If a firm is both technically and allocatively inefficient its cost will increase. Since allocative inefficiency results from misallocation of inputs, cost of allocative inefficiency (CAI) can be obtained if the input over(under) use can be analytically derived. This is only possible for production functions for which input demand functions can be explicitly derived. Schmidt and Lovell (1979) addressed this problem using a Cobb-Douglas production function with the cost minimizing behavior. In this paper, we propose a mixture of Cobb-Douglas (CD) production functions to get a more flexible system that allows obtaining costs of technical and allocative inefficiency analytically. Inflexibility of the CD function is addressed by making its parameters (input elasticities) functions of environmental/predetermined variables. Our empirical evidence show considerable heterogeneity in parameters and multimodal distributions of many quantities of interest, which support our formulation.

如果一家公司在技术上和配置上都效率低下，其成本将会增加。由于分配效率低下是由于投入的分配不当造成的，因此，如果可以分析得出投入的过度使用（不足），则可以获得分配效率低下（CAI）的成本。这仅对于可以明确导出输入需求函数的生产函数才有可能。Schmidt和Lovell（1979）使用Cobb-Douglas生产函数解决了这个问题，并降低了成本。在本文中，我们提出了混合Cobb-Douglas（CD）生产函数的方法，以获得更加灵活的系统，该系统可以分析性地获得技术和分配效率低下的成本。CD功能的不灵活性可以通过使其环境参数/预定变量的参数（输入弹性）函数来解决。