Inequality and Inefficiency in Joint Projects

A group of agents voluntarily participates in a joint project, in which efforts are not perfectly substitutable. The output is divided according to some given vector of shares. A share vector is unimprovable if no other share vector yields a higher sum of payoffs. When the elasticity of substitution across efforts is two or lower, only the perfectly equal share vector is unimprovable, and all other vectors can be improved via Lorenz domination. For higher elasticities of substitution, perfect equality is no longer unimprovable. Our results throw light on the connections between inequality and collective action.