If it's a blog post, people want to know they're dealing with a person. Most people don't care who published the article, but do pay attention if it was written by someone they respect. The mainstream media makes a horrible mess of technology reporting, often, but if I see a piece on security in the Guardian by Bruce Schneier I pay attention and read it - simply because I know he knows his topic. So it is all about the people, rather than the brand - unless you're Coke or Cadbury etc where different rules can apply!
Your brand may publish good content, but it's actually the person who wrote it who is the authority and may be interesting to get to know - because they post funny stuff, have opinions on a range of topics etc, rather than be mono-dimensional banging on and on about the business.
People, in the main, want to connect on social networks to brands - Robert Scoble rather than Rackspace for example. You'll have an easier time connecting with people as you than trying to represent your brand. Now, you may not be an authority on any topic yet, but that's the background, and intent, of authorship.
The connection with your brand, and the fact you'll be sharing content from the page, and your blog etc, will promote your brand. Do it too often and people will disconnect, so as ever, it's a fine art.
So where does that leave us, the nobodies who aren't world-reknowned for some topic? It leaves us trying to create enough quality content, consistently enough, that both G+ and the serps start to see us as authorities on particular topics. Reshares of overtly commercial messages seem to do especially badly on G+, perhaps because it's presently an advert-free zone.
The upshot of all this makes it very time-consuming, so if you're not putting in the xx hours daily on G+ connecting and interacting with as many as possible, no one will notice, and no one will care. Which is the rather sad, and fundamental, flaw in authorship and G+: it's a popularity contest plain and simple and actually nothing to do with authority. Perhaps a secondary indicator of, and there's certainly correlation...
So how to build that brand? Be a social media maven, constantly interacting and connecting. Do it as both you, and the page, along with other employees - they'll all have their own voice and style - which is ideal, they'll all connect to different people. If you can't put several hours a day in, try and find a community or niche that you can join actively enough to get noticed and respected in, and build connections from there.
Do 20 minutes a day of resharing the latest daily blog post along with a tiny bit of interaction and you'll get precisely nowhere.
Good luck!