Comment: General Competitive Analysis in an Economy with Private Information
评论Prescott和Townsend（1984）关于私人信息经济中一般均衡的经典论文，指出其例子中随机分配在确定性分配集凸时也能实现帕累托改进，纠正了读者可能产生的误解。
Prescott and Townsend (1984) extend the literature on general equilibrium theory to economies in which agents have private information about their preferences. They examine the extent to which the classical welfare theorems carry over in this environment. The existence of nonverifiable information imposes limits on the economy's contract structure. Contracts cannot be written to require an agent to reveal information unless truthful revelation is optimal. Incentive compatiblity constraints, typically nonlinear, are thereby introduced into the corresponding planner's problem. As a result, the space of feasible deterministic allocations is typically not convex. The authors circumvent this problem by allowing for random allocations, where the planner is choosing over the space of probability distributions of consumption allocations. The incentive compatibility constraints in this space are linear in the planner's choice variables, rendering the set of feasible consumption allocations convex. Some of the attainable random allocations Pareto dominate the set of incentive-feasible allocations attainable via deterministic allocation rules. Randomized allocations have two functions. They convexify the planner's choice set, and they may allow for Pareto superior allocations to be achieved. Prescott and Townsend's presentation may leave readers with the misleading conclusion that the nonconvexity of the choice set under deterministic allocations is necessary for random allocations to be Pareto superior. But, one can attain Pareto superior allocations with lotteries even when the choice set under deterministic allocation rules is convex. This note demonstrates that Prescott and Townsend's own example has this property.