Taking the device out of the equation
In the past the task of designing a website revolved around the desktop computer metaphor, when there were only a handful of resolutions to account for. Mobile has been a a key driving force behind this change, and the device pool is only getting bigger. People now access the internet on the train, while watching TV and on dates - and importantly not just as a novelty, but as a convenience. Mobile has become such a core part of our interaction with the web that Webtrends have predicted that by 2015 the number of mobile users on the internet will have surpassed desktop users. This isn't only significant it's game changing.
Here at 3Degrees we design with responsive in mind (if the project demands it we also adopt a 'mobile first' approach for the design) and always use a responsive framework for our front-end development. Even if we're developing a dedicated mobile interface we'll still deploy a responsive front-end for desktop and tablet - as there's still a lot of variation that needs to be accounted for. Ultimately the premise of a fixed width is flawed in that the best you'll ever achieve is a compromise, and we don't like compromises.
We don't charge extra for responsive design, it's not an additional service, bolt-on or marketing ploy, it's just how we work.