Knowledge spillovers occur when a firm researches a new technology and that
technology is adapted or adopted by another firm, resulting in a social value
of the technology that is larger than the initially predicted private value. As
a result, firms systematically under--invest in research compared with the
socially optimal investment strategy. Understanding the level of
under--investment, as well as policies to correct it, is an area of active
economic research. In this paper, we develop a new model of spillovers, taking
inspiration from the available microeconomic data. We prove existence and
uniqueness of solutions to the model, and we conduct some initial simulations
to understand how indirect spillovers contribute to the productivity of a
sector.