How many robots should we invest? A theoretical analysis with two-sector production facility

Abstract

With the ascending of AI, robots have become important production factors and have been put into production on a large scale. In this paper, we build up a two-sector production model considering the robots investments, in which the manufacturer decides how many robots to invest. We find that the optimal robots quantity is increasing in the capital. It is decreasing in the variable costs and concave in the quantity of labour who can be replaced by robots easily. Further, we analyse the impacts of robots investments on workforce wages. As the number of robots increases, the wage in the tradition production sector increases while the wage in the production sector with robots decreases, which means that the wage gap between these two sectors deepens. We provide more managerial insights not only from the perspective of the two-sector manufacturer but also from the point of view of a social planner.