The purpose of this paper is to introduce the concept of power density [Watts/m²] into economics. By introducing an explicit spatial structure into a simple general equilibrium model we are able to show how the power density of available energy resources determines the extent of energy exploitation, the density of urban agglomerations, and the peak level of income per capita. Using a simple Malthusian model to sort population across geographic space we demonstrate how the density of available energy supplies creates density in energy demands by agglomerating economic activity. We label this result the density-creates-density hypothesis and evaluate it using data from pre and post fossil-fuel England from 1086 to 1801.