Technically, responsive design rests on three building blocks: flexible grids (widths defined in percentages rather than fixed pixels), scalable images and so-called media queries in the CSS that activate different layout rules depending on screen width. On a smartphone the menu collapses into an expandable «burger» icon, columns stack on top of each other and font sizes adjust. So there aren't two websites but one that transforms.
Today responsive design is a must, not a nice-to-have. More than half of web traffic in Switzerland comes from mobile phones, and Google evaluates websites on a «mobile first» basis – primarily using the mobile version. A site that works poorly on a smartphone loses both visitors and search visibility.
When implementing, a good agency ensures tap targets are large enough for fingers, loading times are short even on mobile networks, fonts are readable without zooming and no content disappears on small devices. Testing happens on real devices and across different browsers, not just on the developer's screen.
With reputable providers responsive design has no separate price – it is included in every modern website. If you still have an older, non-responsive site, expect roughly CHF 2,000 to 8,000 for the conversion depending on scope; a completely new SME website usually costs around CHF 3,000 to 15,000 (without guarantee).