Output scaling in a cost function setting

✍ Scribed by Rolf Färe; Thomas Mitchell

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 464 KB
• Volume: 3
• Category: Article
• ISSN: 0895-562X
• DOI: 10.1007/bf00163436

✦ Synopsis

A significant result in production theory is that even under a very weak condition on the technology, the cost function is well defined and linearly homogeneous in factor prices. We could term this homogeneity a "scaling law," for an equiproportionate scaling of all factor prices results in an identical scaling of the value of the cost function. The purpose of this paper is to determine sets of conditions under which an analogous result may hold for the output variable in the cost function. Our analysis initially focuses on the cost function of a multioutput technology so that the output variable in the cost function is vector-valued. The results we obtain are that some "output-scaling laws" exist if and only if the underlying technology is ray-homothetic. In the final section we consider the meaning of the results for the single-output case.