Pengujian Separability dan Penentuan Bentuk Fungsi daiam Sub-sektor Industri Manufaktur Indonesia

A production function is a mathematical relation between input and output. In deriving aggregate production function, economists usually use value-added, which equals gross output minus intermediate input, rather than gross output itself. Input variables are represented by capital and labour. Implicit in this relation is an assumption which states that contributions of capital and labour is separable from contribution of other production factors, intermediate input. Assumption of separability implies that marginal rate of technical substitution between a pair of factors in a group are independent of the amount of factors outside the group. In other words, the magnitude of partial elasticity of substitution between factors inside and factors outside the group are equal for all factors in the group. In case of production process employing both domestic (capital and labour) and imported (raw materials) production factors, separability between domestic and imported factors of production implies that the degree of substitutability between capital and labour is independent of the amount of imported raw materials used in production process. The purpose of this article is to test the separability assumption and to estimate the partial elasticity of substitution between domestic and imported production factors. Using a transcendental logarithmi (translog) production and cost function to a group of medium and large manufacturing industries (2-digit ISIC) for the period 1981 - 1985, the author finds that except for ISIC 33 Indonesian manufacturing industries can be stated in a well-behaved and homothetic translog cost function. The homothetic nature of the function implies that ratio of inputs used is independent of the level of output. The test of separability reveals that all kind of separability assumption have to be rejected. This means that the use of value added in place of gross output should be abandoned. In estimating the partial elasticity of substitution domestic and imported production factors, the author finds that elasticity of substitution between labour and imported raw materials is larger than elasticity of substitution between capital and imported raw materials. This findings imply that an increase in prices of imported factors will stimulate a redistribiftion of income from owners of capital to labour.