Disembodied Technical Change in a Two-Sector Model

Abstract

There are two aspects of technical change that are essential for a description of the behavior of an economy over time. These are the rate of technical progress and the bias of the change. For a twice-differentiable production function, F(K, L, t) homogeneous of the first degree, with positive marginal products and a diminishing marginal rate of substitution everywhere, where K is capital; L, labor; t, time; these two aspects can be characterized by two indices:2 $$T = \frac{{{F_t}}}{F} = \frac{{K{F_{{K^t}}} + L{F_{{L^t}}}}}{{K{F_K} + L{F_L}}}$$ ((1)) $$D = \frac{{\partial \left( {{F_K}/{F_L}} \right)}}{{\partial t}}/\frac{{{F_K}}}{{{F_L}}} = \frac{{{F_{{K^t}}}}}{{{F_K}}} - \frac{{{F_{{L^t}}}}}{{{F_L}}}.$$ ((2))