On the Uniqueness of the Representation of Commodity-Augmenting Technical Change

Abstract

Under the assumption of almost homogeneity, which includes homogeneity, it is not possible to assign augmentation factors uniquely and unambiguously to the various commodities. An infinite number of possibilities exist. Thus, under almost homogeneity, one must be cautious in interpreting such statements as the improvement in technology comes primarily from labor augmentation or the rate of augmentation of labor is so many percentage points higher than that of capital. Such statements may be useful in providing a summary description of the technology given the choice of a particular representation. They do not have any intrinsic technological significance in themselves. In particular, they do not necessarily reflect improvements in the quality of specific outputs and inputs. Under the assumption of almost homogeneity but not constant returns, it is not possible to identify even the relative biases of the augmentation factors uniquely and unambiguously. Under the assumption of constant returns, however, it is possible to identify the relative biases of the augmentation factors uniquely and unambiguously if and only if the production function does not satisfy any other generalized Euler equation for an almost homogeneous function. In the three-commodity case, this implies that the production function must be homogeneous of degree one but not Cobb–Douglas. The nonuniqueness in the Cobb–Douglas case is well known.