Inequality, Welfare, and the Cost of Coordination Failure

Coordination failures arise when society gets stuck in a “bad” equilibriumwhen a Pareto superior one exists. How does wealth inequality affect coordinationfailure? This paper models a large, heterogeneous society where individuals’ consumptionsavings choices are influenced by investment spillovers. The cost of coordination failure(CCF) in this society is the welfare difference between the “good” (high investment) andthe “bad” (low investment) equilibrium. We provide natural conditions under which theCCF is increasing under mean-preserving spreads in wealth inequality.We also establish a trifurcation result in which high enough inequality creates acoordination failure where none had existed. Starting from a stable equilibrium whereinvestment is unaffected by inequality, the equilibrium becomes unstable as inequalityincreases, and two other stable equilibria — a good one and a bad one — emerge. In thebad equilibrium, inequality always reduces both aggregate investment and aggregatewelfare. In the good one, inequality is always investment-enhancing. Furthermore,there is a range of parameters where inequality is actually Pareto-improving in the goodequilibrium. In all cases, the welfare gap (the CCF) between the two equilibria increaseswith inequality