The Habakkuk hypothesis in a neoclassical framework

We present a new way to picture technological change in an otherwise standard Ramsey framework. Technological change takes the form of alterations of the production function itself, rather than changes in total factor productivity. These changes can take two directions that we dub respectively ‘complementation' and ‘substitution'. Complementation results in a production function that is superior for lower values of capital, while substitution results in a production function that is superior for higher values of capital. Under the most general conditions, when the agent is initially at steady state, both options bring strictly positive utility gains to the agent. We analyze sequence of steady states with exogenous and endogenous direction of technological change. With exogenous growth, we prove that when the production functions are Cobb-Douglas or CES (with the same elasticity of substitution), output and consumption grow asymptotically at a common rate and the capital share tends to one under continual substitution; while continual complementation makes output and consumption converge to a common limit and the capital share tend to nil. With endogenous direction of technological change and under the most general conditions, the agent has a bias towards complementation which brings quicker gains than substitution. We assume that the production functions are Cobb-Douglas and that utility is logarithmic. Then, when the potential rate of complementation is strictly greater than the potential rate of substitution, the labor share oscillates around some endogenous long-run value, determined by the rates of complementation/substitution and by the impatience rate. This growth regime reproduces the Kaldor facts.