Econometrica: Nov, 1976, Volume 44, Issue 6
Capital Aggregation in a General Equilibrium Model of Production
Murray Brown, Winston W. Chang
In this paper, we focus on capital aggregation in a general equilibrium model of production. Various potential aggregates involving intrasectoral and intersectoral, as well as full aggregation are discussed in connection with the various aggregation procedures. It will be shown that the satisfaction of the Gorman conditions allows for full aggregation within a general equilibrium model of production. We shall derive new conditions for aggregation using a composite commodity approach that appears to be somewhat weaker than the conditions associated with restrictions-on-functional-form theorems. Our main conditions relate to the equality of sectoral labor shares. The data for testing those conditions appear to be readily available. It is shown that the equal labor share condition can be applied to models with joint and nonjoint products. In addition, the conditions for aggregation are derived for a model with many primary inputs and also for a model with unequal rates of depreciation. Two sections are devoted to the main correspondences between certain aggregation procedures in the literature from the point of view of a general equilibrium model. The implications of our analysis for the form of the unit cost function and of the aggregate production function are discussed. In particular, if our aggregation condition holds, then the aggregate production function can be Cobb-Douglas, if one of the sectoral forms is also Cobb-Douglas, irrespective of the forms of the other sectoral production functions.