Balanced growth and degrowth with human capital

Abstract

In a simple discrete-time version of Lucas (1988) we find that the Balanced Growth Path (BGP) is always the unique optimal planner’s solution: with linear or strictly concave production functions, with unbounded utility functions, with or without human capital depreciation. When the ”speed” of human capital accumulation is high, the optimal working time is constant and below its upper bound. Capital grows at a constant factor, but degrowth is also possible when this factor is less one (under positive capital depreciation). When this speed is low, optimal working time is at its boundary and capital declines at its depreciation factor (degrowth).