With the increasing application of distributed energy resources and novel information technologies in the electricity infrastructure, innovative possibilities to incorporate the demand side more actively in power system operation are enabled. A promising, controllable, residential distributed generation technology is a microcombined heat and power system (micro-CHP). Micro-CHP is an energy-efficient technology that simultaneously provides heat and electricity to households. In this paper, we investigate to what extent domestic energy costs could be reduced with intelligent, price-based control concepts (demand response). Hereby, first the performance of a standard, so-called heat-led micro-CHP system is analyzed. Then, a model-predictive control (MPC) strategy aimed at demand response is proposed for more intelligent control of micro-CHP systems. Simulation studies illustrate the added value of the proposed intelligent control approach over the standard approach in terms of reduced variable energy costs. Demand response with micro-CHP lowers variable costs for households by about 1%-14%. The cost reductions are highest with the most strongly fluctuating real-time pricing scheme.