Unemployment and Innovation

This paper analyzes equilibrium, dynamics, and optimal decisions on the factor bias of innovation in a model of induced innovation. In a model with full employment, we show that (a) if the elasticity of substitution is always less than or greater than unity, there is a unique steady state equilibrium; (b) if the elasticity of substitution is less than unity, the steady state is stable, but convergence is oscillatory; (c) if the elasticity of substitution is greater than unity, the steady state is a saddle point; and (d) if the elasticity of substitution is less than unity for both high and low effective capital labor ratios but greater than unity for intermediate values, then there can be multiple steady states. In a model where efficiency wages lead to equilibrium unemployment, we show that if the elasticity of substitution is less than unity, there will be a bias towards excessive labor augmenting innovation, resulting in too high unemployment, with convergence to the unique steady state being oscillatory, rather than monotonic. Similarly, if the elasticity of substitution between skilled and unskilled labor is less than unity, and there is efficiency wage unemployment for unskilled labor only, there is will be excessively skill-biased innovation. This paper provides an alternative resolution to the Harrod-Domar conundrum of the disparity between the natural and warranted rate of growth to that of Solow, with strong policy implications, for instance, concerning the effects of income distribution and monetary policy both in the short run and the long.