Productivity, billable hours, and expert craftsmen

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I read a great article about productivity and I think there is a side issue alluded to that needs to be addressed. A common problem is that the actual direct amount of time to do something is minuscule compared to the prep work necessary to be able to execute rapidly and effectively.

The story I'm reminded is something like this:

A man had a squeak in his floor and no matter what he tried to do he could not get rid of it. He finally called a master carpenter referred to him by a neighbor and explained the problem. The carpenter walked in, paced about the room for a minute, pulled out a hammer, hit the floor with it and the squeak disappeared.

The carpenter handed over the bill and the homeowner was livid: "Are you crazy? You want to charge me $100 for just hitting the floor with a hammer?"

Without missing a beat, the carpenter grabbed the bill, scribbled a few changes and handed it back. The bill now read:
Hitting floor with hammer:                      $2
Knowing where on the floor to hit the hammer:  $98

knowing where to hammer produces a lot of variations of this story but the overall theme is very important. Expert knowledge is a rare and valuable commodity and often falls into the category of "you get what you pay for". The trick is knowing when you need that expert and when a novice is good enough.

On the other side of the equation, experts shouldn't worry about charging high amounts for small amounts of time when appropriate. For example, imagine the carpenter above walked around for 10 hours tearing up the walls and otherwise making a mess and then subsequently fixed the squeak, but gave the owner a bill for $100 @ $10/hr.

Would this make the homeowner be happier?

EDIT - I had forgotten about the picasso version of this.. I'm not sure which I like better.

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