Cost shares, output elasticities, and substitutability constraints

The equilibrium conditions for an economic system that produces output with several factors of production and which is subject to technological constraints are derived. Optimization of either output minus cost or integrated utility yields the conditions that output elasticities must be equal to a modification of the usual factor cost shares, where shadow prices due to the constraints add to factor prices. In a model, where capital, labor and energy (exergy) are the factors of production, the technological constraints are identified as limits to capacity utilization and automation. The shadow prices depend on the output elasticities. These elasticities are determined for Germany, Japan and the USA by econometric estimations of energy-dependent production functions that are derived from the twice differentiability requirement and the law of diminishing returns.