As I have been reading Piketty, I have tried to understand his thesis by examining my own experience. He argues that the ratio of capital to national income (GDP minus depreciation) will increase and that returns on capital will remain relatively constant. As a result, capital returns will command a higher percentage of GDP over time and wages will command lower and lower percentages. This will tend to feed on itself because capital is concentrated in the hands of the wealthy so that the wealthy's share of total income (capital plus wages) will increase leading to the reinvestment of ever higher percentages of GDP each year which will lead the ratio to increase to ever higher levels.
Piketty correctly measures capital by current fair market value (use of original cost would create all sorts of problems). As I think through my own experiences, I have begun to realize that a major factor in businesses I have been involved with has been technological obsolescence. While Piketty takes account of traditional depreciation in the form of wear and tear on equipment and other forms of capital, he does not seem to come to grips with technological obsolescence. In my lifetime, I have seen entire businesses - like video cassette rentals and dial up internet - emerge, expand and disappear. My wife worked for a video production company whose major problem was that the equipment it bought lost virtually all of its value after three or four years due to the availability of better and less expensive new products. Law firms I worked for replaced word processing equipment and computers on a regular basis. We are all familiar with Moore's Law and the tremendous advances in computer technology it has permitted. The dark side of this trend is that there has been enormous turnover and lots of equipment has to be scrapped shortly after it is unpacked.
I don't think Piketty includes this dynamic in his analysis. And - using his model - increases in capital investment may not increase the ratio of total capital to GDP as predicted. This is because new capital is likely to be deployed in R&D and new product development and deployment. The more new capital that is invested, the faster the rate of technological obsolescence. If we calculate total capital by estimating fair market value, then new capital will tend to destroy old capital through technological obsolescence and an equilibrium may be attained.
I have to think this through some more but it is definitely one possible hole in Piketty's analysis. It may not invalidate his conclusions but it may temper some of the impacts.