The mathematical conditions for the existence of macroeconomic production functions that are state functions of the economic system are pointed out. The output elasticities and the elasticities of substitution of energy-dependent Cobb-Douglas, CES and LinEx production functions are calculated. The output elasticities, which measure the productive powers of production factors and whose numerical values have been obtained for Germany, Japan, and the USA, are for energy much larger and for labor much smaller than the cost shares of these factors. Energy and its conversion into physical work accounts for most of the growth that mainstream economics attributes to "technological progress" and related concepts. It decisively determines the economic state of nations. Consequences for automation and globalization and perspectives on growth are discussed. (C) 2011 Elsevier Ltd. All rights reserved.