These implications of the model are taken up briefly in the final sections of the
paper. Section 3 describes the functional forms that are used to describe the preferences
and the technology for the model. It defines an equilibrium that allows for both
monopolistic competition and external effects arising from knowledge spillovers. Section 4
offers a brief intuitive description of a balanced growth equilibrium for the model. Section
5 formally characterizes the equilibrium and compares it to the social optimum that could
be achieved by an omniscient, omnipotent planner. The paper closes with a discussion of
the implications of the model concerning trade, research, and growth. Algebraic details of
the derivations are placed in an appendix.