Larger companies are most likely head up in big cities, in the US we think of New York, Los Angeles, Chicago etc. E-commerce allows them to easily extend their brand to smaller, local communities that would normally not have to opportunity to travel and purchase their products/merchandise. Also, bigger companies can get in touch with the local companies to help get their products into these local markets. For example, a boutique shop in Tampa, Fl called Penelope T holds high-end clothing from several designers that are located in New York and Los Angeles. Not only selling these items in stores, they also have an online presence that gives consumers the opportunity to purchase these high-end brands locally while remaining global. Although, I think it is only fair to point out a flaw in Cairncross' prediction...it is safe to say that a lot of large and small companies make use of this "local and global" idea and apply it to E-commerce. However, I know a many smaller, local brands that do not have any online presence and only market themselves to a specific audience and still remain to do very well in their business. In the same token, larger, high end companies do not allow E-commerce directly from their site but would partner up other retail E-commerce companies and sell their product this way. Again, both scenarios are justifiable; I think with technology evolving companies are going to feel the need to create an online presence because it can only be beneficial.
In addition to E-commerce, we can again apply this trend to social media. I think a huge point social media makes is that is can and does reach so many people on a global level. However I think it definitely depends on the company and what they are using social media for to decide how effective this trend plays out. For example, if a local Tallahassee company is promoting their brand and holding an event then that obviously has the ability to reach a large market, because it is online and widely accessed, but given its purpose it will only have an affect on those local to their company. However, if a small company in Tallahassee such as Coton Colors promotes a sale on all of their social media outlets then this will affect a much larger, and global, market. Looking at larger companies and their usage of social media, I think this can only benefit their "local provision". The larger companies already have a global reach, so social media helps inform those local markets and really connect people from all over the world on a global and local scale.