Energy and capital

Energy is required both to build the capital stock and to produce goods and services from the use of the capital stock. These two energy demands are together constrained by the available energy in the macroeconomy. Here, I develop a mathematical theory expressing the relationship between available energy and the capital stock as a first-order differential equation. Three specific solutions are derived for the cases of a steady-state economy with fixed capital stock, for an economy with a linearly increasing capital stock, and for an exponentially growing capital stock. Empirical data for the United Kingdom's nineteenth century economy are used to examine the energy required to access energy supplies; the energy intensity of capital formation; and the energy intensity of capital use. Magnitudes and trends in the energy intensity of capital use differ for four sectors of the economy-mining, residential, utilities, and railways. Data for the United Kingdom's ratio of available energy to capital from 1850 to 1913, are examined for the case of a linearly increasing capital stock. This corroborates the overall theoretical model and demonstrates that the change in energy to capital ratio is impacted by the magnitude of the capital stock. Further analysis of the mining sector shows that higher coal prices follow after increases in capital investment and increased coal production. This helps demonstrate how energy constraints play out in the macroeconomy. This article met the requirements for a gold - gold JIE data openness badge described at .