Here's what works for me: on the second "silly" support request they send I put them in a "cool down" queue that gets answered a day later. If they keep asking simple questions they move into the two day wait queue. (Obviously, this only works if your support is by email.)
I worked as a consultant for a company once where they would go even one step further and would actively encourage customers that used too much customer support to switch to another provider. The trick is doing this in such a way that the customer does not realize he's being told to leave lest you get a bad reputation. I'm not going to divulge all my trade secrets here, but I've found a way to do something similar for my business, perhaps you can think of one for yours too.
A customer losing strategy is opposite to most startup who are looking to gain customers. It's a good problem to have and a sign of headaches that need to be managed.
If you could share a bit more on how you help the customer realize they might want to move, most startups are trying hard enough to acquire customers, not lose them.
Many startups are so desperate to find customers that they are even holding on to the ones that cost too much support. (Note that in a startup support cost often takes away valuable time from the founders and thus is more an "opportunity" cost than a monetary cost, they should have spent that time growing the business with more valuable customers).
I chose to do only e-mail support because it self-selects out a type of customer that wants to use the phone (also phone support scales poorly, especially when expanding internationally). There are ways you can encourage the "dummy" user to desire phone support, and then gently point out that there are _other_ providers that have that. If you do this properly the dummy client will actually feel they've had good customer service (and you could argue that they have, we just weren't meant for each other) and your over eager competition gets stuck with the dummies.
Edit: I thought I should mention, for a startup it can often be unclear which customer is/will be valuable and you can learn a lot from the "wrong" ones, so be careful with "selective denial" unless you've run the numbers and are sure what you are doing
Create a canned automatic response to someone submitting a request/support email that goes something like this.
"We have worked really hard to make this app/service as easy and intuitive to use as possible. On top of that we decided to price it very low to make it even easier and affordable for people to take advantage of. 80% of our paying customers never contact us for help or support. We honestly just don't have the time or resources available to explain how to use our service. If our help section and FAQs can't fix your problem, then you probably shouldn't be using this app, or we're gonna have to ask you to pay for support.
Option 1: Click here and we will immediately cancel your account and refund you.
Option 2: Click here to upgrade your account for support
Option 3: Figure it out!
Have a Nice Day!"
Or something like that. Perhaps it can written to be more friendly or in a more suitable tone. But you get the idea.
If you don't have the resources for providing support and can't help yourself being rude, then maybe you shouldn't give the free/cheap option in the first place.
There are other options besides behaving like a dick.
Personally I like how mobile operators handle this. Whenever I call their free support line, I am placed on wait for at least a half an hour, with a message along the lines of "our operators are currently busy, please hold ; if you'd like priority then call this number ...".
Software is support. Sure, there are ways to mitigate the cost and quantity of support, but once the product is built support is one of the primary functions of the business.
Is it that the Personal plans are done by small businesses where the owner is trying to run their shop and do IT work whilst larger businesses tend to have a knowledgeable sole-purpose "tech guy"?
Edit: Ah, I hadn't seen that you've written so much about it previously. Thanks! For others, this seems like a good overview of low tier pathological customers by patio11 -- http://news.ycombinator.com/item?id=3186111
(for more see patio11's suggested hnsearch.com [patio11 pathological customers] at http://www.hnsearch.com/search#request/all&q=+patio11+pa...)
1-If the are just 7x more people in the Personal bucket. (I'm guessing you account for this)
2-If there are so many more in the Personal bucket that it is still the primary driver of your revenue, so that is why you keep it?
I'm sure the equation still favors your theory, but I'm also sure by a lower number than what you'd like readers to believe.
so you cannot just get rid of every customer but your high paying ones.
$9 customer - $5 support = $4 per many customers
$199 customer - $1 support = $198 per few customers
Your mileage may vary. If I were doing the math based on phone calls waking me up in the middle of the night, the numbers get skewed due to one pathological customer in the $29 bucket, who has literally called me more than every other customer combined.
P.S. I have fairly exact privileged information regarding this question at a handful of companies and anecdotal evidence from dozens of my software buddies. It is our universal experience that the support load for cheap/free customers crushes the support load for the higher plans, both on an absolute and per-customer basis.