Linearity and Separability of Regional General Equilibrium Input/Output Models Under Static Cobb-Douglas Assumptions

Abstract

El-Hodiri and Nourzad have pointed out that an Input-Output analysis of industrial composition can be justified by assuming a generalized Cobb-Douglas production function. Their approach is a substantial improvement over the traditional fixed-coefficients production function in several respects, which are summarized in the Introduction. This paper extends their insight by giving the Cobb-Douglas Input-Output analysis for a complete static general equilibrium model of a regional economy. If all demands are determined by Cobb-Douglas production functions or utility functions (or have unitary price elasticities), and if all supplies are constant cost (or perfectly elastic), then the following results hold:

1. All relations between dollar flows are linear. (This fact leads to an input-output analysis, with dollar flows taking the place which is occupied by quantity flows in the traditional Leontief analysis.)

2. All relationships between log-prices are linear. Consequently, the general equilibrium model can be completely linearized.

3. The price relationships are completely separable from the dollar flow relationships. In other words, economic flows measured in nominal terms are completely independent of changes in relative prices over time. (Of course, real variables do depend on relative prices, and nominal variables do depend on the general price level.) This fact provides a rigorous rationale for input/output projections which ignore relative price effects.

A comparison is then made to a similar separability result under fixed-coefficient assumptions. It is pointed out that Cobb-Douglas assumptions lead to complete linearity and separability under more general endogeneity conditions than fixed coefficient assumptions.