> the economy is growing at rate g and therefore people's other income sources are growing at rate g
Why does a GDP growth rate of g imply that people's other income sources (wages from labor?) are also growing at rate g?
Wage growth in a country depends on confounding factors like worker productivity, relative bargaining power between workers and owners, outsourcing to other countries, automation, and the mix of manufacturing and service jobs in the economy.
It's very possible for the rate of economic growth to be, say, +3% while rate of change in the share captured by workers is flat or negative.
Yes you're 100% spot on. That other income sources and in particular labor income grow at g is just an assumption in Piketty's theory.
If labor income is growing at a different rate, the "correct" version of the theory should have r-g(labor_income). This would probably give even more extreme because it seems like in many countries the growth rate of labor income is less than the growth rate of the economy, i.e. r-g(labor_income)>r-g(GDP).
If you're interested in the dynamics of the economy and distribution if different variables grow at different rates, see here see e.g. http://www.princeton.edu/~moll/UG-slides.pdf
Why does a GDP growth rate of g imply that people's other income sources (wages from labor?) are also growing at rate g?
Wage growth in a country depends on confounding factors like worker productivity, relative bargaining power between workers and owners, outsourcing to other countries, automation, and the mix of manufacturing and service jobs in the economy.
It's very possible for the rate of economic growth to be, say, +3% while rate of change in the share captured by workers is flat or negative.