Input Price, Quantity, and Productivity Indexes for a Revenue-Constrained Firm

Abstract

This paper develops the micro-economic theory of input price and quantity indexes and input-based productivity indices for a revenue-constrained firm. Generally speaking, a firm transforms inputs into outputs. When priced, outputs generate revenue and inputs incur cost. It is customary to (partially) model the economic behavior of a firm as cost minimization. Then the input price index is calculated as the ratio of minimum costs under two different price regimes. However, in doing so, one has to condition on certain output variables. One route is to take the output quantities as the conditioning variables. The firm’s objective is then conceived as the production of a vector of output quantities with minimal cost. This leads to a theory of input price indexes which is, except for the dimension of the vector of conditioning variables, isomorphic to the theory of the cost-of-living index for consumers.

The author thanks Robert G. Chambers and R. Robert Russell for their comments on a previous version. The views expressed in this paper are those of the author and do not necessarily reflect the policies of Statistics Netherlands.