Energy efficiency and energy prices: A general mathematical framework

Mankind's prosperity has been dependent on availability of affordable energy in the recent centuries. Today, the need of sustainability requires precise energy efficiency evaluation. Unfortunately, the traditional metrics like energy return on investment (EROI) suffer from the system boundaries and from the inability to describe labor and physical capital in terms of energy. Therefore, they tend to omit up to 50% of input energy consumption. The price of energy model (PERM) and cost of energy model (CERM), derived via matrix description of production process, show that the ratio of the average energy input cost to the average useable energy output cost describes energy efficiency completely. The same holds for the ratio of energy prices, if shares of aggregate rents, taxes and subsidies in the input and output prices are similar. The above price (cost) ratio can serve as an EROI check and eliminate the need for a lengthy process analysis. The results enable the extension of energy efficiency metrics by social and environmental effects, measurable mostly in monetary terms.