A Newfound Steady State in Standard Uzawa-Lucas Model with Externality

We follow Xie (1994) and impose a restriction on the model's parameters to show that there are two stable steady states in standard Uzawa-Lucas model with moderate externality. Besides that the unique dynamic path converging to the well-known steady state, there also exists a continuum of dynamic paths converging to the newfound steady state, in which the fraction of human capital allocated to the final goods sector tends to zero. The initial relative price of educational goods and services in terms of final goods determines which dynamic path the economy should follow. Although a continuum of dynamic paths converging to the newfound steady state definitely violates the transversality condition, at least one of them is an equilibrium path. Therefore, the present paper does provide another counterexample to transversality condition for infinite horizon problems