Convex and nonconvex nonparametric technologies have been applied to estimate plant capacity utilization. However, they face challenges in capturing the production characteristic that involves the simultaneous consideration of increasing, constant, and decreasing marginal production rates along the production surfaces, which may be inconsistent with the standard microeconomic production theory. This inconsistency raises concerns regarding the potential bias of plant capacity utilization estimates. Thus, this paper introduces a new plant capacity utilization measure based on the piecewise Cobb–Douglas technology, aligned with the standard microeconomic production theory. This measure is defined using two multiplicative directional distance functions with optimal endogenous directions. It can be interpreted by the Euclidean distance between two points associated with optimal capacities and the Euclidean norm of one optimal endogenous direction vector. The new measure captures potential production slacks to measure plant capacity in the sense of Pareto–Koopmans efficiency. It also suggests a remedy of non-existence of a maximal plant capacity in the Cobb–Douglas function by utilizing the piecewise Cobb–Douglas technology. The proposed plant capacity utilization measure is validated using a secondary dataset of 19 Chilean hydroelectric power plants.

中文翻译：

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采用分段柯布-道格拉斯技术的工厂产能利用率：定义和解释

凸和非凸非参数技术已应用于估计工厂产能利用率。然而，他们在捕捉生产特征方面面临挑战，其中涉及同时考虑沿生产面的边际生产率的增加、恒定和减少，这可能与标准微观经济生产理论不一致。这种不一致引起了人们对工厂产能利用率估计潜在偏差的担忧。因此，本文介绍了一种基于分段柯布-道格拉斯技术的新工厂产能利用率测量方法，与标准微观经济生产理论相一致。该度量是使用两个具有最佳内生方向的乘法方向距离函数来定义的。它可以通过与最佳容量相关的两点之间的欧几里德距离和一个最佳内生方向向量的欧几里德范数来解释。新措施捕捉了潜在的生产松弛，以帕累托-库普曼效率的方式衡量工厂产能。它还建议通过利用分段柯布-道格拉斯技术来解决柯布-道格拉斯函数中不存在最大设备容量的问题。使用 19 座智利水力发电厂的辅助数据集验证了拟议的工厂产能利用率指标。