A note on variable markup, knowledge spillover, and multiple steady states in the variety expansion model

This paper incorporates the variable elasticity of substitution preferences in the variety expansion model developed by Grossman and Helpman [(1991) Innovation and Growth in the Global Economy, MIT Press]. There exists a balanced growth path when the elasticity of substitution is constant with knowledge spillover. When the elasticity of substitution is variable and the knowledge spillover is sufficiently small, a unique and stable steady state exists. When the knowledge spillover is sufficiently large, the steady state is unique and unstable. When the size of the knowledge externality is moderate, multiple equilibria exist.