This paper studies collective contests with endogenous cost sharing, general effort costs and intra-group heterogeneity of prize-valuation. Our objective is to clarify the relationship between cost sharing, intra-group heterogeneity within the competing groups and the elasticity of the marginal...

We incorporate a participation decision in a standard New Keynesian model with matching frictions and show that treating the labor force as constant leads to incorrect evaluation of alternative policies. We also show that the presence of a participation margin mitigates the Shimer critique.