Innovation Dynamics, Patents, and Dynamic-Elasticity Tests for the Promotion of Progress

Abstract

This article develops a differential-equation model for innovation dynamics that significantly resembles a Newtonian model for motion in the presence of air resistance. The model generates a diverse array of trajectories for technological progress as a function of time. Among these, trajectories featuring linear or exponential growth are only special or even exceptional. In contrast, under a broad array of circumstances, the model generates power-law behavior: i.e., yields a prediction that technological progress will grow approximately like the quantity t raised to the power z, where t is a measure of elapsed time and z is a positive exponent. The model also suggests that, under various circumstances, whether a given incremental policy change accelerates or decelerates technological progress can be substantially determined by a “dynamic-elasticity” or “double-ratio” test involving comparison of percentage changes in model parameters. The existence of such double-ratio tests might mean that patents’ effects on innovation are even more sensitive to technologic and industrial circumstance than is commonly appreciated.

Empirical study of U.S. patent numbers supplements the theoretical work described above. Numbers of issued patents are sometimes taken as a crude measure of technological progress. In light of the supralinear-power-law behavior frequently predicted by this article’s model, it might be significant that growth in the cumulative number of U.S. patents appears commonly to correspond to a supralinear power law.