the constraints add to factor prices. In a model, where capital, labor and energy (exergy) are the factors of production … energy-dependent production functions that are derived from the twice differentiability requirement and the law of … diminishing returns. -- Optimization ; technological constraints ; shadow prices ; output elasticities ; energy ; economic growth …

, labor, and energy for Germany, Japan, and the USA since 1960. The computed cointegration vectors represent the output … elasticities of the aggregate energy-dependent Cobb-Douglas function. The output elasticities give the economic weights of the … production factors capital, labor, and energy. We find that they are for labor much smaller and for energy much larger than the …