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Traditionally the role of separability in system of demand functions has been the subject of numerous analyses, with few directed toward systems of supply functions. Separability an important property of production, confirms the existence of aggregation in variables and the decentralization of decision making. Separability implies that marginal rates of substitution between pair of inputs (outputs) in the separated group are independent of the levels of inputs (outputs) outside the group.
Weak separability in the estimation of a systems of demand functions was first explored by Sono(196 1) and Leontief(1947) to deal with aggregation problems in consumer and producer theory respectively. Berndt and Christensen(l973) employed the cost function to test the existence of capital aggregate assuming a labor aggregate in US manufacturing industry. In another study, they test the existence of a labor aggregate assuming a capital aggregate. Woodland(1976) employed a variable profit function and retested the hypothesis employing a translog production function to investigate the permissibility of aggregation(separabi1ity) of inputs. Recent work has been carried out in regards to the separability aspect but no aggregation (separability) test has been performed for both inputs and outputs in the primal approach.