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Activating the demand-side of the electric system is a comeback of an old idea. What decades ago did not work out due to the lack of proper technology, today raises hopes to meliorate some of the most problematic situations in electric system operation such as ever higher peak demands and high wind generation during low demand periods. Smart grid infrastructures are currently implemented in many countries. This communication and control infrastructure allows consumers to receive information on system conditions, for example in the form of price signals, and thus to react to these and reduce, increase or shift their electricity consumption. This paper presents the modelling of demand shifting with two Demand Response mechanisms, Direct Load Control and Dynamic pricing. The outcome of both mechanisms depends, to a great extent, on two parameters: the maximum share of load which consumers are able and willing to shift and the elasticities used to express consumer's level of responsiveness in the dynamic pricing mechanism. An analysis of the sensitivity of the impact of Demand Response is carried out by varying these two parameters over a large range. Results regarding demand participation shares, cost savings, demand variation patterns and used generation technologies are compared for the different sensitivity cases. We find that cost saving increases are not proportional to increments in the maximum share of participating demand and in responsiveness to prices.