Growth and Technical Change: A Smithian Approach

This paper proposes a model of technical change based on Adam Smith's analysis of the role of division of labor in economic growth. Technical change is the discovery of new capital goods which help workers or even replace workers performing precise tasks. As a consequence, the number of opportunities of innovation is an increasing function of the number of tasks performed in the economy. We first model division of labor within firms and then model the research sector. The probability of innovation is not only a function of the quantity of resources allocated to the research sector, but also of the total number of tasks. We show that this theory yields a growth model without scale effects. The market equilibrium yields an optimal equilibrium growth rate, but a sub-optimal transitory dynamic. This sub-optimality can take two forms : either too many researchers and an internal division of labor too small an internal division of labor, or too few researchers and an too high an internal division of labor. We show that the long run growth rate depends on the assumption made on the evolution of the number of tasks during economic development. If the number of tasks increases in the long run, a positive effect of the diversity of capital goods on productivity is not necessary to obtain a positive per capita growth rate.