Increasing Returns to Scale and Welfare: Ranking the Multiple Deterministic Equilibria

We consider a real business cycle model with a productive externality and an aggregate non- convex technology set µa la Benhabib and Farmer embodying capacity utilization, which exhibits indeterminacy of the steady state and multiplicity of deterministic equilibria under plausible values of the increasing returns to scale. The aim of the paper is to rank these different equilibria according to the initial value of consumption using both a linear-quadratic approximation, extensively explained by Benigno and Woodford [2006a, 2006b], and simulation methods. We study the implications of such a ranking in terms of smoothness of the welfare-maximizing trajectory and show that the welfare- maximizing consumption and labor paths are all the smoother since the level of increasing returns is low. At last, we show that this solution provides a good benchmark for judging the desirability of the stabilization policy proposed by Guo and Lansing [1997].