Abstract: A group of agents share a one-input one-output convex technology for producing a public or private good. The agents must agree on a level of output to produce and a way to allocate both the output (in the private good case) and the costs of production. The agents would like everyone's utility level to fall between some lower and upper bound. We consider two such bounds: the stand alone bound and the unanimity bound. An agent's stand alone utility level is the utility he would receive if he had free access to the technology by himself. An agent's unanimity utility level is the utility he would receive if everyone else had the same preferences as him and the agents split the output (in the private good case) and the cost of production equally. Normally there is some symmetry in the strength of an upper bound vs. the strength of a lower bound; in some situations the upper bound is more relevant to the allocation problem, while in other situations the lower bound is more relevant. However, we show that the unanimity bound is stronger than the stand alone bound; the unanimity bound always has an impact on the production decision, while the stand alone bound does not.

　　Subjects: PRODUCER cooperatives; INPUT-output analysis; COSTS, Industrial; COMMERCIAL agents; DECISION making; Agents and Managers for Artists, Athletes, Entertainers, and Other Public Figures; ASSIGNMENT problems (Programming)