While watching football this morning I caught the tail end of a Circuit City commercial about a "One Price Promise". It's a pretty simple statement so what makes it interesting to me is that it's still an issue. Any store crazy enough to change their pricing in store and online is simply missing the boat. Sure your overhead online is lower but your customer doesn't care. Customers shop the channel they want whether it's because they still don't buy online [yes they do still exist - scary, I know] or because they want immediacy or just to put their hands on the product.
Furthermore if you're asking for less online you're encouraging people to abuse your price structure testing offline and buying online. Smartphones, iPhones, phone a friend, people don't stop looking online just because they aren't there anymore. When your prices don't jive the customer isn't going to be fooled and trying to deal with returns from overpricing doesn't help your overhead or brand reputation.
If you want to incentivize online sales make it easy to buy online. Offer simple to returns, useful sales suggestion tools and give out free shipping either without qualifiers or at low levels. These days everyone is online and offline so rather than trying to penalize people into a channel for margin reasons it's time to wake up and realize that multi-channel means getting customers wherever you can. Over charging them in one spot won't win them back in another.
We shouldn't need a commercial telling customers pricing will be fair.
Now back to the game...