Technical Change, Variable Elasticity of Substitution and Economic Growth

We incorporate a variable elasticity of substitution production function into an overlapping generations model à la Diamond (1965). We show that a certain parameter in the production function is a source of biased technical change is a crucial determinant of the economy's growth dynamics. For positive values of this parameter, which lead to an elasticity of substitution between capital and labour which is greater than 1, the economy always reaches a unique and stable steady state which is similar to the conditional convergence in the standard Solow growth model. For negative values of this parameter, which yield an elasticity of substitution below 1, the economy could either fall into a poverty trap; or display two steady states, of which one is stable while the other is not, which could, depending on the value of the initial capital stock, potentially result in divergence towards unbounded growth. These different outcomes are consistent with the observed diversity in international growth experiences. The capital biased technical change generated by a higher value of this parameter improves productivity in steady state, but causes an exacerbation of intergenerational inequality