This paper presents a comprehensive low-voltage residential load model of price-based demand response (DR). High-resolution load models are developed by combing Monte Carlo Markov chain bottom-up demand models, hot water demand models, discrete state space representation of thermal appliances, and composite time-variant electrical load models. Price-based DR is then modeled through control algorithms for thermostatically controlled loads, optimal scheduling of wet appliances, and price elasticity matrices for representing the inherent elastic response of the consumer. The developed model is used in a case study to examine the potential distribution network impacts of the introduction of dynamic pricing schemes. The effects of cold load pick-up, rebound peaks, decrease in electrical and demand diversity, and impacts on loading and voltage are presented.