This paper uses a multiple discrete continuous extreme value (MDCEV) model with perfect and imperfect substitutes to study residential energy demand. A non-linear utility function is employed within a Kuhn-Tucker multiple-discrete economic model of consumer demand, estimated on Italian expenditure data. The simulation algorithm measures demand elasticity with respect to price variations and the marginal effects of other covariates. Results show that household energy demand (space and water heating and transportation) is relatively inelastic with respect to prices (-0.55 and -0.67, respectively), meaning that pricing policies can induce a reduction in the demand for fuels less than proportional to the price variation. The model also allows to forecast the energy demand for space and water heating within a global warming scenario: an increase of 2 degrees Celsius would lead, for example, to a reduction in household energy consumption of 4.07%.