Introduction

The price dual in the Leontief input-output system has played the Cinderella role in practical applications of the model. This results largely from the necessity of using the US dollar as the homogeneous unit of aggregation for inputs and outputs of sectors containing quite diverse products. Prices are assumed fixed and are used, therefore, to convert naturally calibrated input coefficients to cents' worth of input per dollar's worth of output, effectively neutralizing the price dual as an analytical tool. The “dollar's worth” is a homogeneous physical unit for all goods as long as prices do not change. Of course, the choice of this unit masks the heterogeneity of the natural physical units of the sectoral outputs, given the wide variety of products aggregated in the sectors of even the largest input-output models. Constant prices are “virtual” prices of a conglomerate of disparate sectoral products. But, in empirical and theoretical applications of the output primal, the values of outputs and inputs are meaningful units in short-run periods of stable prices and product mixes. They are operationally interpretable.

This analytical device can be used only if the gross output primal model is independent of the price dual. Constant returns to scale, perfect complementarity of inputs in infinitely elastic supply, and exogenization of the bill of final goods achieve this prerequisite. Gross output vectors cannot affect prices and the “dollar's worth” metric of the output primal is defensible.