Automation Technology, Economic Growth, and Income Distribution in an Economy with Dynasties and Overlapping Generations

This study presents a growth model with automation technology that considers two classes (workers and capitalists) who conduct dynamic optimization in different manners. In addition to two production factors, labor and traditional capital, automation capital is included as the third production factor. Long-run dynamics of input ratios of production factors, income distribution, and per capita output growth are investigated. Regardless of the size of workers' discount factor, workers' own traditional capital has no transitional dynamics and stays constant. When capitalists' discount factor is large, in the long run, the growth rate of per capita output is positive and constant: endogenous growth is obtained. In this case, income gap between workers and capitalists continues to increase through time. When capitalists discount factor is small, two different cases appear. First, when the initial value of traditional capital is large, both capitalists' own traditional capital and automation capital converges to constant values. In this case, income gap between workers and capitalists converges to a constant value. Second, when the initial value of traditional capital is small, capitalists' own traditional capital converges to a constant value while capitalists' own automation capital approaches zero. In this case, income gap between workers and capitalists converges to a constant value. When automation capital becomes zero, after then, the dynamical system switches to a dynamical system without automation capital.