Economic models that provide a framework for understanding determinants of household energy consumption and the rate of reliance on cleaner energy are not available, despite the growing number of residential solar houses. This study presents a theoretical framework for understanding the relationship between energy consumption, generation, storage and the reliance on cleaner energy. Our findings suggest that, (i) households which generate energy could consume more energy than households which do not generate energy, (ii) the economically optimal reliance on solar energy depends on energy prices, income and the slope of the marginal energy storage cost, (iii) there is no relationship between reliance on cleaner energy (or energy demand) and the efficiency level of energy-conversion technologies, and (iv) when buy-back rates are equal to the retail rate of electricity, reliance on generated energy could be zero and energy demand of a generating household may be identical to its non-generating counterpart.