Hicks neutrality and homotheticity in technologies with multiple inputs and multiple outputs

摘要

We analyze two popular notions in production theory: the notion of Hicks neutral technical change and the notion of homothetic technology. Both of these notions are characterized by the radial expansions or contractions of the relevant isoquants, yet in different ways. In the case of multiple-input and multiple output, an isoquant is characterized by either the input or output combinations. Thus, for each of these notions, there are two types of conditions: one is based on the input isoquants and the other is based on the output isoquants. We show that for each notion, these two conditions are equivalent under the alpha-returns to scale technology. From this result, we also derive several implications for the properties of well-known productivity indexes, such as the Malmquist productivity index and the Hicks-Moorsteen productivity index. (C) 2020 Elsevier Ltd. All rights reserved.