The Economies of Massed Reserves
指出大数定律不能解释集中储备的规模经济，而是用排队模型计算其预期经济性，并给出量化方法，发现某些情况下经济性超过23%。
The economy of massed reserves, first mentioned by E. A. G. Robinson (1958, pp. 26-27), is now firmly established in industrial organization literature as an example of a potential plant-level scale economy. The massing of reserves results in a savings in proportion of required reserves to expected output as scale of a facility increases. Examples of such reserves are bank tellers, specialized tools and equipment, repairmen, inventories, spare parts, and checkout lines. The potential economies from massing reserves are dependent on underlying stochastic processes governing supply and/or demand of service provided. Theoretical justification for economies of massed reserves has usually been based on an appeal to law of large numbers. For example, Donald Hay and Derek Morris wrote the law of large numbers makes number of breakdowns more predictable in a plant using a large number of machines, so that number of stand-by maintenance staff need not be increased in proportion to size (1979, p. 44). This paper demonstrates that law of large numbers does not provide a theoretical explanation of massed-reserves scale economies. Instead, it is shown that expected economies of massed reserves can be calculated from steady-state properties of well-known queuing models. Queuing models apply to any case where a servicing input is held in reserve to cope with stochastic nature of market or production process. In addition, a method for quantifying expected economies of queuing processes is developed. The magnitude of these expected economies is shown to be significant and calculable. For example, expected economies inherent in a widely applied queuing model are shown to exceed 23 percent in some cases. Section I establishes irrelevance of law of large numbers as a theory of scale economies. Section II provides a formal method for determining scale economies inherent in most often mentioned massed-reserves example: machine repair. Section III shows that same method can be used to calculate scale economies for remaining massed-reserves examples: specialized repair tools and equipment; checkout counter clerks, bank tellers, and other service personnel; capacity; and inventories and spare parts. In addition, it is demonstrated that same method can be used to calculate scale economies for some multiproduct operations.