The Elasticity of Scale and the Shape of Average Costs
区分了两种规模报酬概念，指出沿扩张路径的规模弹性变化决定平均成本曲线形状，而非沿射线变化，并证明文献中关于射线行为的假设与U形平均成本曲线无关。
different concepts of returns to scale. The first, which is most widely used for defining returns to scale,' is the relative increase in output as all input quantities are increased proportionally along a ray through the origin. The second, which is the more relevant concept for micro-economic analysis, is the increase in output relative to costs for variations along the expansion path where input prices are constant and costs are minimized at every output.2 As it turns out, these two concepts yield equal measures for the Elasticity of Scale3 e at every minimum-cost point in the input space. However, the change in E with output is generally different for the two concepts,4 since expansion paths do not coincide with rays, unless the production function is homothetic.5 But it is the change of E along the expansion path-and not along the raywhich determines the shape of the average cost curve (AC), and which is therefore relevant for the analysis of firms and industry behavior under competition.6 These relations are stated and analyzed below. It is shown that assumptions made in the literature7 which are related to the behavior of E along rays, or to the slope of the technically optimal surface (where returns to scale are locally constant), are irrelevantbeing neither necessary nor sufficient for implying classical U-shaped average cost curves. The following definitions and results are used here: