On the Theory of Effective Demand

In his article "On the theory of effectived emand" (Green,1980, Economic Journal), J. Green deals with a class of stochastic rationing schemes whose distribution as perceived by the individual agent depends on his own action and on the aggregate values of demand and supply only. Under certain assumptions the expectation of such a rationing function is claimed to be linear in each agent's own action, provided there are three or more agents (theorem p. 345). However, as will be shown in this note, the theorem is correct only for four or more agents.