In his article 'On the theory of effective demand' (Green, i 980), 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 forfour or more agents. With respect to the critical case of three agents Green himself presents a counter-example (example I, pp. 348/9). As the rationing rule of this example is not linear, Green concludes that it does not fulfil the assumptions of his theorem Yet it does, which implies that Green's proof cannot be viable. Therefore a new proof of the (altered) theorem must be given, which is done in what follows. Without loss of generality, let aggregate demand and supply Z+, Zbe fixed such that Z+ > Z-. Consider a vector z (zl, ..., z1) of individual demands and supplies, such thatzi > ofor i = i) ...,n, zi o can be written zi = Ai Z+, where the Ai's are non-negative weights such that = 1Ai = i. Feasibility, i.e. EqiS(zi, Z+, Z-) = X-, anonymity and continuity of E;i imply a continuous function f: [o, i] [o, i] defined by Ec;b(Ai Z+, Z+, Z-) = f(Ai) Xfor all i. f has the property that for all A1, ..., An such that = 1Ai = i, `lf(Ai) = i. Because of voluntary trade,f(o) = o. It is immediate that Eqi is linear in zi (in the positive half-line) if and only iff is the identity map. To see this, notice that by anonymity,