This is the first part of a two-part paper providing an analytical model of the indirect rebound effect, given a direct rebound estimate, that integrates consumer demand theory with the embodied energy of household spending from environmentally-extended input–output analysis. The second part applies the model developed in part one to simulate the direct and indirect rebound for the average U.S. household in terms of primary energy, CO2e, NOx, and SO2 emissions and for energy efficiency investments in electricity, natural gas, or gasoline services. Part one provides a critical review of the largely independent economic and industrial ecology literatures on the indirect rebound. By studying the two-goods case and the n-goods case, we demonstrate that the indirect rebound is bounded by the consumer budget constraint, and inversely related to the direct rebound. We also compare the common proportional spending and income elasticity spending assumptions with our model of cross-price elasticities including both substitution and income effects for the indirect rebound. By assuming zero incremental capital costs and the same embodied energy as conventional technologies for efficient appliances, we model an upper bound of the indirect rebound. Future work should also consider the increase in consumer welfare possible through the rebound effect.