Just when you think your eCommerce website is complete, fully optimized and finally able to function on its own, here comes some news you 
may need to update it. This is a dance you should get used to, though. eCommerce is always changing. A great example of this is responsive design. If your website doesn’t have it, you’re most likely missing out on a lot of sales.
To put it as simply as possible, responsive web design is how you ensure your website looks exactly how you want it to on any device. This was never an issue, say, 10 years ago. However, now it’s easy to understand why it is. Nowadays, people aren’t just using their computers to access the Internet. They also have tablets and smartphones. Expect those options to increase in the near future too (smart TVs, glasses, watches, etc.).
In the U.S., alone, roughly 40% of the population has a smartphone. Close to 90% of them use it to surf the web every single day. Just short of 70% of them will actually do this while they’re at work. So you can probably get a good idea for how many customers will walk away from your website if it doesn’t display right on their phone (to say nothing about tablets).
The good news is that designing a website that’s responsive is only slightly more expensive than having the traditional kind built. So if you already have a website, consider having a new one built from scratch. Your only other options are creating a secondary one for a little less (which will be more inconvenient) or accepting the fact that a large percentage of the population will be ignoring your site.
Furthermore, responsive design isn’t just about the machines being used to access your website. It also covers the operating systems being used too. Responsive designs can handle iOS, Android and just about anything else.
So if you’re noticing a high bounce rate on, say, your landing page and have done everything else to rectify it, responsive design is most likely the key. People are interested in what you have to offer, just not in how you’re displaying it.
Not having a website with responsive design in this day and age would be like not having a website 10 years ago. You’re simply escorting business away from you. The price is a worthwhile investment in a design that will make sure customers aren’t leaving you for an inexcusable reason.
Source:
http://knowledge.ridivi.com/why-responsive-web-design-matters-for-your-website/2301
http://www.anhosting.com/blog/2012/11/how-many-people-use-smartphones-to-browse-websites/