing exponentially, he could just be getting new investors in, so his stake is shrinking. For most large US firms being run by their founder, the founder's stake has shrunk, EG Larry PAge owns 'only' 17% of Alphabet. $\endgroup$ – Fix.B. Jul 24 '16 at 0:05
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While the owners of a successful business will generally experience an exponential growth compared to their employees, there are some factors to consider:

  1. I find it unrealistic for any business to maintain a growth rate of 100% over many years. (As per the example) You can only sell twice as much if you can find twice as many buyers.

  2. As a business grows, it is likely to start hiring more people and paying them better as they need better skills.

  3. The business also takes the risk. The worker is generally guaranteed his X, but stockholders may have to expect the occasional decline in profit, or even a loss. The company may even go out of business in which case they cannot recover much, if any, of their investment. Those who take the risks, get the reward. Businesses failing also mean that bad investors can often lose fortunes, it's not always a good investment.

  4. There is nothing stopping the employee from owning part of the company by investing in some shares. Then he too may experience this exponential growth. He must also keep in mind, however, that he must now also accept the risks of such an investment.

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First, let us make a distinction between the functional distribution of income, related to how payment goes to factors of production, i.e, labour and capital, via wages and rents, and the personal distribution of income, which refers to how such factor payments are distributed across individuals or households. After commenting about this, we can start to talk about wealth inequality.

If we assume your two unsupported claims are true (namely (i) workers pay increase linearly, and (ii) profits increase exponentially), it would be true that the functional distribution of income would shift in favor of capital. This is, the labour share would fall exponentially to zero.

This however has several problems. First, bargaining by workers (e.g. through unions) would induce them to demand higher wages. Second, if captialists are getting a return higher than the opportunity cost of capital, there is incentive to create more companies. You can imagine many workers turning into entrepreneurs, reducing the supply of labour and thereby leading to higher wages; competition would also increase, reducing (even if not eliminating) "abnormal" profits. Third, such result is historically untrue. The labour share has remained either constant or fallen slowly, but by no means has decreased exponentially. It remains at a 50-60% level or so, depending on the country and definition:

enter image description here

(source here)

Interestingly, the profit share (which is normally included in the capital share, but it need not to be) has remained more or less stable in many countries (see Figure 6 here), but has gone up in the last decades in the US (a country that has experienced a large increase in income and wealth inequality, not the least because a significant fall in the labour share). Yet, this increase has been linear rather than exponential:

enter image description here

(source here)

Regarding the personal income distribution, it is well known that capital income is more unequally distributed than labour income. Therefore, a shift in the distribution of factor income towards capital is to increase inequality at the individual and household level (due to positive assortative mating). Whether this is intrinsic to capitalism or not it's not self-evident, I would say.

Finally, from factor income and personal income to wealth inequality there is a long way. Evidence also indicates that wealth inequality is more unequally distributed than income, and a simple capitalisation approach would prove this. But again, even if it is true that wealth inequality has worsen in the last years, given that the premises by which you started are empirically false. If capitalism is the culprit here, it is for other reasons. If you want to argue that high inequality is intrinsic to Capitalism (like Piketty, 2014 does), there are other arguments (e.g. power, taxation, reserve army of labour, technological change). Yo do not need the one you are mentioning, which seems to be at odd with the evidence.

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