The Input Side of the Firm: Direct Functions and Indices
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The central behavioral assumption in this chapter is that the firm minimizes the cost of its input conditional on exogenously determined quantities of output. Consequentially, the first section recalls some basic facts about the cost function. Thereafter three efficiency measures will be discussed. The second section introduces the input price index, discusses its properties, and derives several nonparametric approximations. The third section briefly considers the concept of a marginal input price index. The fourth section is devoted to the input quantity index, which is based on the input distance function. Section 3.5 discusses the relation between the input price index and the input quantity index. In section 3.6 we turn to the input based productivity index numbers. In order to derive nonparametric approximations for these indices it appears necessary to supplement the basic assumption by an assumption concerning profit maximization. In section 3.7 we show why certain assumptions are necessary in order to arrive at empirically computable expressions for the productivity index numbers. We also link these index numbers to measures of total factor productivity change.
KeywordsProductivity Index Input Price Shadow Price Index Number Output Quantity
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