The Economics of Superstars: Reply
回应Bowbrick的评论，通过一个家庭消费差异化产品的模型，分析集体决策与个人决策在规模经济下的权衡，说明集体选择可能促进平庸化，但并非必然。
Peter Bowbrick raises some interesting issues that deserve elaboration. Consider a differentiated product with attribute q that sells for p(q) per unit in the market. Assume an economy of scale in consumption of a particular type of good among a small group of buyers, a family, for example. Positive consumption of that variety requires incurring a fixed set-up cost k, independent of the quantity consumed. The fixed cost is incurred every time a member chooses an independent variety. For example, the location of consumption may be away from home. Then k represents the cost of transport in an auto with excess capacity. More generally, k derives from scale economies in home production, for which the good in question is intermediate product. Several types of outcomes are possible. Each member can go it alone and make a purely private consumption decision. This has the virtue of allowing members to consume their most preferred varieties, but entails duplication of set-up costs. Alternatively, the group may make a collective decision and choose a single variety that is consumed by all members.' The group decision is equivalent to choosing a public good. The variety actually chosen compromises among the most preferred choices of each person, but exploits the scale economy and allows greater consumption of other goods as compensation. Some possibilities are illustrated in Figure 1 for a group of size 2. Bid-price functions (price-attribute indifference curves) for both members are shown by the curves labeled 0' (the utility direction is southeast). The opportunity locus is k + p(q) when consumption decisions are made independently. The optimum good for each person is characterized by equality between marginal rates of substitution between q and other goods and the incremental cost of q for each person: d8O/dq = p'(q), i = 1, 2 (points a, and a2 in Figure 1). Alternatively, the per capita opportunity locus becomes (k/2) + p(q) when members choose a single variety and share fixed costs. The figure illustrates a case where a public decision Pareto dominates individualistic ones. This happens whenever the per capita group constraint cuts through the shaded area in the figure, the locus of possible Pareto-improving group allocations relative to independent decisions at a, and a2. All points between b, and b2 raise utility of at least one member without lowering utility of the other. All these points potentially satisfy a Samuelsonian public goods condition, (l/n)Ei dO'I/dq = p'(q), depending on welfare weights among group members. For example, both persons achieve larger utility at point c than at their mostpreferred independent locations. Cost savings due to exploiting group scale economies more than compensate for compromising on a variety somewhere in the middle. More structure is needed to nail the precise location of the compromise, say, a Nash bargaining game or an effectively altruistic head. The resolved preference structure might replace my original specification of preferences, but the essential argument regarding concentration and skew of market shares and reward among sellers is otherwise not affected. Nevertheless, the point is clear that small collective decisions of this sort promote a tendency toward mediocrity of choices within groups, in the literal sense of the median. This illustrates one aspect of the blandness of goods to which Bowbrick refers, but is not necessarily assured, because group decisions need not dominate individualistic ones. Experimentation with the figure reveals that a public goods decision is more likely: (i) the larger the scale economy; (ii) the greater the uniformity of preferences; *University of Chicago and National Opinion Research Center. I am indebted to the National Science Foundation for financial support. 'Coalitions of various subgroups should be considered, but space does not permit that development here.